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Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network
| Updated：2023-04-13
|
Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network
- Optics and Precision Engineering Pages: 1-15(2023)
- Affiliations：
1.China University of Petroleum， College of Information Science and Engineering， Beijing 102249， China
2.Beijing Key Laboratory of Petroleum Data Mining， China University of Petroleum， Beijing 102249， China
- Author bio：
E-mail： lianyuanfeng@cup.edu.cn
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- Funds：
- DOI： CLC： TP394.1;TH691.9
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Published Online：13 April 2023，
Revised：17 December 2022，
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Cite this article
连远锋,李光洋,沈韶辰.融合超像素与多模态感知网络的遥感影像车辆检测[J].光学精密工程,
LIAN Yuanfeng,LI Guangyang,SHEN Shaochen.Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network[J].Optics and Precision Engineering,
连远锋,李光洋,沈韶辰.融合超像素与多模态感知网络的遥感影像车辆检测[J].光学精密工程, DOI：10.37188/OPE.XXXXXXXX.0001
LIAN Yuanfeng,LI Guangyang,SHEN Shaochen.Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network[J].Optics and Precision Engineering, DOI：10.37188/OPE.XXXXXXXX.0001
Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network
融合超像素与多模态感知网络的遥感影像车辆检测 Vehicle detection method based on remote sensing image fusion of superpixel and multi-modal sensing network 1 2 corresp first-author E-mail： lianyuanfeng@cup.edu.cn E-mail： lianyuanfeng@cup.edu.cn lianyuanfeng@cup.edu.cn 1 李光洋（1998-），男，安徽六安人，硕士，2021年于中国石油大学（北京）获得学士学位，主要从事深度学习研究。E-mail： 2021211257@student.cup.edu.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342488&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342487&type= 24.87100029 35.45399475 李光洋 （1998-），男，安徽六安人，硕士，2021年于中国石油大学（北京）获得学士学位，主要从事深度学习研究。E-mail： 2021211257@student.cup.edu.cn 2021211257@student.cup.edu.cn 1 中国石油大学（北京） 信息科学与工程学院，北京 102249 中国石油大学（北京） 信息科学与工程学院，北京 102249 China University of Petroleum， College of Information Science and Engineering， Beijing 102249， China China University of Petroleum， College of Information Science and Engineering， Beijing 102249， China 中国石油大学（北京） 石油数据挖掘北京市重点实验室，北京 102249 中国石油大学（北京） 石油数据挖掘北京市重点实验室，北京 102249 Beijing Key Laboratory of Petroleum Data Mining， China University of Petroleum， Beijing 102249， China Beijing Key Laboratory of Petroleum Data Mining， China University of Petroleum， Beijing 102249， China 针对遥感影像车辆检测中背景干扰、目标密集和目标异质性等因素引起的识别精度下降问题，提出了一种融合超像素与多模态感知网络的遥感影像车辆检测方法。首先，基于混合超像素的区域合并规则，通过超像素二分图融合算法将两种模态的超像素分割结果进行融合，提升了不同模态图像超像素分割结果的准确性。其次，提出一种多模态边缘感知网络的遥感影像车辆检测方法MEANet （multi-modal edge aware network），引入OPT-FPN模块（Optimized Feature Pyramid Networks）来增强网络学习多尺度目标特征的能力。最后，通过边缘感知模块聚合超像素和多模态融合模块生成的两组边缘特征，进而生成车辆目标的准确边界。在ISPRS Potsdam和ISPRS Vaihingen遥感影像数据集上进行实验，最终的 <math id="M1"><mi>m</mi><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342489&type= 5.58799982 3.21733332 分数分别为91.05%和85.11%。实验结果表明，本文提出的方法在多模态遥感影像车辆高精度检测中有着较好的检测准确度和较好的应用价值。 Aiming at the reduction of recognition accuracy caused by background interference， target density and target heterogeneity in remote sensing image vehicle detection， a remote sensing image vehicle detection method combining superpixel and multi-modal perception network is proposed. Firstly， based on the region merging rules of hybrid superpixels， the superpixel bipartite graph fusion algorithm is used to fuse the superpixel segmentation results of the two modalities， which improves the accuracy of the superpixel segmentation results of different modal images. Secondly， MEANet （multi-modal edge aware network）， a vehicle detection method of remote sensing images based on multi-modal edge aware network， is proposed. Opt-fpn module （Optimized Feature Pyramid Networks） is introduced to enhance the ability of the network to learn multi-scale target features. Finally， the two sets of edge features generated by the superpixel and multimodal fusion module were aggregated through the edge perception module， and then the accurate boundary of the vehicle target was generated. Experiments are carried out on the ISPRS Potsdam and ISPRS Vaihingen remote sensing image datasets， and the final <math id="M2"><mi>m</mi><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342492&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342491&type= 6.43466663 3.72533321 scores are 91.05% and 85.11%， respectively. The experimental results show that the method proposed in this paper has good detection accuracy and good application value in high-precision vehicle detection of multimodal remote sensing images. 超像素 多模态感知 遥感影像 车辆检测 super pixel multimodal perception remote-sensing image vehicle detector 1 引 言 1 车辆检测对车流量计算、预测交通拥堵和智慧城市构建等应用领域具有重要意义。随着遥感技术的不断进步，使得自动矢量化提取高分辨率遥感影像中的车辆轮廓信息成为可能。如何高精度、低延时、自动化地从高分辨率遥感影像中检测车辆，成为学者们研究的热点。通常遥感影像中车辆目标的提取方法可分为传统机器学习方法和深度学习的方法。传统机器学习检测方法使用不同尺寸的滑窗遍历图像上的每个位置，然后利用特征描述算子提取特征并利用分类器进行分类。Moranduzzo等人 ［ 1 1 ］ 使用尺度不变特征转换（Scale Invariant Feature Transform， SIFT）特征训练SVM分类器实现车辆检测。Kembhavi等人 ［ 2 2 ］ 通过使用偏最小二乘法（PLS）特征，结合颜色概率图和HOG特征对车辆进行检测。Wei等人 ［ 3 3 ］ 和Tuermer等人 ［ 4 4 ］ 使用方向梯度直方图（Histogram of Oriented Gradient， HOG）和Harr特征训练Adaboost分类器实现车辆目标分类。Papageorgiou等人 ［ 5 5 ］ 通过Haar小波变换进行特征提取，利用SVM分类器进行分类。Liang等人 ［ 6 6 ］ 将HOG特征与Harr特征组合起来使用多核SVM算法实现车辆检测，由于多核SVM比普通SVM算法需要更多的训练时间，因此不适合在大规模的数据上使用。 近年来，超像素分割算法被应用于边缘约束学习，通过分层对比特征进行显著性目标检测 ［ 7 7 ］ 。陈允杰等人 ［ 8 8 ］ 基于超像素方法提升HSI的分类精度。Cui等人 ［ 9 9 ］ 提出了一种基于超像素建模的CFAR算法，通过构建超像素级混合伽马分布来描述杂波统计模型并对陆地目标进行检测。廖苗等人 ［ 10 10 ］ 对于超像素难以有效划分图像目标边界的问题，提出了利用局部信息进行多层级简单线性迭代聚类的方法，有效地解决了图像过分割和欠分割问题。任凤雷等人 ［ 11 11 ］ 将DeepLabv3+模型与超像素分割算法相结合。李静等人 ［ 12 12 ］ 基于归一化转动惯量（Normalized Moment of Inertia， NMI）特征的超像素块相似性度量对遥感图像进行分割，降低了超像素对噪声的敏感性，提高了影像分割的精度。 近年来，卷积神经网络（Convolutional Neural Network， CNN）已经广泛应用于遥感目标检测领域。姚群力等人 ［ 13 13 ］ 提出一种多尺度遥感目标检测框架，实现了对多尺度遥感目标的稳健检测。Chen等人 ［ 14 14 ］ 构建了一种复杂结构的深度卷积神经网络并将其应用到遥感影像车辆检测识别中。于野等人 ［ 15 15 ］ 在FPN的基础上融入特征显著性图以提高浅层特征的表达能力。张康等人 ［ 16 16 ］ 在深度学习方法中，利用卷积神经网络权值共享、平移不变性等特点，在图像分类中取得较好地效果。王振庆等人 ［ 17 17 ］ 提出了一种端到端的全卷积神经网络IEU-Net，并结合其设计的IELoss损失函数，通过忽略边缘预测策略进行建筑物提取。杨州等人 ［ 18 18 ］ 提出将多尺度特征融合与DCNN相结合的算法，在图像场景分类中取得较好的成果。陈欣等人 ［ 19 19 ］ 针对复杂背景下遥感小目标的检测问题，在原SSD算法中引入通道注意力模块，通过构建权重参数空间，将注意力集中在关注目标区域的通道，有效降低了背景干扰。谷雨等人 ［ 20 20 ］ 为了改善红外图像弱小目标检测的效果，提出了基于改进多尺度分形特征的检测算法，同时进行了图像增强和感兴趣区域自适应阈值分割，可以较好地检测到具有较高局部对比度的红外图像小目标。Couprie等人 ［ 21 21 ］ 利用CNN提取RGB和深度图的组合特征用于对象检测和语义分割。Fan等人 ［ 22 22 ］ 在特征金字塔网络FPN的基础上构建了深度净化单元进行深度图滤波，同时设计了三通道特征学习模块用于跨模态特征融合。 为了提高复杂背景下遥感图像车辆目标检测精度，本文提出了一种融合超像素与多模态感知网络的遥感影像车辆检测方法。首先，基于混合超像素的区域合并规则，通过超像素二分图融合算法将两种模态的超像素分割结果进行融合，提升了不同模态图像超像素分割结果的准确性。其次，提出一种多模态边缘感知网络的遥感影像车辆检测方法MEANet，利用OPT-FPN模块得到遥感影像的多尺度特征，并使用多模态融合模块对两种模态的多尺度特征进行跨模态融合。最后，通过边缘感知模块聚合超像素和多模态融合模块生成的两组边缘特征来提升车辆目标检测的准确性。 2 本文方法 1 如 图1 图1 所示，首先将光学图像和对应的高程图像经过超像素分割后的结果分别输入给多模态超像素融合模块，得到融合后的超像素分割结果。然后对光学图像和深度图像进行卷积处理生成对应的光学特征和深度特征，再将两种特征经过OPT-FPN模块进行处理和多模态融合，进而生成多尺度的融合特征图。最后通过边界感知模块和解码器得到车辆目标检测结果。 2.1 混合超像素的区域合并规则 2 为了保持目标像素特征的局部一致性，这里使用超像素方法分别对光学图像和高程图像分别进行过分割，并定义了多模态超像素合并规则。假设 光学图像为 <math id="M3"><msup><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342540&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342539&type= 2.79399991 3.04800010 分割后形成 <math id="M4"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342559&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342558&type= 19.81200027 4.23333359 。设 <math id="M17"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342561&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342560&type= 4.48733330 3.97933316 和 <math id="M18"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342563&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342562&type= 4.48733330 3.97933316 分别是光学图像和高程图像相同位置 <math id="M19"><mfenced separators="|"><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342565&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342564&type= 9.05933285 4.82600021 处的两个像元。分别构造邻接图模型 <math id="M20"><msup><mrow><mi>G</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><mfenced separators="|"><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>,</mo><msup><mrow><mi>E</mi></mrow><mrow><mi>P</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342567&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342566&type= 22.69066620 4.48733330 和 <math id="M21"><msup><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msup><mo>=</mo><mfenced separators="|"><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup><mo>,</mo><msup><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342568&type= 22.26733208 4.48733330 。其中， <math id="M22"><msup><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342571&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342570&type= 4.65666676 3.13266683 表示顶点集合，对应于光学图像的每个超像素； <math id="M23"><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342573&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342572&type= 4.57200003 3.13266683 表示高程图每个超像素顶点集合； <math id="M24"><msup><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342575&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342574&type= 3.89466691 3.04800010 和 <math id="M25"><msup><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342533&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342532&type= 4.06400013 3.04800010 分别为光学图像和高程图像边集合。光学图像 <math id="M26"><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342687&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342686&type= 3.04800010 3.04800010 中位置为 <math id="M27"><mfenced separators="|"><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342537&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342536&type= 9.05933285 4.82600021 的像素点表示为 <math id="M28"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342584&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342583&type= 4.48733330 3.97933316 ，其在高程图像 <math id="M29"><msup><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342586&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342585&type= 2.96333337 3.04800010 的对应位置 <math id="M30"><mfenced separators="|"><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342588&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342587&type= 9.05933285 4.82600021 处的像素点记为 <math id="M31"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342589&type= 4.48733330 3.97933316 ，设 <math id="M32"><mi>F</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342591&type= 2.62466669 2.79399991 为一一映射关系，则有 <math display="block" id="M33"><msub><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>⋂</mo><msub><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342594&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342593&type= 17.27199936 4.57200003 ， <math display="block" id="M34"><msubsup><mo>∪</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></msubsup><mrow/><msub><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><msup><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342596&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342595&type= 19.89666748 4.23333359 ， <math display="block" id="M35"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mo>=</mo><mi>F</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342598&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342597&type= 20.23533440 4.91066647 ， <math display="block" id="M36"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>=</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342600&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342599&type= 22.86000061 4.91066647 . 设 <math id="M37"><msup><mrow><mi>G</mi></mrow><mrow><mi>I</mi></mrow></msup><mo>=</mo><mfenced separators="|"><mrow><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>ρ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342602&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342601&type= 22.26733208 4.74133301 为图像 <math id="M38"><mi>I</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342604&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342603&type= 1.60866666 2.79399991 经过分割后形成的超像素 <math id="M39"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343022&type= 2.20133328 2.79399991 所构成的图。其中，顶点集 <math id="M40"><mi>V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342996&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342995&type= 3.21733332 2.87866688 表示所有超像素 <math id="M41"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343022&type= 2.20133328 2.79399991 ，边集表示相邻超像素间的连接关系， <math id="M42"><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342611&type= 2.11666679 3.64066648 为边的权重。若 <math id="M43"><msub><mrow><mi>e</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>∈</mo><mi>E</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342614&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342613&type= 11.59933376 4.06400013 表示超像素 <math id="M44"><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342616&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342615&type= 3.38666677 3.72533321 和 <math id="M45"><msub><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342617&type= 3.80999994 3.72533321 之间的边，则 <math id="M46"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>∈</mo><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342620&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342619&type= 11.34533310 4.57200003 表示 <math id="M47"><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342622&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342621&type= 3.38666677 3.72533321 和 <math id="M48"><msub><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342624&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342623&type= 3.80999994 3.72533321 之间的相似度。这里定义了9种多模态区域合并规则： 定义1.相关性：若光学图像中某个区域相对应的超像素块记为 <math id="M49"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342625&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342576&type= 3.04800010 4.57200003 ，对应的高程图的超像素块记为 <math id="M50"><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342627&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342626&type= 2.03200006 3.72533321 ，则 <math id="M51"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342731&type= 3.04800010 4.57200003 和 <math id="M52"><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342631&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342630&type= 2.03200006 3.72533321 在 <math id="M53"><msup><mrow><mi>G</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342633&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342632&type= 4.31799984 3.04800010 下的相关性值为： <math display="block" id="M54"><mi mathvariant="normal">c</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced><mo>=</mo><mfrac><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⋂</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342635&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342634&type= 28.95599937 11.09133339 ， 其中， <math id="M55"><mfenced open="|" close="|" separators="|"><mrow><mo>⋅</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342636&type= 3.04800010 3.97933316 表示超像素集合内包含的像素数目。 如 图2 图2 所示，构建区域邻接图（region adjacent graph，RAG），将初始分割结果中的每个超像素抽象为一个节点，超像素相邻即代表节点连通，边的权重为相邻超像素的合并代价，通常认为相邻超像素特征越相似，合并代价越小，越趋于合并。 定义2.对偶结点：若光学图像中某个区域相对应的超像素块记为 <math id="M56"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342642&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342641&type= 3.04800010 4.57200003 ，则其对偶结点为在 <math id="M57"><msup><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342652&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342651&type= 4.23333359 3.04800010 中相关性取最大值的结点，即 <math display="block" id="M58"><mtable columnalign="left"><mtr><mtd><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msub><mfenced open="|" close="" separators="|"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∈</mo><mi>S</mi></mrow></mfenced><mtext> </mtext><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mtext> </mtext></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mo>∀</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>∈</mo><mi>S</mi></mrow></msub><mo>,</mo><mfenced open="" close="}" separators="|"><mrow><mi>c</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced><mo>≥</mo><mi>c</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342646&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342645&type= 40.47066879 12.19200039 . 定义3.联合结点：设光学图像中超像素块 <math id="M59"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342731&type= 3.04800010 4.57200003 的联合结点为 <math id="M60"><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342650&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342649&type= 10.75266743 4.82600021 ，当且仅当在 <math id="M61"><msup><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342652&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342651&type= 4.23333359 3.04800010 中存在 <math id="M62"><msub><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342654&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342653&type= 2.37066650 3.72533321 ，并且 <math id="M63"><msub><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342656&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342655&type= 2.37066650 3.72533321 为 <math id="M64"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342658&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342657&type= 3.04800010 4.57200003 的对偶结点。 定义4.伴随结点：设光学图像中某个区域相对应的超像素块记为 <math id="M65"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342659&type= 3.04800010 4.57200003 ，则其在 <math id="M66"><msup><mrow><mi>G</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342661&type= 4.23333359 3.04800010 中的伴随结点定义为： <math display="block" id="M67"><mtable><mtr><mtd><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mfenced open="|" close="" separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mo>∈</mo><msup><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msup><mtext> </mtext><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi></mrow></mfenced><mtext> </mtext></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced open="" close="}" separators="|"><mrow><mo>∃</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>∈</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mtext> </mtext><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></mrow></mfenced><mo>∈</mo><mi>F</mi></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342663&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342577&type= 41.31733322 13.12333298 . 定义5.超像素中心点及方差：设光学图像中某个区域相对应的超像素块记为 <math id="M68"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342578&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342664&type= 3.04800010 4.57200003 ，则 <math id="M69"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342580&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342579&type= 3.04800010 4.57200003 的中心点 <math id="M70"><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342582&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342581&type= 9.05933285 4.82600021 及超像素块方差 <math id="M71"><mi>σ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342673&type= 8.80533314 4.82600021 分别定义为： <math display="block" id="M72"><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><mfrac><mrow><msub><mo>∑</mo><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>∈</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></mrow></mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342676&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342675&type= 29.88733101 11.85333347 ， <math display="block" id="M73"><mi>σ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mo>∑</mo><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>∈</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><mi>d</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>,</mo><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342666&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342665&type= 45.97399902 6.26533365 ， 其中， <math id="M74"><mi>d</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>,</mo><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342668&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342667&type= 21.42066574 5.50333309 为像素 <math id="M75"><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>P</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342669&type= 4.48733330 3.97933316 与中心点 <math id="M76"><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342672&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342671&type= 9.05933285 4.82600021 之间的欧拉距离。 定义6.伴随方差：设光学图像中某个区域相对应的超像素块记为 <math id="M77"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342731&type= 3.04800010 4.57200003 ，则 <math id="M78"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342731&type= 3.04800010 4.57200003 的伴随结点超像素块方差 <math id="M79"><msub><mrow><mi>σ</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342693&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342692&type= 11.09133339 4.82600021 定义为： <math display="block" id="M80"><msub><mrow><mi>σ</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mo>∑</mo><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mo>∈</mo><mi>P</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></msub><mrow><mi>d</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>I</mi></mrow><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mrow><mi>S</mi></mrow></msubsup><mo>,</mo><mi mathvariant="bold-italic">μ</mi><mfenced separators="|"><mrow><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342694&type= 60.95999908 6.68866634 . 定义7.总体方差：设光学图像中 <math id="M81"><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342687&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342686&type= 3.04800010 3.04800010 分割成 <math id="M82"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 个超像素集合 <math id="M83"><mi>P</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342700&type= 30.39533424 4.82600021 ，则 <math id="M84"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342715&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342714&type= 2.62466669 2.79399991 的总体方差 <math id="M85"><mi>σ</mi><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342705&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342704&type= 8.38199997 3.97933316 定义为： <math display="block" id="M86"><mi>σ</mi><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>M</mi></mrow></msubsup><mrow><mi>σ</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342707&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342706&type= 30.98800087 4.91066647 . 定义8.总体伴随方差：若光学图像 <math id="M87"><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342709&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342708&type= 3.04800010 3.04800010 分割成 <math id="M88"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 个超像素集合 <math id="M89"><mi>P</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342713&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342712&type= 30.39533424 4.82600021 ，则 <math id="M90"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342715&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342714&type= 2.62466669 2.79399991 的总体伴随方差 <math id="M91"><msub><mrow><mi>σ</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msub><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342717&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342716&type= 10.66800022 3.97933316 定义为： <math display="block" id="M92"><msub><mrow><mi>σ</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msub><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>M</mi></mrow></msubsup><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342719&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342718&type= 35.64466476 4.91066647 . 设光学图像 <math id="M93"><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342721&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342720&type= 3.04800010 3.04800010 分割成 <math id="M94"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 个超像素集合 <math id="M95"><mi>P</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342725&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342724&type= 29.12533188 4.82600021 ，其联合结点集合为 <math id="M96"><mi>T</mi><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342727&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342726&type= 27.85533524 5.50333309 ， <math id="M97"><mfenced open="" close="}" separators="|"><mrow><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mfenced><mo>,</mo><mo>…</mo><mo>,</mo><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342677&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342728&type= 53.59400177 5.50333309 ，其目标模型定义如下： <math display="block" id="M98"><mi>E</mi><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced><mo>=</mo><mi>η</mi><mi mathvariant="normal">*</mi><mi>σ</mi><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced><mo>+</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>η</mi></mrow></mfenced><mi mathvariant="normal">*</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msub><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342679&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342678&type= 55.11800003 4.82600021 ， 其中， <math id="M99"><mi>η</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342681&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342680&type= 1.86266661 3.64066648 为权重系数，用来平衡总体方差相和总体伴随方差项的比重，本文定义 <math id="M100"><mi>η</mi><mo>=</mo><mn mathvariant="normal">0.3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342683&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342682&type= 12.44600010 3.64066648 。像素块距离度量结果为最小能量下的标识： <math display="block" id="M101"><msup><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><msub><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mi>E</mi><mfenced separators="|"><mrow><mi>P</mi></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342685&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342684&type= 32.93532944 4.74133301 . 定义9.分裂规则：若光学图像 <math id="M102"><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342687&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342686&type= 3.04800010 3.04800010 分割成 <math id="M103"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 个超像素集合 <math id="M104"><mi>P</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342736&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342735&type= 30.39533424 4.82600021 ，其联合结点集合为 <math id="M105"><mi>T</mi><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342738&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342737&type= 67.56400299 6.26533365 <math id="M106"><mfenced open="" close="}" separators="|"><mrow><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342739&type= 24.38400078 6.26533365 ，如果 <math id="M107"><msub><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342741&type= 3.97933316 3.55599999 为 <math id="M108"><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342744&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342743&type= 3.30200005 3.72533321 的像素子集且满足 <math id="M109"><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub><mo>⊆</mo><mi>S</mi><msup><mrow><mi>C</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342746&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342745&type= 22.69066620 4.82600021 ， <math id="M110"><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342730&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342729&type= 19.30400085 4.57200003 ， <math id="M111"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342731&type= 3.04800010 4.57200003 分裂之后联合结点集合为： <math display="block" id="M112"><msup><mrow><mi>T</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo></mtd></mtr><mtr><mtd><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo><mo>⋯</mo><mo>,</mo><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>M</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342747&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342748&type= 66.37866211 13.63133430 则像素块 <math id="M113"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342764&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342763&type= 3.04800010 4.57200003 满足分裂规则当且仅当： （1） <math id="M114"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></mfenced><mo>≥</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342766&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342765&type= 14.64733315 4.82600021 且 <math id="M115"><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced><mo>≥</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342768&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342767&type= 14.73200035 4.82600021 ； （2） <math id="M116"><mi>E</mi><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>≥</mo><mi>E</mi><mfenced separators="|"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>'</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342770&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342769&type= 23.79133224 3.97933316 ； （3） <math id="M117"><mi>c</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced><mo>≤</mo><mi>c</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub><mo>,</mo><mi>S</mi><mi>C</mi><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342771&type= 50.20733261 5.50333309 。 2.2 混合超像素二分图融合模型 2 在多模态遥感影像中，如果某个像素在光学图像和高程图像中属于不同超像素块，基于对应像素点在不同模态的超像素块间的从属关系进行合并，可以减少包含多个地物目标区域的分割错误，纠正初分割中的存在的欠分割和过分割导致的边缘不准确问题。这里采用谱聚类方法，给定二分图 <math id="M118"><mi>G</mi><mfenced separators="|"><mrow><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>B</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342774&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342773&type= 18.03400040 3.97933316 ，其中 <math id="M119"><mi>V</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>,</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342776&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342775&type= 21.75933456 4.48733330 ， <math id="M120"><msup><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342778&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342777&type= 4.65666676 3.13266683 和 <math id="M121"><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342780&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342779&type= 4.57200003 3.13266683 分别为像素和超像素顶点； <math id="M122"><mi>E</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msup><mrow><mi>E</mi></mrow><mrow><mi>P</mi><mi>S</mi></mrow></msup><mo>,</mo><msup><mrow><mi>E</mi></mrow><mrow><mi>S</mi><mi>S</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342782&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342781&type= 23.02933502 4.48733330 分别表示像素边；假设存在两种模态的超像素层，则有 <math id="M123"><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi><mn mathvariant="normal">1</mn></mrow></msup><mo>⋃</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342784&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342783&type= 27.00866890 4.48733330 ，每个模态的超像素对象层均由不同算法生成，则二分图模型对应的相似矩阵 <math id="M124"><mi>B</mi><mo>=</mo><msub><mrow><mfenced separators="|"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>×</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342785&type= 21.42066574 5.75733376 定义为： <math display="block" id="M125"><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mi>α</mi></mtd></mtr><mtr><mtd><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mi>d</mi><mfenced separators="|"><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></mrow></msup></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342788&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342787&type= 19.64266586 13.63133430 . 建立联合像素与超像素的交叉相似矩阵 <math id="M126"><mi mathvariant="bold-italic">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342790&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342789&type= 2.79399991 2.79399991 ，将基于像素模型的广义特征问题转换为基于超像素模型的特征问题。分别计算其在横向与纵向上的对角矩阵，即构建 <math id="M127"><msub><mrow><mi>D</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mi>B</mi><mi>l</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342792&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342791&type= 22.94466591 3.97933316 ， <math id="M128"><msub><mrow><mi>D</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msup><mi>l</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342793&type= 25.31533241 4.48733330 。超像素相似矩阵 <math id="M129"><msub><mrow><mi>W</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>=</mo><msup><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>X</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msubsup><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342795&type= 23.62199974 3.97933316 对应的拉普拉斯矩阵为 <math id="M130"><msub><mrow><mi>L</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>-</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>Y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342798&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342797&type= 23.87599945 3.72533321 ，通过Transfer Cuts求解特征向量 ［ 23 23 ］ <math display="block" id="M131"><msub><mrow><mi>L</mi></mrow><mrow><mi>Y</mi></mrow></msub><mi>v</mi><mo>=</mo><mi>λ</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>Y</mi></mrow></msub><mi>v</mi><mtext> </mtext><msub><mrow><mi mathvariant="normal">L</mi></mrow><mrow><mi>Y</mi></mrow></msub><mi>y</mi><mo>=</mo><mi>τ</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>Y</mi></mrow></msub><mi>y</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342800&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342799&type= 40.13199997 4.57200003 . 拉普拉斯矩阵 <math id="M132"><msub><mrow><mi>L</mi></mrow><mrow><mi>Y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342802&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342801&type= 4.14866638 3.72533321 的前 <math id="M133"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342820&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342819&type= 1.69333339 2.79399991 个最小的特征值以及对应的特征向量表示为 <math id="M134"><msubsup><mrow><mfenced open="{" close="}" separators="|"><mrow><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mrow><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342806&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342805&type= 18.11866570 6.01133299 。由式 <math id="M135"><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><mn mathvariant="normal">2</mn><mo>-</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>k</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342808&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342807&type= 47.15933609 4.74133301 和 <math id="M136"><msub><mrow><mi>μ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><msubsup><mrow><mi>D</mi></mrow><mrow><mi>X</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msubsup><mi>B</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342810&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342809&type= 29.97200012 8.72066593 可以计算出变换后的特征向量 <math id="M137"><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>υ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342812&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342811&type= 19.89666748 5.50333309 ，其中 <math id="M138"><mfenced separators="|"><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>k</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342814&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342813&type= 23.87599945 3.97933316 。根据 <math id="M139"><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342816&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342815&type= 12.78466606 4.57200003 的分布，将 <math id="M140"><msup><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>⋃</mo><msup><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342818&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342817&type= 12.69999981 3.21733332 个顶点划分为 <math id="M141"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342820&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342819&type= 1.69333339 2.79399991 个类。混合超像素的区域合并流程如 算法1 算法1 所示。 算法1 ：混合超像素区域合并算法 输入：遥感光学图像和高程数据 输出：光学图像区域合并结果 1：分别读入光学图像和高程图像，得到的预分割结果 <math id="M142"><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342822&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342821&type= 2.45533323 2.37066650 ， <math id="M143"><mi mathvariant="normal">B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342750&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342749&type= 2.20133328 2.37066650 ； 2：使用定义9对遥感影像预分割结果进行分裂操作； 3：构建二分图； 3.1：设置 <math id="M144"><mi>V</mi><mo>=</mo><msup><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>⋃</mo><mi>P</mi><mo>⋃</mo><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342752&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342751&type= 19.81200027 2.70933342 ； 3.2： <math id="M145"><mi>W</mi><mo>=</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342823&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342753&type= 10.58333302 3.13266683 ； 3.3：for <math id="M146"><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>m</mi><mo>+</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342824&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342754&type= 21.33600044 2.79399991 do 3.4： for <math id="M147"><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342756&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342755&type= 15.23999977 3.13266683 do 3.5： 计算 <math id="M148"><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342758&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342757&type= 4.48733330 3.21733332 ； 3.6： <math id="M149"><mi>W</mi><mo>=</mo><mi>W</mi><mo>⋃</mo><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342760&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342759&type= 17.61066628 3.30200005 ； 3.7： end for 3.8：end for 4：使用Transfer Cuts算法计算分割向量 <math id="M150"><mi>V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342828&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342827&type= 2.79399991 2.45533323 ； 5：基于向量 <math id="M151"><mi>V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342828&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342827&type= 2.79399991 2.45533323 对 <math id="M152"><mi>I</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342830&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342829&type= 1.35466671 2.37066650 进行区域融合。 2.3 优化残差OPT-FPN模块 2 本文基于Momentum 动量法设计了一种新的OPT模块，能够增强车辆目标特征的表达能力，其推导过程如下： <math display="block" id="M153"><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>-</mo><mi>α</mi><mo>∇</mo><mi>f</mi><mfenced separators="|"><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced><mo>-</mo><mi>η</mi><mo>∇</mo><mi>f</mi><mfenced separators="|"><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342834&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342833&type= 53.34000015 4.06400013 ， 其中， <math id="M154"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342858&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342857&type= 1.94733346 2.79399991 和 <math id="M155"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342860&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342859&type= 2.28600001 3.64066648 分别为学习率和动量参数， <math id="M156"><mo>∇</mo><mi>f</mi><mfenced separators="|"><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342840&type= 11.26066685 4.06400013 为目标函数 <math id="M157"><mi>f</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342856&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342855&type= 2.45533323 3.64066648 在 <math id="M158"><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342854&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342853&type= 2.79399991 3.72533321 处的梯度， <math id="M159"><mi>f</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342856&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342855&type= 2.45533323 3.64066648 为满足Lipschitz性质的光滑函数。优化 <math id="M160"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342858&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342857&type= 1.94733346 2.79399991 和 <math id="M161"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342860&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342859&type= 2.28600001 3.64066648 的组合可以实现加速收敛。 假设神经网络传播过程中，信号从第一层到最后一层的传递表示为： <math display="block" id="M162"><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mi>Φ</mi><mfenced separators="|"><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342862&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342861&type= 25.56933212 3.97933316 ， 其中， <math id="M163"><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342864&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342863&type= 2.96333337 3.72533321 为网络中第 <math id="M164"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 层的输出， <math id="M165"><mi>Φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342868&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342867&type= 2.87866688 2.79399991 表示激活函数。设 <math id="M166"><mi>W</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342870&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342869&type= 4.06400013 2.87866688 为对称的正定矩阵，令 <math id="M167"><mi>U</mi><mo>=</mo><mroot><mrow><mi>W</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342872&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342871&type= 15.07066536 4.14866638 且 <math id="M168"><mi>z</mi><mo>=</mo><mi>U</mi><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342896&type= 11.59933376 2.79399991 ，则对于非线性激活函数 <math id="M169"><mi>Φ</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342841&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342875&type= 8.55133343 3.97933316 ，存在函数 <math id="M170"><mi>Ψ</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342843&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342842&type= 9.05933285 3.97933316 ，当 <math id="M171"><msup><mrow><mi>Ψ</mi></mrow><mrow><mi>'</mi></mrow></msup><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced><mo>=</mo><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342844&type= 22.26733208 3.97933316 时有： <math display="block" id="M172"><mo>∇</mo><munder><mo movablelimits="false">∑</mo><mrow><mi>i</mi></mrow></munder><mrow><mi mathvariant="normal">Ψ</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>V</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>T</mi></mrow></msubsup><mi>ξ</mi></mrow></mfenced><mo>=</mo><mi>U</mi><mi>Φ</mi></mrow><mfenced separators="|"><mrow><msup><mrow><mi>U</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>θ</mi></mrow></mfenced><mo>=</mo><mi>U</mi><mi>Φ</mi><mfenced separators="|"><mrow><mi>U</mi><mi>θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342846&type= 62.14533615 6.85799980 . 目标函数 <math id="M173"><mi>f</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342849&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342848&type= 8.12800026 4.06400013 定义为： <math display="block" id="M174"><mi>f</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msup><mrow><mi>z</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>-</mo><munder><mo movablelimits="false">∑</mo><mrow><mi>i</mi></mrow></munder><mrow><mi>Ψ</mi><mfenced separators="|"><mrow><msubsup><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msubsup><mi>z</mi></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342851&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342850&type= 43.68799973 9.39799976 ， 其中， <math id="M175"><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342883&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342852&type= 3.80999994 3.72533321 表示 <math id="M176"><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342885&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342884&type= 3.30200005 2.79399991 的第 <math id="M177"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 列，对 <math id="M178"><mi>f</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342889&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342888&type= 8.12800026 4.06400013 两边求导，可以得到： <math display="block" id="M179"><mo>∇</mo><mi>f</mi><mfenced separators="|"><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>-</mo><mi>U</mi><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>U</mi><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342890&type= 38.52333450 4.06400013 . 使用 公式（16） 公式（16） 来优化 <math id="M180"><mi>f</mi><mfenced separators="|"><mrow><mi>z</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342893&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342892&type= 8.12800026 4.06400013 ，可以得到： <math display="block" id="M181"><mtable><mtr><mtd><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>α</mi></mrow></mfenced><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>+</mo><mi>α</mi><mi>U</mi><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>U</mi><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced><mo>-</mo></mtd></mtr><mtr><mtd><mi>η</mi><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><mi>η</mi><mi>U</mi><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>U</mi><msub><mrow><mi>z</mi></mrow><mrow><mi>k</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342894&type= 51.64666748 9.82133293 . 将 <math id="M182"><mi>z</mi><mo>=</mo><mi>U</mi><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342896&type= 11.59933376 2.79399991 代入到 公式（21） 公式（21） 中可得： <math display="block" id="M183"><mtable><mtr><mtd><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>α</mi></mrow></mfenced><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>-</mo><mi>η</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo></mtd></mtr><mtr><mtd><mi>α</mi><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>W</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mfenced><mo>+</mo><mi>η</mi><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>W</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>k</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342899&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342898&type= 44.28066635 9.82133293 ， 其中， <math id="M184"><mi mathvariant="normal">Φ</mi><mfenced separators="|"><mrow><mi>W</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342901&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342900&type= 12.61533356 3.97933316 为第 <math id="M185"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 层前馈网络。为了避免高层特征因为减少通道数而丢失信息，在FPN中引入了优化残差OPT模块来保留高层特征的语义信息。如 图1 图1 中的OPT模块所示，在OPT模块中加入残差连接，将浅层的细节特征与高层的语义特征相融合，实现了特征重用，保证了车辆目标特征信息的不丢失，提升了网络对车辆特征的提取能力。OPT-FPN结构如 图1 图1 所示，输入图像通过多个卷积模块生成特征图 <math id="M186"><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342877&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342876&type= 29.46400070 3.97933316 ，通过OPT模块自上而下逐级融合得到特征图 <math id="M187"><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342879&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342878&type= 29.04066467 3.97933316 ，增强了网络对车辆目标的多尺度特征表达能力。 2.4 多模态融合模块 2 对于与背景相似的密集型车辆目标，车辆与地面的光学特征非常相似，而车辆相对于地面存在着高度差异，因此引入图像的高程特征可以提升网络对于密集型车辆目标的识别能力。为了充分利用光学图像和高程图像双模态特征，这里设计了多模态融合模块，如 图1 图1 中的MMF模块所示。多模态融合模块的输入为光学特征 <math id="M188"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342881&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342880&type= 7.36600018 3.04800010 与深度特征 <math id="M189"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342913&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342882&type= 7.61999989 3.04800010 ，分别计算两种模态特征的空间注意力引导矩阵 <math id="M190"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 和通道注意力引导矩阵 <math id="M191"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343000&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342999&type= 3.30200005 2.79399991 。空间注意力引导矩阵 <math id="M192"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342918&type= 3.89466691 2.87866688 的计算如下： <math display="block" id="M193"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">U</mi><mfenced separators="|"><mrow><mi>b</mi><mi>n</mi><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></mrow></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mfenced separators="|"><mrow><mi>b</mi><mi>n</mi><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></mrow></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342920&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342919&type= 57.23466873 14.39333248 ， <math display="block" id="M194"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">U</mi><mfenced separators="|"><mrow><mi>b</mi><mi>n</mi><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></mrow></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mfenced separators="|"><mrow><mi>b</mi><mi>n</mi><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></mrow></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342922&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342921&type= 56.72666931 14.39333248 ， 其中， <math id="M195"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342923&type= 7.45066643 3.04800010 和 <math id="M196"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342926&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342925&type= 7.19666624 3.04800010 分别为深度图的空间调整矩阵和光学图的空间调整矩阵。对深度特征和光学特征进行 <math id="M197"><mn mathvariant="normal">3</mn><mo>×</mo><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342945&type= 8.63599968 2.79399991 的卷积操作，然后进行标准化，通过 <math id="M198"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342906&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342905&type= 9.65200043 2.79399991 函数进行激活，得到空间调整的深度特征 <math id="M199"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342908&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342907&type= 7.45066643 3.04800010 和光学特征 <math id="M200"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342910&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342909&type= 7.19666624 3.04800010 ；将 <math id="M201"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342912&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342911&type= 7.45066643 3.04800010 与 <math id="M202"><msup><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342944&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342943&type= 7.19666624 3.04800010 进行 <math id="M203"><mn mathvariant="normal">3</mn><mo>×</mo><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342945&type= 8.63599968 2.79399991 的卷积操作，经过标准化和 <math id="M204"><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342948&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342947&type= 11.85333347 3.64066648 函数激活，得到深度特征的空间注意力引导矩阵 <math id="M205"><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342953&type= 8.46666718 3.04800010 和光学特征的空间注意力引导矩阵 <math id="M206"><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342958&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342957&type= 8.21266651 3.04800010 。多模态融合模块用 <math id="M207"><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342953&type= 8.46666718 3.04800010 对 <math id="M208"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342964&type= 7.36600018 3.04800010 进行特征调整，用 <math id="M209"><msup><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342958&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342957&type= 8.21266651 3.04800010 对 <math id="M210"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342966&type= 7.61999989 3.04800010 进行特征调整，分别得到深度特征 <math id="M211"><msup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342934&type= 7.87400007 3.04800010 和光学特征 <math id="M212"><msup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342937&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342936&type= 7.61999989 3.04800010 ；将 <math id="M213"><msup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342934&type= 7.87400007 3.04800010 和 <math id="M214"><msup><mrow><mi>U</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342937&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342936&type= 7.61999989 3.04800010 分别与 <math id="M215"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342966&type= 7.61999989 3.04800010 和 <math id="M216"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342964&type= 7.36600018 3.04800010 进行残差连接，最终得到空间注意力引导特征图 <math id="M217"><msup><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342973&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342942&type= 6.77333355 3.04800010 和 <math id="M218"><msup><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342975&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342974&type= 6.51933336 3.04800010 。通道注意力引导矩阵 <math id="M219"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343000&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342999&type= 3.30200005 2.79399991 的计算如下： <math display="block" id="M220"><msup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">P</mi><mfenced separators="|"><mrow><mi>G</mi><mi>A</mi><mi>P</mi><mfenced separators="|"><mrow><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342979&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342978&type= 44.19599915 5.16466665 ， <math display="block" id="M221"><msup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">P</mi><mfenced separators="|"><mrow><mi>G</mi><mi>A</mi><mi>P</mi><mfenced separators="|"><mrow><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342981&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342980&type= 43.68799973 5.16466665 ， 其中， <math id="M222"><mi>G</mi><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342983&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342982&type= 8.12800026 2.79399991 为全局平局池化，MLP为多层感知器。分别将 <math id="M223"><msup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342961&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342960&type= 7.95866632 3.04800010 和 <math id="M224"><msup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342963&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342962&type= 7.70466709 3.04800010 与 <math id="M225"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342964&type= 7.36600018 3.04800010 和 <math id="M226"><msup><mrow><mi>X</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342966&type= 7.61999989 3.04800010 对应的进行矩阵相乘，得到通道注意力引导特征图 <math id="M227"><msup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342969&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342968&type= 7.28133297 3.04800010 和 <math id="M228"><msup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342971&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342970&type= 7.02733374 3.04800010 。多模态融合模块通过矩阵拼接的方式实现不同注意力引导矩阵的特征融合，即： <math display="block" id="M229"><mi>L</mi><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mfenced separators="|"><mrow><msup><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup><mo>,</mo><msup><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">M</mi></mrow></msup><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">B</mi></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342988&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342972&type= 54.01733780 4.48733330 ， 其中， <math id="M230"><mi>L</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342989&type= 2.45533323 2.79399991 为两种模态特征的融合特征， <math id="M231"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342992&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342991&type= 9.65200043 2.79399991 为矩阵拼接操作。 2.5 边界感知模块 2 为了提高车辆目标的边缘检测精度，这里设计了基于超像素的边界感知模块，如 图1 图1 中Boundary aware模块所示。将光学图像、多模态超像素融合结果和多模态多尺度特征图作为输入，超像素块视为图的节点，构建初始的有向图 <math id="M232"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>H</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342994&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342993&type= 24.04533195 3.97933316 ，其中 <math id="M233"><mi>V</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342996&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342995&type= 3.21733332 2.87866688 为节点的集合， <math id="M234"><mi>E</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342998&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342997&type= 2.70933342 2.79399991 为边的集合， <math id="M235"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343000&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342999&type= 3.30200005 2.79399991 为隐藏状态集合。顶点的特征 <math id="M236"><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343002&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343001&type= 2.70933342 3.72533321 可以表示为： <math display="block" id="M237"><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>l</mi><mo>,</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343004&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343003&type= 41.90999985 4.82600021 ， 其中， <math id="M238"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343006&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343005&type= 3.55599999 3.72533321 ， <math id="M239"><msub><mrow><mi>G</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343008&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343007&type= 3.55599999 3.72533321 ， <math id="M240"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343010&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343009&type= 3.38666677 3.72533321 代表第 <math id="M241"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 个超像素中所有像素的RGB平均值； <math id="M242"><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343013&type= 10.66800022 4.82600021 代表第 <math id="M243"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 个超像素中心点的 <math id="M244"><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343015&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343014&type= 2.20133328 2.79399991 ， <math id="M245"><mi>y</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343016&type= 2.11666679 3.72533321 坐标； <math id="M246"><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343018&type= 1.26999998 2.79399991 取第 <math id="M247"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 个超像素内数量最多的像素标签值； <math id="M248"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343022&type= 2.20133328 2.79399991 为从多模态多尺度特征图中提取的特征向量。在节点信息传播的过程中，引入注意力机制，使得相同类标签的节点之间的权重大于不同类标签的节点之间的权重。 节点之间传播过程如 图1 图1 中的EGAT模块所示，对于节点 <math id="M249"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 ，依次计算当前节点与具有不同类别邻居节点之间的注意系数 <math id="M250"><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343027&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343026&type= 5.84200001 3.72533321 ： <math display="block" id="M251"><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>=</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mfenced separators="|"><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343028&type= 20.91266632 4.91066647 . 进行归一化，即： <math display="block" id="M252"><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343031&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343030&type= 25.31533241 9.82133293 . 节点 <math id="M253"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343032&type= 1.10066664 2.79399991 聚合后的特征 <math id="M254"><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343035&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343034&type= 6.26533365 3.72533321 表示为： <math display="block" id="M255"><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">U</mi><mfenced separators="|"><mrow><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">P</mi><mfenced separators="|"><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mrow><mi>h</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343036&type= 53.34000015 6.68866634 . 如 图1 图1 中的WFF模块所示，通过不同尺度的卷积操作来调整卷积神经网络输出的感受野大小，并且将不同感受野的卷积神经网络特征与图神经网络的特征进行 <math id="M256"><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343039&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343038&type= 10.66800022 2.79399991 操作，最终将融合特征与卷积神经网络的输出进行残差连接，即： <math display="block" id="M257"><mi>I</mi><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mfenced separators="|"><mrow><msup><mrow><mi>F</mi></mrow><mrow><mi>G</mi></mrow></msup><mo>,</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>F</mi></mrow><mrow><mi>C</mi></mrow></msup></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343048&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42342987&type= 41.99466705 5.24933338 ， <math display="block" id="M258"><mi>Z</mi><mo>=</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">v</mi><mfenced separators="|"><mrow><msup><mrow><mi>F</mi></mrow><mrow><mi>C</mi></mrow></msup><mo>+</mo><mi>I</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343040&type= 29.63333130 4.48733330 ， 其中， <math id="M259"><msup><mrow><mi>F</mi></mrow><mrow><mi>G</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343043&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343042&type= 4.31799984 3.04800010 为图神经网络特征， <math id="M260"><msup><mrow><mi>F</mi></mrow><mrow><mi>C</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343045&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343044&type= 4.14866638 3.04800010 为卷积神经网络输出特征， <math id="M261"><mi>Z</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343046&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343049&type= 2.53999996 2.79399991 为WFF模块的输出特征。 3 结果与讨论 1 实验使用的硬件平台配置为Intel Core i7-10700F CPU、16GB内存、RTX 3070-8G显卡；采用Pytorch深度学习框架、CUDA11.3以及cuDNN8.0深度学习GPU加速库。为了验证本文算法的有效性，分别在ISPRS Potsdam和ISPRS Vaihingen遥感影像数据集上开展实验研究。ISPRS Potsdam波茨坦语义标记数据集由38张5cm空间分辨率的正射向航空RGB图像（ <math id="M262"><mn mathvariant="normal">6</mn><mtext> </mtext><mn mathvariant="normal">000</mn><mo>×</mo><mn mathvariant="normal">6</mn><mtext> </mtext><mn mathvariant="normal">000</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343051&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343050&type= 21.25133324 2.87866688 像素）和通过密集图像匹配生成的相应高程图DSM组成。选择其中五张图像（图像编号： <math id="M263"><mn mathvariant="normal">2</mn><mo>_</mo><mn mathvariant="normal">12</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343052&type= 7.45066643 3.30200005 ， <math id="M264"><mn mathvariant="normal">5</mn><mo>_</mo><mn mathvariant="normal">12</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343047&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343054&type= 7.36600018 3.30200005 ， <math id="M265"><mn mathvariant="normal">7</mn><mo>_</mo><mn mathvariant="normal">7</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343064&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343063&type= 5.50333309 3.30200005 ， <math id="M266"><mn mathvariant="normal">7</mn><mo>_</mo><mn mathvariant="normal">8</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343066&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343065&type= 5.50333309 3.30200005 ， <math id="M267"><mn mathvariant="normal">7</mn><mo>_</mo><mn mathvariant="normal">9</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343068&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343067&type= 5.50333309 3.30200005 ）进行验证，其余图像用于模型训练。将每个样本裁剪成 <math id="M268"><mn mathvariant="normal">256</mn><mo>×</mo><mn mathvariant="normal">256</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343074&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343073&type= 16.00200081 2.79399991 像素大小，每隔90°旋转1次，并进行左右镜像处理，共计训练样本16 928个，测试样本2645个。ISPRS Vaihingen韦兴根数据集由33张9 cm空间分辨率的正射向航空RGB图像（ <math id="M269"><mn mathvariant="normal">2</mn><mtext> </mtext><mn mathvariant="normal">494</mn><mo>×</mo><mn mathvariant="normal">2</mn><mtext> </mtext><mn mathvariant="normal">064</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343072&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343071&type= 21.25133324 2.87866688 像素）和通过密集图像匹配生成的相应高程图组成。同样将每个样本裁剪成 <math id="M270"><mn mathvariant="normal">256</mn><mo>×</mo><mn mathvariant="normal">256</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343074&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343073&type= 16.00200081 2.79399991 像素大小，每隔90°旋转1次，并进行镜像处理，共计训练样本1 925个，测试样本329个。 3.1 超像素分割实验 2 为了验证不同 <math id="M271"><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343078&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343077&type= 2.96333337 3.72533321 取值对超像素分割的影响效果，这里选取了四张ISPRS Potsdam数据集中的遥感影像进行分割实验，如 图3 图3 所示。可以看出，随着 <math id="M272"><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343078&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343077&type= 2.96333337 3.72533321 值的增加，具有相同特征的超像素块被执行合并操作，但存在不同程度的像素误合并现象。当 <math id="M273"><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">400</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343080&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343079&type= 13.29266548 3.72533321 时，能够将车辆目标进行较为准确地分割与合并。 图4 图4 展示了DBSCAN ［ 24 24 ］ ，LRW ［ 25 25 ］ ，LSC ［ 26 26 ］ ，SEEDS ［ 27 27 ］ ，TPS ［ 28 28 ］ 和本文算法的超像素分割结果。可以看出，DBSCAN和LRW方法的分割结果在图像左上角区域存在误划分为阴影区域的情况，SEEDS和TPS方法存在局部小块区域的误划分问题。本文的多模态超像素融合结果的边界准确性高，且受光照影响小。 3.2 车辆目标检测实验 2 本文使用精确率 <math id="M276"><mi mathvariant="normal">p</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343092&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343091&type= 13.46199989 3.64066648 、召回率 <math id="M277"><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343094&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343093&type= 8.21266651 2.79399991 、全局准确性 <math id="M278"><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343213&type= 5.75733376 2.79399991 、平均交并比（ <math id="M279"><mi mathvariant="normal">m</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343114&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343113&type= 8.97466660 2.79399991 ）和 <math id="M280"><mi mathvariant="normal">F</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343100&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343099&type= 4.31799984 2.79399991 - <math id="M281"><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343102&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343101&type= 7.87400007 2.79399991 作为目标检测结果的衡量指标。 表2 表2 给出了在ISPRS Potsdam数据集上本文方法与FCN-32s ［ 29 29 ］ ，FCN-8s ［ 29 29 ］ ，U-net ［ 30 30 ］ ，SegNet ［ 31 31 ］ ，PSPNet ［ 32 32 ］ ，DeepLabv3+ ［33］ 和G-FRNet ［ 34 34 ］ 的比较结果。可以看出，本文方法车辆目标检测结果优于其他模型。在 <math id="M282"><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343213&type= 5.75733376 2.79399991 ， <math id="M283"><mi>m</mi><mi>F</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343199&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343198&type= 7.11199999 2.79399991 和 <math id="M284"><mi>m</mi><mi>I</mi><mi>o</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343118&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343193&type= 9.14400005 2.79399991 评价指标上分别达到 <math id="M285"><mn mathvariant="normal">92.39</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343216&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343215&type= 13.12333298 3.47133350 ， <math id="M286"><mn mathvariant="normal">91.05</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343194&type= 13.12333298 3.47133350 和 <math id="M287"><mn mathvariant="normal">84.61</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343120&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343119&type= 13.12333298 3.47133350 ，比G-FRNet分别提高了 <math id="M288"><mn mathvariant="normal">0.45</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343061&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343060&type= 11.26066685 3.47133350 ， <math id="M289"><mn mathvariant="normal">0.4</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343123&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343062&type= 9.48266602 3.47133350 和 <math id="M290"><mn mathvariant="normal">0.7</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343125&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343124&type= 9.48266602 3.47133350 ，同时大幅超过PSPNet和U-net方法。 模型 Surface Building Low-veg Tree Car MIoU mF1 OA FCN-32s 76.14 89.81 72.01 68.98 66.84 74.76 84.48 87.15 FCN-8s 77.52 90.34 72.62 65.98 77.32 76.76 85.54 87.44 U-net 77.20 91.16 73.23 69.00 79.29 77.98 86.67 87.84 SegNet 72.84 87.99 67.68 60.33 75.00 72.77 82.76 84.93 PSPNet 79.16 91.73 73.37 69.76 75.61 77.92 86.61 88.26 DeepLabv3+ 79.60 91.21 75.48 70.33 78.19 78.96 87.28 88.92 G-FRNet 85.16 95.55 80.56 76.77 81.53 83.91 90.65 91.94 our 85.72 96.00 81.91 76.82 82.59 84.61 91.05 92.39 表3 表3 给出了在ISPRS Vaihingen数据集上本文方法与FCN-32s，FCN-8s，U-net，SegNet，PSPNet，DeepLabv3+和G-FRNet的比较结果。可以看出，在 <math id="M291"><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343213&type= 5.75733376 2.79399991 ， <math id="M292"><mi>m</mi><mi>F</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343199&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343198&type= 7.11199999 2.79399991 和 <math id="M293"><mi>m</mi><mi>I</mi><mi>o</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343118&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343193&type= 9.14400005 2.79399991 评价指标上分别达到了 <math id="M294"><mn mathvariant="normal">89.66</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343218&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343217&type= 13.12333298 3.47133350 ， <math id="M295"><mn mathvariant="normal">85.11</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343196&type= 13.12333298 3.47133350 和 <math id="M296"><mn mathvariant="normal">74.90</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343121&type= 13.12333298 3.47133350 ；比G-FRNet分别提高了 <math id="M297"><mn mathvariant="normal">1.18</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343141&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343140&type= 11.26066685 3.47133350 ， <math id="M298"><mn mathvariant="normal">4.85</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343143&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343142&type= 11.26066685 3.47133350 和 <math id="M299"><mn mathvariant="normal">6.2</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343145&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343144&type= 9.48266602 3.47133350 。在类别Car上，本文方法在 <math id="M300"><mi>I</mi><mi>o</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343147&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343146&type= 6.43466663 2.79399991 指标比U-net提升了 <math id="M301"><mn mathvariant="normal">6.77</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343149&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343148&type= 11.26066685 3.47133350 。总体来看，本文方法在车辆检测任务上比其他网络模型具有较为明显的优势。 模型 Surface Building Low-veg Tree Car background MIoU mF1 OA FCN-32s 73.12 83.47 59.99 73.51 41.20 10.50 56.97 68.76 84.10 FCN-8s 78.30 85.53 59.87 74.60 61.36 18.28 62.99 74.56 85.91 U-net 79.09 85.83 63.95 76.06 64.61 17.92 64.58 75.67 86.76 SegNet 73.48 82.49 57.24 72.81 43.75 1.23 55.17 65.91 83.43 PSPNet 78.21 87.15 62.58 75.56 56.13 19.34 63.16 74.71 86.44 DeepLabv3+ 79.48 87.90 62.90 75.94 64.12 19.62 64.99 76.10 86.98 G-FRNet 80.13 89.33 68.15 79.41 52.68 42.50 68.70 80.26 88.48 our 86.13 93.50 64.94 75.34 71.38 58.12 74.90 85.11 89.66 图5 图5 给出了在ISPRS Potsdam数据集和ISPRS Vaihingen数据集上，本文方法与FCN-32s，FCN-8s，U-net，SegNet，PSPNet，DeepLabv3+和G-FRNet七种方法在precision和recall指标上的对比结果。可以看出，本文的方法在两个数据集上的表现均明显优于其它方法。 图6 图6 展示了八种方法在ISPRS Potsdam数据集上的测试结果。可以看出，本文方法检测的轮廓结果较为完整且与真实车辆边缘吻合度高。通过 图6 图6 第1行可以看出车辆目标较为密集，FCN-32S，FCN-8S，SegNet和Unet均存在误检的情况；第2行SegNet和PSPNet的检测结果出现了车辆漏检的现象；第3行中左下角的黑色车辆存在背景干扰的问题，Unet和DeeplabV3+均无法准确地进行检测。第4行图像中，PSPNet与DeeplabV3+受树木、建筑物阴影遮挡干扰，无法完整地检测出车辆。本文方法能够在一定程度上减小了树木、阴影等对车辆目标检测的干扰，可以有效地检测与背景相似的车辆。 图7 图7 为本文算法在ISPRS Vaihingen数据集上的车辆检测结果。从 图7 图7 的第1行与第2行可以看出，SegNet和PSPNet的检测结果较差；第3行存在车辆被树木遮挡的情况，而DeepLabv3+无法将被树木遮挡的车辆目标进行有效检测；第4行图像中存在与车辆特征相似的物体，SegNet，PSPNet和DeepLabv3+均存在误检现象，而本文方法均能够进行准确区分，可以将大部分与背景相似的车辆和密集型车辆检测出来，并在车辆轮廓边缘等细节部分有着更高的分割准确性。 3.3 消融实验 2 为了验证OPT-FPN模块与多模态融合模块对分割结果的影响，这里在ISPRS Potsdam数据集上分别对OPT-FPN模块与多模态融合模块进行消融实验。 3 . 3 . 1 OPT - FPN模块消融实验 3 本文2.3节引入OPT-FPN模块，以提高网络识别多尺度目标的能力。为了验证该模块的有效性，这里去除OPT-FPN模块，结果如 表3 表3 所示。其中 <math id="M302"><mi>N</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343162&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343115&type= 4.82600021 2.87866688 表示引入优化残差OPT-FPN模块的网络模型， <math id="M303"><mi>N</mi><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343116&type= 4.82600021 2.87866688 表示没有引入优化残差OPT-FPN模块的网络模型。从 表3 表3 可以发现，在 <math id="M304"><mi mathvariant="normal">m</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343114&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343113&type= 8.97466660 2.79399991 指标上 <math id="M305"><mi>N</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343162&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343115&type= 4.82600021 2.87866688 比 <math id="M306"><mi>N</mi><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343116&type= 4.82600021 2.87866688 提升了 <math id="M307"><mn mathvariant="normal">0.91</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343164&type= 11.26066685 3.47133350 ；添加OPT-FPN模块后，模型的分割精度显著提高，局部细节的分割效果更接近GT，如 图8 图8 所示。实验结果表明OPT-FPN模块对于多尺度目标的检测结果具有较好的提升作用，可以实现多尺度特征的有效融合。 3 . 3 . 2 多模态融合模块消融实验 3 为了验证2.4节多模态融合模块的作用，这里去除多模态融合模块，在ISPRS Potsdam数据集上重新训练网络。如 表4 表4 所示， <math id="M308"><mi>M</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343174&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343173&type= 5.41866684 2.87866688 表示包含多模态融合模块的模型， <math id="M309"><mi>M</mi><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343176&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343175&type= 5.41866684 2.87866688 表示不包含多模态融合模块的模型。可以看出， <math id="M310"><mi>M</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343174&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343173&type= 5.41866684 2.87866688 较 <math id="M311"><mi>M</mi><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343176&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343175&type= 5.41866684 2.87866688 在Car类上 <math id="M312"><mi mathvariant="normal">I</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343178&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343177&type= 6.09600019 2.79399991 指标提升了 <math id="M313"><mn mathvariant="normal">1.24</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343117&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343179&type= 11.34533310 3.47133350 。从 图9 图9 可以看出，引入多模态融合模块的分割结果有着更准确的边界效果。因此，多模态融合模块提高了模型对于密集和光学特征相似目标之间的检测精度。 Models Surface Building Low-veg Tree Car mIoU <math id="M314"><mi>N</mi><mn>1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343181&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343180&type= 4.14866638 2.45533323 85.72 96.00 81.91 76.82 82.59 84.61 <math id="M315"><mi>N</mi><mn>2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343183&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343182&type= 4.14866638 2.45533323 85.10 95.76 80.55 75.94 81.16 83.70 <math id="M316"><mi>M</mi><mn>1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343185&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343184&type= 4.65666676 2.45533323 85.72 96.00 81.91 76.82 82.59 84.61 <math id="M317"><mi>M</mi><mn>2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343187&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343186&type= 4.65666676 2.45533323 83.26 94.05 77.42 73.66 81.35 81.95 4 结 论 1 本文提出了一种融合超像素与多模态感知网络的遥感影像车辆检测方法。该方法通过超像素二分图融合算法将两种模态的超像素分割结果进行融合，提升了不同模态图像超像素分割结果的准确性。基于多模态感知网络MEANet，引入OPT-FPN模块来增强网络学习多尺度目标特征的能力。通过边缘感知模块聚合超像素和多模态融合模块生成的两组边缘特征，进而生成车辆目标的准确边界。在ISPRS Potsdam和ISPRS Vaihingen遥感影像数据集的实验表明， <math id="M318"><mi>m</mi><mi>I</mi><mi>o</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343118&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343193&type= 9.14400005 2.79399991 指标为 <math id="M319"><mn mathvariant="normal">84.61</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343120&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343119&type= 13.12333298 3.47133350 和 <math id="M320"><mn mathvariant="normal">74.90</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343121&type= 13.12333298 3.47133350 ， <math id="M321"><mi>m</mi><mi>F</mi><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343199&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343198&type= 7.11199999 2.79399991 指标为 <math id="M322"><mn mathvariant="normal">91.05</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343194&type= 13.12333298 3.47133350 和 <math id="M323"><mn mathvariant="normal">85.11</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343196&type= 13.12333298 3.47133350 ， <math id="M324"><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343213&type= 5.75733376 2.79399991 指标为 <math id="M325"><mn mathvariant="normal">92.39</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343216&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343215&type= 13.12333298 3.47133350 和 <math id="M326"><mn mathvariant="normal">89.66</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343218&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42343217&type= 13.12333298 3.47133350 ，本文所提出的方法提升了遥感图像分割结果的准确性，能够解决遥感影像车辆检测中由于背景干扰和目标异质性等因素引起的识别精度下降问题。未来将基于知识蒸馏优化网络模型，进一步提高遥感图像目标检测的实时性。 参考文献 MORANDUZZO T ， MELGANI F . 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A CFAR target-detection method based on superpixel statistical modeling ［J］. IEEE Geoscience and Remote Sensing Letters ， 2021 ， 18 （ 9 ）： 1605 - 1609 . doi: 10.1109/lgrs.2020.3006033 http://dx.doi.org/10.1109/lgrs.2020.3006033 A CFAR target-detection method based on superpixel statistical modeling 廖苗 ， 李阳 ， 赵于前 ， 等 . 一种新的图像超像素分割方法 ［J］. 电子与信息学报 ， 2020 ， 42 （ 2 ）： 364 - 370 . doi: 10.11999/JEIT190111 http://dx.doi.org/10.11999/JEIT190111 一种新的图像超像素分割方法 LIAO M ， LI Y ， ZHAO Y Q ， et al . A new method for image superpixel segmentation ［J］. Journal of Electronics & Information Technology ， 2020 ， 42 （ 2 ）： 364 - 370 . （in Chinese） . doi: 10.11999/JEIT190111 http://dx.doi.org/10.11999/JEIT190111 A new method for image superpixel segmentation 任凤雷 ， 何昕 ， 魏仲慧 ， 等 . 基于DeepLabV 3+ 与超像素优化的语义分割 ［J］. 光学 精密工程 ， 2019 ， 27 （ 12 ）： 2722 - 2729 . doi: 10.3788/ope.20192712.2722 http://dx.doi.org/10.3788/ope.20192712.2722 基于DeepLabV3+与超像素优化的语义分割 REN F L ， HE X ， WEI ZH H ， et al . 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