强噪声下自适应Canny算子边缘检测

强噪声下自适应Canny算子边缘检测 Adaptive Canny operator edge detection under strong noise first-author 刘宇涵（1997-），男，重庆忠县人，硕士研究生，2020年于南京工业大学获得学士学位，主要从事机器视觉及图像处理的研究。E-mail： zxlyh1997@2020.cqut.edu.cn http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461108&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461113&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461111&type= 22.01332855 32.00402451 刘宇涵 （1997-），男，重庆忠县人，硕士研究生，2020年于南京工业大学获得学士学位，主要从事机器视觉及图像处理的研究。E-mail： zxlyh1997@2020.cqut.edu.cn zxlyh1997@2020.cqut.edu.cn corresp E-mail： cqyanhe@163.com E-mail： cqyanhe@163.com 闫　河（1972-），男，陕西勉县人，博士，教授，硕士生导师，主要从事图像多尺度几何分析、目标跟踪、模式识别等的研究。E-mail： cqyanhe@163.com http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461116&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461125&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461120&type= 22.01332855 32.00400925 闫　河 （1972-），男，陕西勉县人，博士，教授，硕士生导师，主要从事图像多尺度几何分析、目标跟踪、模式识别等的研究。E-mail： cqyanhe@163.com cqyanhe@163.com 重庆理工大学 两江人工智能学院，重庆 401147 重庆理工大学 两江人工智能学院，重庆 401147 Liangjiang College of Artificial Intelligence， Chongqing University of Technology， Chongqing 401147， China Liangjiang College of Artificial Intelligence， Chongqing University of Technology， Chongqing 401147， China 针对传统Canny算子不能有效滤除图像在解码处理和传输过程产生的椒盐噪声、无法保留边缘细节的问题，提出强噪声下Canny算子图像边缘检测算法。依据椒盐噪声的极值性、灰度差值性，将像元点划分为噪声点、疑似噪声点；根据分类之后的像元点自适应地改变滤波器窗口的大小和权值，在降低噪声影响的同时能较好地保留图像细节。引入8个方向模板的 Sobel算子计算梯度幅值以提高滤波后的边缘定位效果。使用迭代自适应阈值算法与Otsu算法选择最佳阈值，实现阈值自适应设定，提高边缘连接效果。实验结果表明：图像去噪后的结构相似度为0.949，峰值信噪比相较于传统算法提升了10.97 dB。边缘评价指标提高27.2%，F1值提高了34.6%。该算法能有效去除椒盐噪声，具有更好的边缘细节保护能力。 The traditional Canny operator cannot effectively filter out the salt and pepper noise generated during the decoding process and transmission of an image， and cannot retain the edge details. To overcome this， an improved Canny operator image edge detection algorithm for operation under strong noise was proposed. According to the extreme value and gray difference of salt and pepper noise， the pixel points were divided into noise points and suspected noise points. The size and weight of the filter window were adaptively changed according to the pixel points after classification， which could reduce the influence of noise while retaining the image details. Then， the Sobel operators for eight directional templates were introduced to calculate the gradient amplitude to improve the edge positioning effect after filtering. Finally， iterative adaptive threshold algorithm and Otsu algorithm were used to select the best threshold to achieve adaptive threshold setting and improve the edge connection effect. The results of the comparative experiment show that after denoising the noisy image， the structural similarity is 0.949， the peak signal-to-noise ratio is increased by 10.97 dB compared with the traditional algorithm， the average edge evaluation is increased by 27.2%， and the F1 value is increased by 34.6%. The proposed algorithm retains the excellent performance of the Canny operator， can effectively remove salt and pepper noise， and has better edge detail protection capabilities. 计算机视觉 边缘检测 图像去噪 Canny算法 自适应滤波 自适应阈值 computer vision edge detection image denoise Canny operator adaptive filter adaptive threshhold 1 引　言 1 椒盐噪声属于非线性噪声，一般服从随机分布，主要由图像的极值组成。信号脉冲强度的随机变化会引入椒盐噪声，它常产生于图像采集、信道传输及解码处理过程中 ［ 1 1 ］ ，会严重降低图像质量，不利于图像目标边缘检测的准确性和完整性，导致图像的后续分析和处理困难。图像边缘一般存在于灰度值变化较大的位置，且边缘与噪声信号一样具有高频特征，当图像中存在噪声时，易将噪声误当作边缘或将边缘误当作噪声，边缘检测常常变得很困难 ［ 2 2 - 3 3 2-3 ］ 。文献［ 4 4 ］指出若噪声较强，边缘会出现粘连的情况，且伪边缘数量随着噪声密度的增加而急剧增加。因此，在边缘检测时对图像进行去噪处理有着重要意义。1986年，Canny ［ 5 5 ］ 提出一种名为Canny的边缘检测算法。传统Canny算法虽易于运行，但采用的滤波器为线性的高斯滤波，易受噪声干扰，且对非线性的椒盐噪声处理效果不佳，会破坏图像中原本的边缘细节信息。边缘检测时对背景噪声较为敏感，会出现边缘细节丢失的情况，导致图像处理效果不太理想 ［ 6 6 - 7 7 6-7 ］ 。文献［ 8 8 ］指出传统Canny算法易受光照影响等外界环境的影响，不能有效去除噪声。文献［ 9 9 ］和［10］指出传统Canny算子阈值分割过程未考虑噪声干扰，存在筛选过度问题，导致检测边缘不完整，出现伪边缘的情况。 近年来，学者们对Canny算法做出了不少改进。文献［ 11 11 ］提出中值滤波与均值滤波相结合的滤波方法抑制椒盐噪声，虽然适当提高了Canny算法的抗噪性，减少了边缘丢失现象，但在强噪情况下边缘检测的准确性和完整度并不好。文献［ 12 12 ］为减少噪声引起的边缘断缺现象，提出了一种混合滤波器抑制噪声，并使用最大类间方差（Otsu）自适应阈值法实现目标边缘的检测。该方法对弱噪声图像目标边缘检测具有一定效果，但所采用的混合滤波法易降低图像质量，最终导致目标检测的边缘加粗。文献［ 13 13 ］针对强噪声下边缘检测任务采用平滑聚类法抑制噪声，考虑图像的灰度变化及灰度信息自适应求解阈值，采用软阈值方法实现目标边缘像素的甄别，该方法对强噪声图像目标边缘检测具有较好的性能，但在微小目标密集区域易把噪声点误判为边缘。 用线性滤波方法无法有效抑制非线性噪声。为更好地抑制椒盐噪声，减少去噪引起的图像模糊，保护边缘细节，本文利用椒盐噪声的极值性及差值性，将像素点分为疑似噪声点及噪声点，抑制部分噪声，再采用自适应模糊中值滤波（Adaptive Fuzzy Median Filter， AFFM）代替传统Canny算子的高斯滤波器对图像进行卷积操作，保留图像细节，同时去除噪声。为准确捕捉细微边缘信息，本文引入八方向5×5算子模板实现目标特征点的检测，再通过非极大值抑制、自适应阈值迭代算法和最大类间方差法（Otsu）实现目标边缘像素点的准确甄别。该方法在噪声环境下提高了图像边缘检测的完整度，可去除噪声并保留边缘细节，为后续图像处理提供边缘完整、连接度高的边缘图像。 2 改进的Canny边缘检测算法 1 传统Canny算法使用高斯滤波对图像进行处理，而高斯滤波是线性滤波，无法有效抑制图像中出现的非线性噪声；并且自适应性差，需人为更改高斯滤波窗口的尺寸，再通过实验测试使性能达到最佳。所以在传统算法中，滤波窗口是人为固定，不能兼顾去噪的效果及保存图像边缘细节 ［ 14 14 ］ ；使用2×2的邻域计算梯度幅值，该方法检测方向较少，容易遗漏真实边缘，同时对噪声敏感，因此易检测到虚假边缘 ［ 15 15 ］ ；非极大值抑制后，高、低阈值需要凭借经验人为选取。 本文为提高边缘检测算法对噪声的抑制能力、自适应性以及边缘连接能力，在已有方法基础上提出了强噪声下Canny算子边缘检测算法。 2.1　自适应模糊中值滤波 2 自适应模糊中值滤波的运行过程包括噪声点检测、模糊加权函数构建及自适应模糊中值滤波的实现。 2 . 1 . 1　噪声点检测 3 自然图像的像素灰度通常为持续渐变的梯度，椒盐噪声点的灰度值是正常像素值与噪声值叠加在一起的。为了保护图像细节特征，需区分出椒盐噪声点、疑似噪声点，为进一步滤波操作准备。椒盐噪声具有极值性，其灰度值与图像灰度极值相近，但仅凭这一判断依据进行噪声点检测还是不够精准，需将灰度平滑区域纳入考虑范围。 本文基于下述基础理论，提出一种椒盐噪声检测方法。 （1）图像平滑区域通常被边缘划分，且区域内一般为正常像素点； （2）通过分析图像灰度值，发现椒盐噪声点通常表现为灰度值的极大值或极小值。 用 G 表示输入的原图像， <math id="M1"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461132&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461128&type= 9.73666668 3.97933316 为图像 <math id="M2"><mi>G</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461138&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461135&type= 2.79399991 2.79399991 中像素点 <math id="M3"><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> 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mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461411&type= 3.64066648 3.80999994 为疑似噪声点集合，为了达到区分图像中椒盐噪声点、疑似噪声点的目的，本文对像素点进行检测。根据椒盐噪声的极值特性，同时考虑灰度平滑区域，本文具体措施如下： （1）如果像素点 <math id="M16"><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461577&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461574&type= 7.11199999 3.97933316 与周围像素点的灰度差值较小，即 <math id="M17"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461207&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461206&type= 13.20800018 4.82600021 ， <math id="M18"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461227&type= 13.37733269 4.82600021 均很小，设定阈值 <math id="M19"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461211&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461210&type= 2.96333337 3.72533321 ，若 <math id="M20"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461213&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461212&type= 20.82799911 4.82600021 ，则保留像素点 <math id="M21"><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461217&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461215&type= 7.11199999 3.97933316 ； （2）若像素点 <math id="M22"><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461577&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461574&type= 7.11199999 3.97933316 与周围像素点的灰度差值差别显著，即 <math id="M23"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461898&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461896&type= 13.20800018 4.82600021 ， <math id="M24"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461227&type= 13.37733269 4.82600021 值均较大，若 <math id="M25"><mtext> </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>></mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">且</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>≥</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461235&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461233&type= 64.17733002 4.82600021 则该点属于处于灰度渐变区的噪声点，此点不加入 <math id="M26"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461411&type= 3.64066648 3.80999994 集合； （3）若像素点（ <math id="M27"><mi>i</mi><mo>,</mo><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461245&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461243&type= 4.06400013 3.64066648 ）与周围像素点灰度差值至少有一方向的灰度值较小，但与其他方向灰度差值较大，即 <math id="M28"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461289&type= 13.20800018 4.82600021 较大，但 <math id="M29"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461295&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461293&type= 13.37733269 4.82600021 值较小，若 <math id="M30"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>></mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mi mathvariant="normal">且</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461256&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461254&type= 63.50000000 4.82600021 ，则该点可能为边缘点，也可能为噪声点，将此点加入 <math id="M31"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461411&type= 3.64066648 3.80999994 集合。 上述步骤中，通过实验分析设定阈值 <math id="M32"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">32</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461264&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461262&type= 11.51466751 3.72533321 ， <math id="M33"><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">42</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461268&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461266&type= 11.51466751 3.72533321 。若像素为噪声点， <math id="M34"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461289&type= 13.20800018 4.82600021 ， <math id="M35"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461295&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461293&type= 13.37733269 4.82600021 均较大，否则 <math id="M36"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461289&type= 13.20800018 4.82600021 ， <math id="M37"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461295&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461293&type= 13.37733269 4.82600021 取值较小，可据 <math id="M38"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461289&type= 13.20800018 4.82600021 ， <math id="M39"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461295&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461293&type= 13.37733269 4.82600021 判断像素点是否为噪声点。 根据以上推理，可建立判断椒盐噪声及疑似噪声点的数学模型，具体表示如下： <math display="block" id="M40"><mi>N</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">O</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi><mo>,</mo><mtext>  </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>></mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mtext> </mtext><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mtext> </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>≥</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mtext> </mtext><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>></mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mtext> </mtext><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mtext> </mtext><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461298&type= 110.23600006 16.93333435 ， <math display="block" id="M41"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo stretchy="false">|</mo><mi>N</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>≠</mo><mi mathvariant="normal">O</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461305&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461303&type= 48.68333054 4.74133301 . 2 . 1 . 2　模糊加权函数 3 为良好地抑制椒盐噪声，平滑其他非椒盐噪声，同时解决经中值滤波后出现图像模糊的情况，采用模糊加权函数对滤波窗口中的灰度值进行加权处理。计算 <math id="M42"><msub><mrow><mi mathvariant="bold-italic">W</mi></mrow><mrow><mi>n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461309&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461307&type= 4.91066647 3.80999994 窗口中灰度的最大值 <math id="M43"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461313&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461310&type= 5.50333309 4.57200003 、 最小值 <math id="M44"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461318&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461316&type= 5.16466665 4.57200003 和均值 <math id="M45"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461325&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461320&type= 6.34999990 4.57200003 。由于椒盐噪声点具有极值特性，当 <math id="M46"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461330&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461328&type= 5.16466665 4.57200003 < <math id="M47"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461336&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461333&type= 9.73666668 3.97933316 < <math id="M48"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461341&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461340&type= 6.34999990 4.57200003 时， <math id="M49"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461401&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461398&type= 9.73666668 3.97933316 为噪声像素点的概率与 <math id="M50"><mfrac><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>-</mo><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>-</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461355&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461352&type= 20.99733353 9.14400005 负相关，即该值越大， <math id="M51"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461361&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461358&type= 9.73666668 3.97933316 为噪声点的概率越大。当 <math id="M52"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461367&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461364&type= 6.34999990 4.57200003 < <math id="M53"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461372&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461370&type= 9.73666668 3.97933316 < <math id="M54"><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461378&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461376&type= 5.50333309 4.57200003 时，与上述概念同理。根据推理得出模糊加权函数为： <math display="block" id="M55"><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>-</mo><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>-</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>≤</mo><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>≤</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></mtd></mtr><mtr><mtd><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo>-</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfrac><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>≤</mo><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>≤</mo><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461385&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461381&type= 71.79733276 21.16666603 . 得到模糊加权函数 <math id="M56"><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461390&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461388&type= 10.15999985 3.97933316 ，可利用该函数对疑似噪声点集合进行模糊加权。 2 . 1 . 3　自适应滤波 3 若是能在进行卷积的同时判断图像各区域噪声污染的程度即卷积窗口内疑似噪声点数量，根据噪声污染程度选择适宜的窗口执行滤波处理，从理论程度上减少了时间复杂度的同时提升了滤波质量。 若图中噪声密度较大，滤波窗口中可能存在大量噪声点。所以本文先进行噪声点检测，将窗口内部异常点全部进行了剔除处理，留下窗口疑似噪声点全部进行了滤波处理，尽可能地保持图像原始灰度特征。同时，采用模糊加权函数来逼近窗体中心像素点的灰度值，以避免噪声点对像素中值滤波产生的干扰。 使用 <math id="M57"><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461392&type= 4.99533367 3.72533321 窗口对以 <math id="M58"><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461401&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461398&type= 9.73666668 3.97933316 为待检测像素中点进行 <math id="M59"><mi>n</mi><mo>×</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461881&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461880&type= 8.63599968 2.79399991 （ n 为不小于3的奇数， n 初始为3）的窗口滤波操作。由之前异常点及疑似噪声点检测可得疑似噪声点集合 <math id="M60"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461411&type= 3.64066648 3.80999994 ，设 <math id="M61"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461420&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461417&type= 9.56733322 3.97933316 为输出灰度值。 若 <math id="M62"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461425&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461423&type= 13.20800018 4.82600021 ， <math id="M63"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461432&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461428&type= 13.37733269 4.82600021 均较小时（小于10），小于10可证明灰度差值近似为0，根据噪声点的灰度差值特性判断此点为非噪声点，此时按像素点灰度值原值输出， <math id="M64"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461437&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461435&type= 9.56733322 3.97933316 为输出灰度值，且窗口进行滑动。 <math display="block" id="M65"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461442&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461439&type= 23.87599945 3.97933316 . 用 <math id="M66"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461448&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461445&type= 4.57200003 3.80999994 表示 <math id="M67"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461451&type= 3.64066648 3.80999994 的中值，即有： <math display="block" id="M68"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">m</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></mrow></mfenced><mo>,</mo><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>≠</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461456&type= 42.41799927 4.82600021 . 当图像中噪声较为密集时，3×3的滤波窗口内可能不存在疑似噪声点，表现为 <math id="M69"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461564&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461561&type= 12.19200039 4.57200003 ，则无法计算 <math id="M70"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461909&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461907&type= 4.57200003 3.80999994 ，增大窗口的尺寸，步长为 <math id="M71"><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461912&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461911&type= 15.32466698 2.96333337 。若通过强行让窗口中存在疑似噪声点，去增大窗口大小，会增大算法复杂度，且引入的像元点与中心点的像素点的灰度相关性较低，所以需设置最大滤波窗口，使窗口尺寸限定在一定范围内，本文将最大滤波窗口设置为 <math id="M72"><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">11</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461483&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461480&type= 14.05466747 3.72533321 。 设最小滤波窗口 <math id="M73"><msub><mrow><mi mathvariant="bold-italic">W</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461489&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461486&type= 12.69999981 4.82600021 内左上角4个像素点已经通过滤波处理，将这些点的灰度值直接保存在 <math id="M74"><mi mathvariant="bold-italic">S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461522&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461519&type= 2.37066650 2.79399991 集合中，可以表示为： <math display="block" id="M75"><mi mathvariant="bold-italic">S</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mtable><mtr><mtd><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>j</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>j</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>,</mo><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461499&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461497&type= 52.32400131 10.83733368 ， 式中： <math id="M76"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461505&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461502&type= 9.56733322 3.97933316 表示像素点 <math id="M77"><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461511&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461507&type= 7.11199999 3.97933316 滤波后的灰度值。因为 <math id="M78"><mi mathvariant="bold-italic">S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461516&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461514&type= 2.37066650 2.79399991 集合中像素点均完成滤波，可认为 <math id="M79"><mi mathvariant="bold-italic">S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461522&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461519&type= 2.37066650 2.79399991 集合中的像素点都是非噪声点。 若满足式 <math id="M80"><mfenced open="|" close="|" separators="|"><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mtext> </mtext></mrow></msub></mrow></mfenced><mo>></mo><mi>T</mi><mo>,</mo><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461528&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461525&type= 35.22133255 4.82600021 为阈值（经实验 <math id="M81"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461783&type= 2.53999996 2.79399991 =30时效果最佳）。则对窗口中 <math id="M82"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461540&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461537&type= 4.57200003 3.80999994 和像素点灰度值进行模糊加权，经滤波处理后的灰度值 <math id="M83"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461546&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461543&type= 9.56733322 3.97933316 为： <math display="block" id="M84"><mi>h</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>,</mo><mfenced open="|" close="|" separators="|"><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mtext> </mtext></mrow></msub></mrow></mfenced><mo>≤</mo><mi>T</mi></mtd></mtr><mtr><mtd><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>⋅</mo><mi>g</mi><mo 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如果滤波窗口大于 <math id="M85"><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461558&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461555&type= 5.50333309 3.72533321 ，且 <math id="M86"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461564&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461561&type= 12.19200039 4.57200003 ，采用已处理的像素点集合 <math id="M87"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461918&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461917&type= 2.20133328 2.79399991 的均值作为像素点 <math id="M88"><mo 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55.79533768 4.74133301 . 对Lena图进行滤波操作（非局部滤波），计算出灰度等级直方图，选取高峰、低峰进行分析比较，如 图1 图1 所示。定义 图1 图1 中左上方区域为区域1，另一个区域为区域2。 图1 图1 （b）为中值滤波处理结果，区域1及区域2对比原图，灰度有较大的区别，由此表明，中值滤波破坏了整体的稳定性，并损坏了图像的梯度结构。 图1 图1 （c）的两区域相较于图 1（a） 1（a） ， 1（b） 1（b） 中的灰度增强效果一般，滤掉了大量图像灰度特征，但图像梯度保持较好，并提高了图像对比度，其灰度特征与 图1 图1 （a）相似。 图1 图1 （d）使用一种混合滤波器和改进的均值滤波器同时对图像进行滤波，区域1与 图1 图1 （a）相比图像的增强效果较弱，改变了图像的灰度特征，加强了图像对比度差值。区域2的梯度出现过平滑现象，与 图1 图1 （a）比较梯度明显平缓。 图1 图1 （e）使用中值滤波与均值滤波相结合的方法对图像进行滤波，区域1、区域2较 图1 图1 （a）基本失去了原有灰度特征，因采用了两种结合的滤波器，图像失真明显，相较于图 1（b） 1（b） ， 1（d） 1（d） ，图像增强的幅值并不大，但对比度有明显提升。 图1 图1 （f）为本文使用的自适应模糊中值滤波算法得到的灰度直方图，区域1和区域2与 图1 图1 相比未出现较大的梯度剧变情况，良好地保持了原图的灰度特征，较大程度地保留了原图细节。 2.2　八方向梯度幅值计算方法 2 Canny算法使用传统Sobel算子，仅考虑两方向的梯度信息，无法鲁棒地分析图像，易被噪声干扰。对于图像边缘方向特征考虑较少，常丢失部分边缘细节 ［ 16 16 ］ 。 为减少噪声对图像的影响，并增强轮廓线条检测，保留边缘细节，本文采用八方向的边缘检测算子对图像边缘进行检测，分别为0°，22.5°，45°，67.5°，90°，112.5°，135°和157.5° ［ 17 17 ］ 。 边缘检测模板如 式（12） 式（12） 所示： <math display="block" id="M90"><msub><mrow><mi>S</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><mfenced open="[" close="]" 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mathvariant="normal">0</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">1</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461623&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461620&type= 46.73600006 23.45266724 ， <math display="block" id="M96"><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">135</mn><mo>°</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">1</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn mathvariant="normal">1</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">2</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">2</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">1</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">1</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461629&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461626&type= 51.47733307 23.45266724 ， <math display="block" id="M97"><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">157.5</mn><mo>°</mo></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">2</mn></mtd><mtd><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">2</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn mathvariant="normal">1</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">4</mn></mtd><mtd><mn mathvariant="normal">1</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">2</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">4</mn></mtd><mtd><mo>-</mo><mn mathvariant="normal">2</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461636&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461632&type= 53.59400177 23.45266724 . 所以，当前像素点灰度值的合成梯度幅值 <math id="M98"><mi>S</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461641&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461638&type= 9.82133293 3.97933316 及合成梯度角度 <math id="M99"><mi>A</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461646&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461643&type= 10.32933331 3.97933316 分别为： <math display="block" id="M100"><mi>S</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461653&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461649&type= 13.63133430 3.97933316 <math display="block" id="M101"><mroot><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>x</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>y</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">45</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">135</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">22.5</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">67.5</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">112.5</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">157.5</mn><mo>°</mo></mrow></msub><msup><mrow><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461659&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461656&type= 149.94465637 5.41866684 ， <math display="block" id="M102"><mi>A</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>y</mi></mrow></msub><mfenced separators="|"><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></mfenced></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>x</mi></mrow></msub><mfenced separators="|"><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461665&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461662&type= 36.32199860 11.00666618 . 2.3　自适应迭代法阈值与Otsu 算法结合确定阈值 2 在传统Canny算子中，需通过实验检验设置合理的阈值，缺乏自适应性。高、低阈值的选取直接决定了检测边缘的多少，并对边缘的连续性有较大影响。为了尽可能保留图像各区域的边缘细节，有效抑制伪边缘，本文提出一种将迭代法与Otsu法相结合求阈值的计算方法。Otsu的基本思想是选取一个最优阈值，使得该阈值分割得到的两类间具有最佳的分离性。迭代法的基本思想是由图像的灰度性质选择一个阈值作为初始阈值，按规则更新阈值，最终达到最优效果为止。流程如下： （1）先计算迭代法的阈值，非极大值抑制后的图像，取灰度最大值 <math id="M103"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461669&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461667&type= 6.18066692 3.72533321 ，最小值 <math id="M104"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461673&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461670&type= 5.75733376 3.72533321 ，设定 <math id="M105"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461679&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461676&type= 6.18066692 3.72533321 和 <math id="M106"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461686&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461682&type= 5.75733376 3.72533321 的平均值为初始阈值，阈值 <math id="M107"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461783&type= 2.53999996 2.79399991 为： <math display="block" id="M108"><mi>T</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461696&type= 30.98800087 7.87400007 . （2）分别计算 <math id="M109"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461783&type= 2.53999996 2.79399991 分割出的两部分的平均灰度值，用 <math id="M110"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461713&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461709&type= 3.97933316 3.72533321 和 <math id="M111"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461720&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461717&type= 3.97933316 3.72533321 表示，灰度级数为 <math id="M112"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461725&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461722&type= 1.10066664 3.64066648 ， <math id="M113"><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461728&type= 2.62466669 3.72533321 表示灰度级为 <math id="M114"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461737&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461735&type= 1.10066664 2.79399991 时像素点个数。 <math display="block" id="M115"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></munderover></mstyle><mrow><mo> </mo></mrow><mi>i</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></munderover></mstyle><mrow><mo> </mo></mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461743&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461739&type= 19.72733307 18.54199982 ， <math display="block" id="M116"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mi>T</mi></mrow><mrow><mi>j</mi></mrow></munderover></mstyle><mrow><mo> </mo></mrow><mi>i</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mi>T</mi></mrow><mrow><mi>j</mi></mrow></munderover></mstyle><mrow><mo> </mo></mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461749&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461746&type= 19.30400085 19.38866615 . （3）得出新的区域均值之后，按照步骤（1）的流程，计算 <math id="M117"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461756&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461752&type= 3.97933316 3.72533321 ， <math id="M118"><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461761&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461759&type= 3.97933316 3.72533321 的平均值作为新阈值 <math id="M119"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461774&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461771&type= 6.09600019 3.72533321 。比较新旧阈值，若两值差值的绝对值小于特定值，则结束算法， <math id="M120"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461774&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461771&type= 6.09600019 3.72533321 为新阈值；若绝对值大于特定值，将 <math id="M121"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461780&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461777&type= 6.09600019 3.72533321 赋值给 <math id="M122"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461783&type= 2.53999996 2.79399991 ，重新运算步骤（2），直到满足条件，得到最优阈值 <math id="M123"><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461791&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461788&type= 4.82600021 4.06400013 ，结束迭代。 <math display="block" id="M124"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">w</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced separators="|"><mrow><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>G</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461797&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461794&type= 30.05666542 7.87400007 . （4）计算Otsu算法阈值 <math id="M125"><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461803&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461800&type= 4.82600021 4.06400013 ，与迭代法 <math id="M126"><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461809&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461806&type= 4.82600021 4.06400013 相比较。设图像的灰度等级范围为｛1，2，…， L ｝，在Ostu算法中，让 T 在 <math id="M127"><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>,</mo><mi>L</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461815&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461812&type= 16.17133331 3.55599999 内依次取值，使 <math id="M128"><mi>σ</mi><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461821&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461818&type= 6.94266701 3.97933316 最大的 <math id="M129"><mi>t</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461827&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461823&type= 1.10066664 2.79399991 值即为Ostu算法获取的最佳阈值： <math display="block" id="M130"><mtable><mtr><mtd><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub><mo>=</mo><munder><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mi>L</mi></mrow></munder><mfenced open="{" close="}" separators="|"><mrow><mi>σ</mi><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced></mrow></mfenced><mo>=</mo></mtd></mtr><mtr><mtd><munder><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>≤</mo><mi>t</mi><mo><</mo><mi>L</mi></mrow></munder><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced><msubsup><mrow><mi>u</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced><mo>+</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced><msubsup><mrow><mi>u</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mfenced separators="|"><mrow><mi>t</mi></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461830&type= 53.76333237 15.57866764 ， 式中： <math id="M131"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461837&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461835&type= 8.72066593 4.48733330 表示灰度值在 <math id="M132"><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>,</mo><mi>t</mi><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461848&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461846&type= 8.55133343 3.55599999 之间的概率， <math id="M133"><msub><mrow><mi>u</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461844&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461843&type= 8.12800026 4.48733330 表示在 <math id="M134"><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>,</mo><mi>t</mi><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461848&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461846&type= 8.55133343 3.55599999 的灰度均值与总灰度均值差， <math id="M135"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461852&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461850&type= 8.72066593 4.48733330 表示灰度值在 <math id="M136"><mo stretchy="false">[</mo><mi>t</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>L</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461855&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461854&type= 22.18266678 3.55599999 之间的概率， <math id="M137"><msub><mrow><mi>u</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461861&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461858&type= 8.12800026 4.48733330 表示在 <math id="M138"><mo stretchy="false">[</mo><mi>t</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>L</mi><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461866&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461864&type= 22.18266678 3.55599999 的灰度均值与总灰度均值差。 为尽可能获得更多图像边缘细节，本文算法取两阈值中的较小值，可得到图像更多细节，方便后续图像进行目标检测等进一步操作。 <math display="block" id="M139"><msub><mrow><mi>T</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461870&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461868&type= 29.80266571 5.67266655 . 以汽车铭牌图像为例，选取引言中文献［ 11 11 ］以及文献［ 13 13 ］进行比较，因其他文献在阈值选取部分大多使用Otsu阈值分割法，与文献［ 11 11 ］和［ 13 13 ］中使用的方法重复，在此不进行对比。阈值计算为全局计算。 边缘检测结果如 图2 图2 所示， 图2 图2 （b）区域1除边缘存在较多噪点外，整体轮廓清晰，偶尔有断连现象；区域2的关键信息与背景灰度差值较小，易受噪声影响，所以出现大量伪边缘。算法缺乏对复杂背景情况下疑似噪声点区域的有效处理能力。 图2 图2 （c）区域1出现连接断裂现象，因为文献［ 13 13 ］获取到的阈值较高，导致铭牌的边缘细节丢失；区域2虽对比 图2 图2 （b）区域2的检测效果有所提升，但未有效抑制伪边缘。文献［ 13 13 ］算法对图像背景中疑似噪声点区域具有较好的处理效果，但缺乏保留铭牌各区域边缘细节的能力。 图2 图2 （d）区域1的边缘细节保留完整，未出现边缘断连现象，区域2部分对背景中疑似噪点区域具有较好的处理效果，边缘检测效果好于前两种算法。 2.4　边缘检测过程 2 本文算法的具体检测流程如下： Step1.建立大小为 <math id="M140"><mi>n</mi><mo>×</mo><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461881&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461880&type= 8.63599968 2.79399991 （初始值为3）的滤波窗口； Step2.计算均值 <math id="M141"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461886&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461883&type= 13.20800018 4.82600021 及最小值 <math id="M142"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461890&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461888&type= 13.37733269 4.82600021 ，代入 式（4） 式（4） 进行判断，将疑似噪声点加入 <math id="M143"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461894&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461892&type= 3.64066648 3.80999994 集合； Step3.若 <math id="M144"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">g</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461898&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461896&type= 13.20800018 4.82600021 ， <math id="M145"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461901&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461900&type= 13.37733269 4.82600021 均小于10时，保持灰度原值输出并转至Step7；否则转至Step4； Step4.若 <math id="M146"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mo>≠</mo><mi mathvariant="normal">∅</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461905&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461903&type= 12.19200039 4.57200003 ，计算 <math id="M147"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">m</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461909&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461907&type= 4.57200003 3.80999994 转至Step5；否则令 <math id="M148"><mi>n</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461912&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461911&type= 15.32466698 2.96333337 并转至Step6； Step5.计算模糊加权函数 <math id="M149"><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461914&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461913&type= 10.15999985 3.97933316 ，然后利用 式（10） 式（10） 计算出滤波后的灰度值并转至Step7； Step6.若 <math id="M150"><mi>n</mi><mo>></mo><msub><mrow><mi>n</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461916&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461915&type= 12.19200039 3.72533321 ，则利用 式（11） 式（11） 计算 <math id="M151"><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461918&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24461917&type= 2.20133328 2.79399991 集合中的均值作为输出，转至Step7；否则转至Step2； Step7.判断是否所有像素点完成滤波，若均已完成则转至Step8； 否则移动窗口，转至Step2； Step8.使用八方向的边缘检测算子对图像边缘进行检测，完成非极大值抑制，之后转至Step9； Step9.计算Otus阈值及迭代法阈值，选取较小值作为分割阈值。 3 实验及结果分析 1 3.1　算法有效性实验 2 为验证本文算法的有效性，将本文算法与传统Canny算法、文献［ 11 11 ］、文献［ 12 12 ］、文献［ 13 13 ］算法比较。在图像中加入密度为10%，50%的椒盐噪声，实验结果如 图3 图3 ~ 图4 图4 所示。 由图可知，使用传统Canny算法边缘检测的图像存在大量的伪边缘。当椒盐噪声密度较大时，传统Canny算法无法有效检测边缘。文献［ 11 11 ］算法提取的边缘图像相对于Canny算法的噪声明显减少，因文献［ 11 11 ］对滤波窗口排序，改变了图像本身的梯度结构及灰度排序，使得图像产生较多伪边缘，同时因阈值处理方式的缺陷产生边缘断裂现象。 图3 图3 ~ 图4 图4 为文献［ 12 12 ］算法的处理结果，该算法采用混合滤波器。相比于前两种算法，边缘的连接程度有所提升。该算法舍弃图像的最大最小像素值，虽在一定程度上消除了椒盐噪声，但改变图像本身的灰度特性，滤波后图像边缘加粗，导致图像真实边缘缺失。文献［ 13 13 ］相较于Canny算法的去噪效果有所提升，但噪声点仍大量存在，干扰图像的边缘显示，未将图像边缘进行独立分割，该算法对密度较高的椒盐噪声的去噪效果不佳。本文算法相较于其他算法，视觉效果更好，不仅去除了噪声对图像边缘的影响，且图像边缘细节较好，未出现断连现象，与背景有明确的区分。该算法在密度较高的椒盐噪声下能准确地检测出真实边缘，同时伪边缘相较于其余4种算法更少，图像边缘更为清晰。 3.2　算法客观指标评价实验 2 为避免实验中出现单一指标的误差，进一步证明本文提出的滤波方法的有效性，统计Canny算法所用滤波、文献［ 11 11 ］、文献［ 12 12 ］、文献［ 13 13 ］算法及本文算法的结构相似度（Structural Similarity，SSIM）以及峰值信噪比（Peak Signal to Noise Ratio，PSNR） ［ 18 18 ］ ，作为分析对比的依据。本文使用含椒盐噪声的512×512 Lena、631×364的铭牌、224×223的House和512×512的Cameraman等自然图像进行测试。理想情况下，滤波未改变图像灰度梯度及灰度值的情况下，SSIM等于1；当图像变化较大时，SSIM趋近于0。从 表1 表1 和 表2 表2 可以看出，本文的SSIM和PSNR数值均好于其他算法，去噪效果最好，图像中的噪声明显被抑制，细节保留较为完整，且图像失真较小。 图　像 噪　声 Canny 文献［ 11 11 ］ 文献［ 12 12 ］ 文献［ 13 13 ］ 本文算法 2 Lena 10% 25.600 479 31.622 082 32.661 475 25.642 697 36.030 233 50% 16.948 481 29.608 746 31.455 466 20.939 416 32.397 528 2 铭牌 10% 23.545 948 23.739 415 25.331 403 22.669 117 26.669 650 50% 17.099 906 23.668 014 24.562 227 21.588 198 24.693 479 2 House 10% 23.411 272 28.979 864 33.464 278 24.103 210 35.038 253 50% 16.867 139 22.779 478 26.984 742 19.073 687 30.557 406 2 Cameraman 10% 22.021 617 24.089 169 27.452 412 23.386 599 30.779 394 50% 15.580 691 22.132 384 23.215 094 18.181 333 24.912 216 dB 图　像 噪　声 Canny 文献［ 11 11 ］ 文献［ 12 12 ］ 文献［ 13 13 ］ 本文算法 2 Lena 10% 0.548 623 0.894 513 0.935 061 0.743 021 0.949 691 50% 0.163 644 0.868 753 0.910 783 0.467 398 0.926 842 2 铭牌 10% 0.594 046 0.767 398 0.771 649 0.713 397 0.895 915 50% 0.229 655 0.744 665 0.756 534 0.476 394 0.834 404 2 House 10% 0.436 042 0.914 396 0.920 313 0.883 793 0.934 269 50% 0.184 831 0.906 373 0.808 870 0.500 022 0.909 811 2 Cameraman 10% 0.521 596 0.868 044 0.882 839 0.825 241 0.963 468 50% 0.184 732 0.819 679 0.843 900 0.510 516 0.878 805 为更加直观测试本文算法的执行效果，同时测试本文改进算法在不同噪声下的通用性，采用文献［ 19 19 ］中提出的边缘检测量化方法进行综合评价。该算法为基于连通成分的边缘评价方法， B ， C 与 A 的比值表示边缘连接的完整性，比值越小边缘连接的完整度越高。 统计椒盐噪声（10%）、高斯白色噪声（var=0.1）、泊松噪声（由输入图像决定）、斑点噪声（var=0.1）下传统Canny算法、文献［ 11 11 ］、文献［ 12 12 ］、文献［ 13 13 ］算法和本文算法的边缘评价数值。本文对8幅真实图像进行实验测试，结果如 图5 图5 所示。在不同噪声环境下文献［ 11 11 ］、［ 12 12 ］的边缘完整度近似，但文献［ 12 12 ］的边缘完整度不如文献［ 11 11 ］。在对House图进行实验时，因选取的House图的背景较为单调，文献［ 12 12 ］的边缘检测评价数值更好，检测结果与前文分析结果一致。在不同噪声下文献［ 11 11 ］的效果最差，其主要原因为对噪声的适应性较差，未能良好地去除噪声。本文算法对含高斯白色噪声的图像边缘检测评价表现略差，因高斯白色噪声为线性噪声，非线性滤波器不能较好地抑制。本算法可对孤立噪声点进行检测，所以在含椒盐噪声或斑点噪声环境具有良好的边缘检测效果，对不同噪声具有普适性。 1,2;3,4;5,6;7,8; 本文算法的边缘检测综合评价高于其他文献。与传统Canny算法相比，本文算法的 C / A 和 B / A 值均接近传统Canny算法，进一步证明本算法保留了传统Canny算法的优良性能。本算法能对去噪后的图像保留边缘细节，同时对图像的边缘检测完整度有较好的提升，整体算法的边缘完整度较高。 为了充分证明本文算法对不同噪声密度图像边缘检测性能的优越性，客观地评估算法性能，选取BSDS500 ［ 20 20 ］ 作为数据集。该数据集包含500幅不同场景的实体图像，并含有对应的GT图使用F1值（F-measure）对算法进行评估，F1值越高说明越接近真实GT图。计算各类算法在含10%~50%椒盐噪声和不含噪声时的F1值，结果如 表3 表3 所示。无论是含噪图像还是不含噪声图像，本文算法的F1值表现均优于其他算法。在含噪10%的条件下，本文算法的F1值分别高于Canny算法、文献［ 11 11 ］、文献［ 12 12 ］、文献［ 13 13 ］算法34.6%，11.7%，6.9%，8.6%。含噪条件从10%变为50%后，Canny算法、文献［ 11 11 ］、文献［ 12 12 ］、文献［ 13 13 ］算法及本文算法的F1均值分别下降了0.081 719，0.062 606，0.057 119，0.160 906，0.054 879。综上所述，本文算法的F1值评价指标表现最佳，表明算法对噪声具有良好的鲁棒性。 噪　声 Canny算法 文献［ 11 11 ］ 文献［ 12 12 ］ 文献［ 13 13 ］ 本文算法 无噪声 0.841 566 0.797 809 0.813 371 0.817 607 0.869 438 含10%噪声 0.614 541 0.740 869 0.773 656 0.761 558 0.827 385 含20%噪声 0.595 752 0.739 941 0.749 552 0.692 009 0.812 981 含30%噪声 0.560 035 0.694 137 0.737 830 0.665 924 0.803 712 含40%噪声 0.541 386 0.680 557 0.721 507 0.621 548 0.798 007 含50%噪声 0.532 822 0.678 263 0.716 537 0.600 652 0.772 506 4 结　论 1 针对传统Canny算子无法有效抑制椒盐噪声且无法保留边缘细节的问题，本文提出了一种噪声点检测方法，将高斯滤波替换为自适应模糊中值滤波，采用八方向梯度计算幅值，尽可能地考虑边缘方向特征以及通过自适应阈值完成边缘的连接。以自然图像为例，去噪后图像的PSNR相较于其他算法提升了0.13~10.97 dB，与原图相比SSIM达0.949，对各类噪声边缘评价指标及F1值表现均优于其他算法。实验结果表明，本文改进的Canny算法能去除椒盐噪声，抑制伪边缘的产生，有效保留图像的边缘细节，为图像后续的目标区域识别等操作提供了准确的轮廓边缘信息。 参考文献 孙海英 . 图像高斯噪声及椒盐噪声去噪算法研究 ［D］. 上海 ： 复旦大学 ， 2012 . 图像高斯噪声及椒盐噪声去噪算法研究 SUN H Y . 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