{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"Lab的多投影颜色校正及亮度融合技术"}]},{"lang":"en","data":[{"name":"text","data":"Multi-projection color correction and brightness fusion technology based on Lab"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"侯","givenname":"培国","namestyle":"eastern","prefix":""},{"lang":"en","surname":"HOU","givenname":"Pei-guo","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":["corresp","first-author"],"corresp":[{"rid":"cor1","lang":"en","text":"E-mail： pghou@@ysu.edu.cn","data":[{"name":"text","data":"E-mail： pghou@@ysu.edu.cn"}]}],"bio":[{"lang":"zh","text":["侯培国（1968-），男，山东临沂人，教授，博士生导师，1990年于东北重型机械学院获得学士学位，1993年于燕山大学获得工学硕士学位，2003年于燕山大学获得工学博士学位，现为燕山大学工程训练中心党委书记、工程训练中心主任，主要从事光电检测、智能传感器等方面的研究。E-mail： pghou@ysu.edu.cn"],"graphic":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529079&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529081&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529080&type=","width":"22.01332855","height":"32.00400543","fontsize":""}],"data":[[{"name":"text","data":"侯培国"},{"name":"text","data":"（1968-），男，山东临沂人，教授，博士生导师，1990年于东北重型机械学院获得学士学位，1993年于燕山大学获得工学硕士学位，2003年于燕山大学获得工学博士学位，现为燕山大学工程训练中心党委书记、工程训练中心主任，主要从事光电检测、智能传感器等方面的研究。E-mail： "},{"name":"text","data":"pghou@ysu.edu.cn"}]]}],"email":"pghou@ysu.edu.cn","deceased":false},{"name":[{"lang":"zh","surname":"张","givenname":"铮","namestyle":"eastern","prefix":""},{"lang":"en","surname":"ZHANG","givenname":"Zheng","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":[],"bio":[{"lang":"zh","text":["张　铮（1997-），女，河北承德人，硕士研究生，2019年于燕山大学电气工程学院获得学士学位，主要从事图像处理与计算机视觉的研究。E-mail： 735089139@qq.com"],"graphic":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529082&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529084&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529083&type=","width":"22.01332855","height":"32.00401306","fontsize":""}],"data":[[{"name":"text","data":"张　铮"},{"name":"text","data":"（1997-），女，河北承德人，硕士研究生，2019年于燕山大学电气工程学院获得学士学位，主要从事图像处理与计算机视觉的研究。E-mail： "},{"name":"text","data":"735089139@qq.com"}]]}],"email":"735089139@qq.com","deceased":false},{"name":[{"lang":"zh","surname":"宋","givenname":"涛","namestyle":"eastern","prefix":""},{"lang":"en","surname":"SONG","givenname":"Tao","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"},{"rid":"aff3","text":"3"}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"祁","givenname":"继辉","namestyle":"eastern","prefix":""},{"lang":"en","surname":"QI","givenname":"Ji-hui","namestyle":"eastern","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":"1"},{"rid":"aff2","text":"2"}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"1","text":"燕山大学 电气工程学院，河北 秦皇岛 066004","data":[{"name":"text","data":"燕山大学 电气工程学院，河北 秦皇岛 066004"}]},{"lang":"en","label":"1","text":"School of electrical engineering， Yanshan university， Qinhuangdao 066004， China","data":[{"name":"text","data":"School of electrical engineering， Yanshan university， Qinhuangdao 066004， China"}]}]},{"id":"aff2","intro":[{"lang":"zh","label":"2","text":"河北省数字影像装备与数字显示技术重点实验室，河北 秦皇岛 066004","data":[{"name":"text","data":"河北省数字影像装备与数字显示技术重点实验室，河北 秦皇岛 066004"}]},{"lang":"en","label":"2","text":"Key Laboratory of digital imaging equipment and digital display technology in Hebei Province， Qinhuangdao 066004， China","data":[{"name":"text","data":"Key Laboratory of digital imaging equipment and digital display technology in Hebei Province， Qinhuangdao 066004， China"}]}]},{"id":"aff3","intro":[{"lang":"zh","label":"3","text":"秦皇岛视听机械研究所，河北 秦皇岛 066004","data":[{"name":"text","data":"秦皇岛视听机械研究所，河北 秦皇岛 066004"}]},{"lang":"en","label":"3","text":"Qinhuangdao Audio-visual Machinery Research Institute， Qinhuangdao 066004， China","data":[{"name":"text","data":"Qinhuangdao Audio-visual Machinery Research Institute， Qinhuangdao 066004， China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"传统的多投影颜色校正和亮度融合在RGB颜色空间下进行，存在校正过程中亮度和色度相互干扰的问题。针对上述问题，提出一种基于Lab颜色空间的颜色校正和亮度融合方法。将亮度与色度单独提取出来，用B样条曲线模型建立起各投影仪原图像与投影显示画面的亮度、色度转换关系，以消除各投影仪投影显示画面之间的颜色差异，并采用融合B样条曲线的伽玛校正对画面重叠区域的亮度进行调节。实验结果表明，相对于RGB颜色空间，在Lab空间进行颜色校正使两个投影显示画面的颜色强度差异在Lab三通道分别减少了4.14，2.41，2.44；相对于RGB颜色空间的伽马校正，在Lab空间将伽马校正与B样条曲线融合进行亮度调节使投影显示画面重叠区域与非重叠区域的颜色强度差异在Lab三通道分别减少了6.12，4.64，3.47。基于Lab的多投影颜色校正及亮度融合技术可对投影显示画面亮度与色度进行更准确的校正，并且给予不同颜色强度对应的伽马系数。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"The traditional multi-projection color correction and brightness fusion are performed in the RGB color space； the brightness and chroma interfere with each other in the correction process， which is a major concern. To solve this problem， a color correction and brightness fusion method based on the Lab color space is proposed. The brightness and chroma are extracted separately， and the brightness and chroma conversion relationship between the original images of each projector and the projected display screen is established using the B-spline curve model to eliminate the color difference between the display screen of each projector， and the brightness of the overlapping area of the screen is adjusted using the gamma correction fused with the B-spline curve. The experimental results show that， compared with the RGB color space， color correction in the Lab color space reduces the difference in color intensity of the two projection display images by 4.14， 2.41， and 2.44 in Lab three channels. Compared with gamma correction in the RGB color space， gamma correction and B-spline curve are fused to adjust brightness in Lab space， which reduces the difference in color intensity between the overlapping and non-overlapping areas by 6.12， 4.64， and 3.47 in Lab three channels. The multi-projection color correction and brightness fusion technology based on Lab can correct the brightness and chroma of the projected display image more accurately， and obtain the gamma coefficient corresponding to different color intensities."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"Lab颜色空间"}],[{"name":"text","data":"颜色校正"}],[{"name":"text","data":"亮度融合"}],[{"name":"text","data":"伽马校正"}],[{"name":"text","data":"B样条曲线"}]]},{"lang":"en","data":[[{"name":"text","data":"Lab color space"}],[{"name":"text","data":"color correction"}],[{"name":"text","data":"brightness fusion"}],[{"name":"text","data":"gamma correction"}],[{"name":"text","data":"B spline curve"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"1 引　言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"随着计算机技术和虚拟现实技术的快速发展，多投影系统作为虚拟现实和实体结合的代表，在性能和显示技术上也需要不断提高，人们对多投影显示画面营造的沉浸感、真实度也有了越来越高的要求。不同型号或者同种型号设置内部参数不同的投影仪以及光照强度和投影幕颜色分布不均匀等外界条件必然会导致同一张图像对应不同投影仪显示画面颜色不一致的问题"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"1","type":"bibr","rid":"R1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"近年来，在多投影颜色校正方面的研究工作有许多。Wang等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"2","type":"bibr","rid":"R2","data":[{"name":"text","data":"2"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"综合考虑了投影机的特性、显示表面的光学特性以及屏幕与投影机之间的相对距离，使用参数模型将投影图像映射到公共可实现响应空间，以获得颜色一致的输出。Christian等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"3","type":"bibr","rid":"R3","data":[{"name":"text","data":"3"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"处理交互反射、投影仪黑度以及场景中的环境光等各种物理杂散光的效果，通过增加一个全局优化步骤来增强投影效果。但是以上两种方法在外界光照强度变化的条件下无法固定参数来保证颜色校正结果的稳定性。Petar等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"4","type":"bibr","rid":"R4","data":[{"name":"text","data":"4"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"把RGB颜色空间转换至CIEXYZ与Lab颜色空间进行建模从而确定参数，但并没有对色度与亮度的不同阶段进行分段校正来保证颜色校正在算法上的灵活性。针对重叠区域亮度过亮的问题，Chen等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"5","type":"bibr","rid":"R5","data":[{"name":"text","data":"5"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"提出了改进的边缘融合算法，以消除光照区域融合的边缘，实现无缝连接，最后加入Gamma算子进一步校正像素亮度，通过信噪比降低了投影仪色差的输出，但不能保证每个阶段的颜色强度具备相同的校正参数，从而引起亮度调节的局限性。Xue等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"6","type":"bibr","rid":"R6","data":[{"name":"text","data":"6"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"在相邻通道之间进行特征图像投影，根据采集到的颜色信息计算颜色模板，应用于一个通道的视频帧中，从而消除由于不同投影灯问题而引起的色差。最后，使用平滑亮度衰减函数来衰减相邻通道之间重叠区域中出现的高光。Marcel等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"7","type":"bibr","rid":"R7","data":[{"name":"text","data":"7"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"通过利用立体图像对的颜色相似性，可以提高基于LUT的颜色校正方法的缓存效率。以上两种方法在实施上都有太多的不确定因素，受环境光照影响过大。Shunichi等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"8","type":"bibr","rid":"R8","data":[{"name":"text","data":"8"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"通过RGB和XYZ颜色空间的双向转换，校正投影仪颜色的不均匀性。刘剑超等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"9","type":"bibr","rid":"R9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"也通过RGB至CIE-XYZ的空间转换来进行颜色校正，但参数之间存在着彼此制约，给颜色校正带来很大的局限性。吴金吉等人"},{"name":"sup","data":[{"name":"text","data":"［"},{"name":"xref","data":{"text":"10","type":"bibr","rid":"R10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"］"}]},{"name":"text","data":"提出一种基于亮度均衡的全局阈值融合算法来保证投影显示画面整体的亮度一致性，但并没有对色度方面进行过多研究。"}]},{"name":"p","data":[{"name":"text","data":"针对多投影仪阵列所造成的投影显示画面之间颜色不一致以及投影重叠区域亮度过大的问题，本文提出了基于Lab的颜色校正和亮度融合方法。通过三次B样条曲线模型建立起原图像和投影显示图像的L、a、b三个通道的转换关系，完成亮度、色度的单独校正。采用衰减函数与改进的伽马校正对重叠区域的图像的L通道进行调节，优化亮度融合结果。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2 基于Lab空间的颜色校正"}],"level":"1","id":"s2"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2.1　Lab颜色空间"}],"level":"2","id":"s2a"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1　Lab颜色空间概述"}],"level":"3","id":"s2a1"}},{"name":"p","data":[{"name":"text","data":"Lab颜色空间是一种设备无关的颜色模型，也是一种基于生理特征的颜色模型，即一种用数字化的方法来描述人的视觉感应的颜色空间。在Lab颜色空间中，每个像素的颜色用一个亮度分量（L）和两个色度分量（"},{"name":"italic","data":[{"name":"text","data":"a"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"b"}]},{"name":"text","data":"）表示，L分量取值范围是［0，100］，"},{"name":"italic","data":[{"name":"text","data":"a"}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"b"}]},{"name":"text","data":"分量取值范围是［-128，127］。其中，"},{"name":"italic","data":[{"name":"text","data":"a"}]},{"name":"text","data":"包括的颜色是从绿色到灰色再到红色；"},{"name":"italic","data":[{"name":"text","data":"b"}]},{"name":"text","data":"是从蓝色到灰色再到黄色。Lab色彩空间不仅有效地将图像的亮度度信息和色度信息分离，而且基本消除了各颜色分量之间的强相关性，可以分别对图像的三个通道进行独立的处理，而不需要修改另外两个通道的信息，从而不会影响原图像的自然效果。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"2　Lab与RGB的颜色空间转换关系"}],"level":"3","id":"s2a2"}},{"name":"p","data":[{"name":"text","data":"Lab颜色空间比RGB颜色空间色域宽，故Lab颜色空间可以表示RGB颜色空间能够描述的全部色彩信息。RGB颜色空间到Lab颜色空间转换不能直接进行，要借助XYZ颜色空间，把RGB颜色空间转换到XYZ颜色空间，再把XYZ颜色空间转换到Lab颜色空间。"}]},{"name":"p","data":[{"name":"text","data":"RGB颜色空间转换到XYZ颜色空间的转换关系式如"},{"name":"xref","data":{"text":"式（1）","type":"disp-formula","rid":"DF1","data":[{"name":"text","data":"式（1）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（1）"}],"data":[{"name":"math","data":{"math":"[X,Y,Z]T=[T]⋅[R,G,B]T","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529086&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529085&type=","width":"46.99000168","height":"3.80999994","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF1"}},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[T]","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529088&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529087&type=","width":"6.34999990","height":"3.55599999","fontsize":""}}}]},{"name":"text","data":"是一个3×3的矩阵："}]},{"name":"dispformula","data":{"label":[],"data":[{"name":"math","data":{"math":"[T]=0.412 4530.357 5800.180 4230.212 6710.715 1600.072 1690.019 3340.119 1930.950 227","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529090&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529089&type=","width":"65.61666107","height":"13.54666710","fontsize":""}}},{"name":"text","data":"。"}],"id":"DF2"}},{"name":"p","data":[{"name":"text","data":"XYZ颜色空间转换到Lab颜色空间的转换关系如"},{"name":"xref","data":{"text":"式（2）","type":"disp-formula","rid":"DF3","data":[{"name":"text","data":"式（2）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（2）"}],"data":[{"name":"math","data":{"math":"L=116*fY/Yn-16a=500*fX/Xn-fY/Ynb=200*fY/Yn-fZ/Zn","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529092&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529091&type=","width":"51.64666748","height":"24.04533195","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF3"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Xn","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529094&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529093&type=","width":"3.80999994","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Yn","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529096&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529095&type=","width":"4.06400013","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Zn","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529098&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529097&type=","width":"3.47133350","height":"3.72533321","fo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456，1.0，1.088 754；函数"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"f","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529100&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529099&type=","width":"1.10066664","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"是一个类似于Gamma函数的校正函数，当"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"t>0.008 856","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529102&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529101&type=","width":"20.82799911","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"时，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"ft=t13","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529104&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529103&type=","width":"13.88533401","height":"4.40266657","fontsize":""}}}]},{"name":"text","data":"；当"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"t≤0.008 856","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529106&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529105&type=","width":"20.82799911","height":"3.30200005","fontsize":""}}}]},{"name":"text","data":"时，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"ft=132962t+429","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529108&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529107&type=","width":"35.30599976","height":"9.48266602","fontsize":""}}}]},{"name":"text","data":"。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2.2　颜色校正响应函数"}],"level":"2","id":"s2b"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1　三次B样条曲线模型"}],"level":"3","id":"s2b1"}},{"name":"p","data":[{"name":"text","data":"Ｂ样条曲线具有连续性、光滑性、局部分段性和几何不变性等优良性质。B样条曲线是分段曲线，每一段参数取值范围都是［0，1］，故可通过修改某一控制点改变该控制点相邻的曲线形状，而不影响远处的曲线形状，从而可实现曲线的局部修改。而且可以在B样条曲线中插入更多节点来获得更多控制点，从而使被影响的区域被限制在很窄的区域内，实现对曲线形状更加精细的调节。仿射不变性适用于B样条曲线。如果对B-样条曲线应用一个仿射或几何变换，得到的结果可以从它的控制点的仿射像构建得到。因此我们可以对控制点进行变换，建立变换前后的转换关系。"}]},{"name":"p","data":[{"name":"text","data":"三次的B样条曲线模型可以分段表示，每一段可通过四个控制点改变曲线形状，三次m+1段B样条曲线模型如"},{"name":"xref","data":{"text":"式（3）","type":"disp-formula","rid":"DF4","data":[{"name":"text","data":"式（3）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（3）"}],"data":[{"name":"math","data":{"math":"Pi,3t=∑k=03Pi+k⋅Fk,3t","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529110&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529109&type=","width":"39.45466614","height":"8.38199997","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF4"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PI","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529112&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529111&type=","width":"3.30200005","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"，"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"=0，1，2，…，"},{"name":"italic","data":[{"name":"text","data":"m"}]},{"name":"text","data":"；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Pi+k","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529114&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529113&type=","width":"6.60400009","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为第"},{"name":"italic","data":[{"name":"text","data":"i"}]},{"name":"text","data":"段B样条曲线的控制点；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PC","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529116&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529115&type=","width":"3.97933316","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"表示B样条基函数，如"},{"name":"xref","data":{"text":"式（4）","type":"disp-formula","rid":"DF5","data":[{"name":"text","data":"式（4）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（4）"}],"data":[{"name":"math","data":{"math":"Fk,3(t)=16∑j=03-k(-1)j·C4j·(t+3-k-j)3","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529118&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529117&type=","width":"64.51599884","height":"8.89000034","fontsize":""}}},{"name":"text","data":"."}],"id":"DF5"}},{"name":"p","data":[{"name":"text","data":"连接所有节点"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Pi,3t","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529120&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529119&type=","width":"9.56733322","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"，所组成的整条曲线就是三次B样条曲线。"}]},{"name":"p","data":[{"name":"text","data":"文献［"},{"name":"xref","data":{"text":"11","type":"bibr","rid":"R11","data":[{"name":"text","data":"11"}]}},{"name":"text","data":"］采用了三次B样条曲线对RGB空间构建颜色传递函数的数学模型，R，G，B三个通道的颜色强度范围均为［0，255］，有效解决了投影显示画面彼此的色差，以三次B样条曲线对边缘融合函数进行仿真，残差不超过5%。但是，由于投影仪自身性质，RGB三通道的颜色强度是相互干扰的，三次B样条曲线是对R，G，B三个颜色通道进行分别校正，不能解决颜色通道之间相互影响的问题。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2.2.2　Lab空间的颜色响应函数"}],"level":"3","id":"s2b2"}},{"name":"p","data":[{"name":"text","data":"本文采用多通道投影系统，各投影仪的显示画面之间存在颜色差异。为得到颜色一致、真实感强的拼接画面，需要对每个投影进行颜色校正。投影仪的颜色校正是通过求取计算机存储的原图像和对应投影仪显示图像的颜色强度映射关系并对原图像进行颜色预扭曲来完成的。"}]},{"name":"p","data":[{"name":"text","data":"基于Lab颜色空间的投影图像颜色校正，需要分别求取各通道颜色响应函数，用OpenCV分别生成L，a，b三个通道的图像颜色样本集合。L，a，b三个通道在OpenCV上的取值范围不同于理论值，在OpenCV上的取值范围均为［0，255］。三个通道样本集生成过程相同，以L通道为例，用OpenCV生成L通道颜色强度分别为0，15，30，45，…，210，225，240，255，a，b通道颜色强度值均为128的18张图像，即为L通道颜色强度样品集，记为"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PIt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529127&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529126&type=","width":"7.70466709","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"，a，b通道样本集合的生成方式与L通道样本集的生成方式相同。分别用各投影仪将L，a，b三个通道各自的18张图像单独投影至屏幕，并用相机依次拍摄投影显示画面，计算照片内投影显示画面的颜色强度平均值，以此作为实际颜色强度值，该集合记为"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PCt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529129&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529128&type=","width":"8.38199997","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"。"}]},{"name":"p","data":[{"name":"text","data":"各通道投影颜色响应函数是非线性的，采用三次B样条曲线模型来表示，通过原图像样本的颜色强度值集合"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PIt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529127&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529126&type=","width":"7.70466709","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"和投影显示画面样本的实际颜色强度值集合"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PCt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529129&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529128&type=","width":"8.38199997","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"建立对应转换关系，可求解出三次B样条曲线响应函数，原图像与摄像空间内投影显示画面的颜色强度转换关系如"},{"name":"xref","data":{"text":"式（5）","type":"disp-formula","rid":"DF6","data":[{"name":"text","data":"式（5）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（5）"}],"data":[{"name":"math","data":{"math":"PIt=BPCt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529131&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529130&type=","width":"27.17799950","height":"4.91066647","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF6"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PI","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529133&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529132&type=","width":"3.30200005","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PIt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529136&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529135&type=","width":"7.70466709","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"为原图像该通道颜色强度值；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"PCt","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529138&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529137&type=","width":"8.38199997","height":"4.06400013","fontsize":""}}}]},{"name":"text","data":"为摄像空间内投影显示画面该通道的实际强度值；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"B","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529141&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529140&type=","width":"2.53999996","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为三次B样条曲线的颜色响应函数。"}]},{"name":"p","data":[{"name":"text","data":"用以上同样方法分别求取各投影仪的L，a，b三个通道的颜色响应函数，对计算机存储的原图像进行颜色预扭曲，完成颜色校正。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"2"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"3　原图像的颜色预扭曲"}],"level":"3","id":"s2b3"}},{"name":"p","data":[{"name":"text","data":"对于多通道投影系统，不同投影仪对应的显示画面在亮度和色度上必然存在不同的范围。因此，比较多个投影仪在亮度及色度的最小显示颜色强度值，选出最大值"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"L","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529145&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529143&type=","width":"2.45533323","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"；再比较多个投影仪在亮度及色度的最大显示颜色强度值，选出最小值"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"H","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529149&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529147&type=","width":"2.96333337","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"。设"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[L,H]","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529153&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529151&type=","width":"11.26066685","height":"3.55599999","fontsize":""}}}]},{"name":"text","data":"为每个投影仪对应显示画面颜色强度的目标范围，即公共颜色区域。对于像素点颜色强度范围为［0，255］的原图像，对应显示画面的颜色强度范围相对较小，则对于原图像的输入颜色强度"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"K","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529158&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529154&type=","width":"2.79399991","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"，其显示画面的目标颜色强度"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Y(K)","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529163&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529161&type=","width":"9.90600014","height":"3.55599999","fontsize":""}}}]},{"name":"text","data":"的表达式如"},{"name":"xref","data":{"text":"式（6）","type":"disp-formula","rid":"DF7","data":[{"name":"text","data":"式（6）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（6）"}],"data":[{"name":"math","data":{"math":"Y(K)=H-L255×K+L","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529169&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529166&type=","width":"41.57133484","height":"7.53533268","fontsize":""}}},{"name":"text","data":"."}],"id":"DF7"}},{"name":"p","data":[{"name":"text","data":"原图像共有M×N个像素，RGB颜色强度集合如"},{"name":"xref","data":{"text":"式（7）","type":"disp-formula","rid":"DF8","data":[{"name":"text","data":"式（7）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（7）"}],"data":[{"name":"math","data":{"math":"I0=∑m=0M-1∑n=0N-1[Rm,n,Gm,n,Bm,n]T","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529174&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529172&type=","width":"46.82066727","height":"8.46666718","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF8"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"I0","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529180&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529177&type=","width":"2.37066650","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为原图像所有像素点的RGB颜色强度集合；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[Rm,n,Gm,n,Bm,n]","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529186&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529183&type=","width":"25.82333374","height":"4.48733330","fontsize":""}}}]},{"name":"text","data":"为原图像第（"},{"name":"italic","data":[{"name":"text","data":"m"}]},{"name":"text","data":"+1）×（"},{"name":"italic","data":[{"name":"text","data":"n"}]},{"name":"text","data":"+1）个像素点的RGB颜色强度。"}]},{"name":"p","data":[{"name":"text","data":"原图像经过颜色预扭曲后，RGB颜色强度集合如"},{"name":"xref","data":{"text":"式（8）","type":"disp-formula","rid":"DF9","data":[{"name":"text","data":"式（8）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（8）"}],"data":[{"name":"math","data":{"math":"I=∑m=0M-1∑n=0N-1([T]-1⋅F-1(B(Y(F([T]⋅[Rm,n,Gm,n,Bm,n]T)))))","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529192&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529189&type=","width":"98.04399872","height":"8.46666718","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF9"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"I","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529198&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529195&type=","width":"1.26999998","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为颜色预扭曲后所有像素点的RGB颜色强度集合；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[T]","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529206&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529201&type=","width":"6.34999990","height":"3.55599999","fontsize":""}}}]},{"name":"text","data":"为RGB到XYZ颜色空间的转换矩阵；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"F","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529211&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529208&type=","width":"2.53999996","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为XYZ到Lab颜色空间的转换函数；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"Y","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529216&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529213&type=","width":"2.87866688","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为输入颜色强度对应的目标颜色强度；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"B","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529221&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529218&type=","width":"2.53999996","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为三次B样条曲线的颜色响应函数。"}]}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"3 基于Lab空间的边缘亮度融合"}],"level":"1","id":"s3"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"3.1　衰减函数与伽马校正"}],"level":"2","id":"s3a"}},{"name":"p","data":[{"name":"text","data":"多个投影仪共同投影，会产生投影重叠区域，重叠区域亮度会高于非重叠区域，形成亮度带，所以需要对重叠区域进行亮度调节，保证重叠区域与非重叠区域亮度一致性以及平滑过渡。"}]},{"name":"p","data":[{"name":"text","data":"为了消除亮度带，使画面重叠区域亮度平滑过渡，所以采用衰减函数和伽马校正对重叠区域进行亮度调节。选取的衰减函数如"},{"name":"xref","data":{"text":"式（9）","type":"disp-formula","rid":"DF10","data":[{"name":"text","data":"式（9）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（9）"}],"data":[{"name":"math","data":{"math":"d(x)=a(2x)p0≤x≤0.51-(1-a)[2(1-x)]0.5≤x≤1","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529227&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529224&type=","width":"72.22066498","height":"10.24466610","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF10"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"x","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529233&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529230&type=","width":"2.03200006","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为重叠区域像素归一化后的横坐标，如"},{"name":"xref","data":{"text":"式（10）","type":"disp-formula","rid":"DF11","data":[{"name":"text","data":"式（10）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（10）"}],"data":[{"name":"math","data":{"math":"x=t-X0X1-X0","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529238&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529236&type=","width":"20.48933220","height":"8.46666718","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF11"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"t","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529244&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529241&type=","width":"1.10066664","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"为像素在归一化前的水平横坐标；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"X0","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529250&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529247&type=","width":"3.80999994","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为重叠区域外边界横坐标；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"X1","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529255&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529252&type=","width":"3.80999994","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为重叠区域内边界横坐标。"}]},{"name":"p","data":[{"name":"text","data":"通常，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"p=3","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529346&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529343&type=","width":"8.55133343","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"时亮度衰减曲线较为平滑，若取"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"a=0.5","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529351&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529348&type=","width":"11.43000031","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"，两个投影显示画面在同一水平坐标处的衰减权值相加为1。"}]},{"name":"p","data":[{"name":"text","data":"理论上，重叠区域像素的颜色强度值乘上衰减函数之后，重叠区域亮度与非重叠区域是一致的，无明显差异。但是，由于投影仪并不是将输入的颜色信息完全线性地投射到屏幕上，而是产生了非线性变化，使得重叠区域水平中央处要比周边区域暗，需要提高"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"a","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529278&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529275&type=","width":"1.86266661","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"的值。"}]},{"name":"p","data":[{"name":"text","data":"但是，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"a","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529278&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529275&type=","width":"1.86266661","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"的值提高后，衰减函数曲线在"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"t=0.5","graphicsData":{"small":"http:/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edge brightness adjustment function curves"}]}],"note":[],"layout":"1;2;3;","grid":[[{"name":"fig","data":{"id":"F1a1","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529301&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529307&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529304&type=","width":"75.01467133","height":"68.79166412","fontsize":""}]}}],[{"name":"fig","data":{"id":"F1a2","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529309&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529317&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529312&type=","width":"75.01467133","height":"68.79166412","fontsize":""}]}}],[{"name":"fig","data":{"id":"F1a3","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529320&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529326&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529323&type=","width":"75.01467133","height":"68.79166412","fontsize":""}]}}]],"alternatives":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529335&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529330&type=","width":"76.21467590","height":"142.63806152","fontsize":""}}}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"3.2　Lab空间的亮度融合函数"}],"level":"2","id":"s3b"}},{"name":"p","data":[{"name":"text","data":"在RGB颜色空间进行亮度融合，需要对R，G，B三个通道分别进行亮度衰减和伽马校正，而在Lab颜色空间上进行亮度融合，由于Lab颜色空间亮度和色度分开表示的特性，只有L通道储存亮度信息，故只需对L通道进行亮度调节。"}]},{"name":"p","data":[{"name":"text","data":"用各投影仪将L通道颜色强度样品集"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"LP","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529341&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529338&type=","width":"3.89466691","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"依次投影至屏幕，L通道上的18张图像的投影显示画面存在彼此重叠区域，设"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"p=3","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529346&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529343&type=","width":"8.55133343","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"且"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"a=0.5","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529351&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529348&type=","width":"11.43000031","height":"2.79399991","fontsize":""}}}]},{"name":"text","data":"，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"γ","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529369&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529367&type=","width":"1.94733346","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"值根据不同的L值进行设定。在摄像空间内确定投影画面重叠区域与非重叠区域各自的L均值，"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"γ","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529369&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529367&type=","width":"1.94733346","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"根据二者的L均值进行调整，直至摄像空间内重叠区域与非重叠区域的L均值相差低于设定的阈值，L通道的该颜色强度所对应的"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"γ","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529369&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529367&type=","width":"1.94733346","height":"3.64066648","fontsize":""}}}]},{"name":"text","data":"值便得以确定。根据摄像空间内重叠区域与非重叠区域的亮度值比较，对L通道的18张图像分别选取各自的伽马系数，根据每一个L值对应的伽马系数构建三次B样条曲线来确定不同亮度值各自的伽马系数，如"},{"name":"xref","data":{"text":"式（12）","type":"disp-formula","rid":"DF13","data":[{"name":"text","data":"式（12）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（12）"}],"data":[{"name":"math","data":{"math":"γL=BS(LP)","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529380&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529376&type=","width":"19.64266586","height":"4.65666676","fontsize":""}}},{"name":"text","data":"，"}],"id":"DF13"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"LP","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529387&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529384&type=","width":"3.89466691","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为L通道样本亮度输入值的集合；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"γL","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529393&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529390&type=","width":"3.38666677","height":"4.57200003","fontsize":""}}}]},{"name":"text","data":"为L通道样本对应伽马系数的集合；"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"BS","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529399&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529396&type=","width":"3.80999994","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"是输入亮度值与对应伽马系数的三次B样条曲线关系式。"}]},{"name":"p","data":[{"name":"text","data":"设图像重叠区域像素点的原RGB颜色强度为"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[R0',G0',B0']","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529404&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529402&type=","width":"18.45733452","height":"4.65666676","fontsize":""}}}]},{"name":"text","data":"，其亮度融合函数如"},{"name":"xref","data":{"text":"式（13）","type":"disp-formula","rid":"DF14","data":[{"name":"text","data":"式（13）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（13）"}],"data":[{"name":"math","data":{"math":"S(x)=(4x3)BS(FL([T]·[R0',G0',B0']T))0≤x≤0.5(1-4(1-x)3)BS(FL([T]·[R0',G0',B0']T))0.5≤x≤1,","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529410&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529407&type=","width":"74.67600250","height":"17.35666656","fontsize":""}}},{"name":"text","data":" "}],"id":"DF14"}},{"name":"p","data":[{"name":"text","data":"其中："},{"name":"inlineformula","data":[{"name":"math","data":{"math":"FL","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529418&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529413&type=","width":"3.97933316","height":"3.72533321","fontsize":""}}}]},{"name":"text","data":"为XYZ到Lab颜色空间L通道的转换函数。"}]},{"name":"p","data":[{"name":"text","data":"设图像重叠区域像素点经亮度调节后的RGB颜色强度为"},{"name":"inlineformula","data":[{"name":"math","data":{"math":"[R',G',B']","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529428&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529424&type=","width":"16.51000023","height":"3.80999994","fontsize":""}}}]},{"name":"text","data":"，其表达式如"},{"name":"xref","data":{"text":"式（14）","type":"disp-formula","rid":"DF15","data":[{"name":"text","data":"式（14）"}]}},{"name":"text","data":"所示："}]},{"name":"dispformula","data":{"label":[{"name":"text","data":"（14）"}],"data":[{"name":"math","data":{"math":"[R',G',B']=[T]-1⋅FL-1(FL([T]⋅[R0',G0',B0']T)⋅S(x))","graphicsData":{"small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529439&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529433&type=","width":"90.08533478","height":"4.65666676","fontsize":""}}},{"name":"text","data":"."}],"id":"DF15"}}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4 实验与分析"}],"level":"1","id":"s4"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4.1　颜色校正结果"}],"level":"2","id":"s4a"}},{"name":"sec","data":[{"name":"sectitle","data":{"title":[{"name":"text","data":"4"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1"},{"name":"italic","data":[{"name":"text","data":"."}]},{"name":"text","data":"1　Lab与RGB的比较结果"}],"level":"3","id":"s4a1"}},{"name":"p","data":[{"name":"text","data":"为了验证投影图像在Lab颜色空间的校正效果要强于RGB，本文先用一台投影仪对投影图像进行投影，对每一颜色通道输入不同的强度值，在摄像空间内检测其他颜色通道强度值的变化情况。RGB颜色空间中的每个颜色通道样本集合依次投影至屏幕，其他两个颜色通道在输入值不变的条件下所显示的输出值变化波动如"},{"name":"xref","data":{"text":"图2","type":"fig","rid":"F2","data":[{"name":"text","data":"图2"}]}},{"name":"text","data":"所示。"}]},{"name":"figgroup","data":{"id":"F2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"RGB颜色空间的输出强度变化波动"}]},{"lang":"en","label":[{"name":"text","data":"Fig.2"}],"title":[{"name":"text","data":"The output strength of RGB color space fluctuates"}]}],"note":[],"layout":"1;2;3;","grid":[[{"name":"fig","data":{"id":"F2a1","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529444&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529454&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529449&type=","width":"75.01467896","height":"69.17266846","fontsize":""}]}}],[{"name":"fig","data":{"id":"F2a2","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529460&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529469&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529464&type=","width":"75.01467133","height":"69.17266846","fontsize":""}]}}],[{"name":"fig","data":{"id":"F2a3","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529478&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529489&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529484&type=","width":"75.01467133","height":"69.17266846","fontsize":""}]}}]]}},{"name":"p","data":[{"name":"text","data":"Lab颜色空间中的每个颜色通道样本集合依次投影至屏幕，其他两个颜色通道在输入值不变的条件下所显示的输出值变化波动如"},{"name":"xref","data":{"text":"图3","type":"fig","rid":"F3","data":[{"name":"text","data":"图3"}]}},{"name":"text","data":"所示。"}]},{"name":"figgroup","data":{"id":"F3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"Lab颜色空间的输出强度变化波动"}]},{"lang":"en","label":[{"name":"text","data":"Fig.3"}],"title":[{"name":"text","data":"Output strength of Lab color space fluctuates"}]}],"note":[],"layout":"1;2,3;","grid":[[{"name":"fig","data":{"id":"F3a1","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529495&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529504&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529500&type=","width":"75.01467133","height":"68.32599640","fontsize":""}]}}],[{"name":"fig","data":{"id":"F3a2","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529508&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529518&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529512&type=","width":"75.01467133","height":"68.32599640","fontsize":""}]}},{"name":"fig","data":{"id":"F3a3","caption":[{"lang":"zh","title":[]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529523&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529531&type=","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=18529527&type=","width":"75.01467133","height":"68.32599640","fontsize":""}]}}]]}},{"name":"p","data":[{"name":"text","data":"在颜色通道输入值不变时，以全部样本输出的平均值作为变化波动的零点，由"},{"name":"xref","data":{"text":"图2","type":"fig","rid":"F2","data":[{"name":"text","data":"图2"}]}},{"name":"text","data":"和"},{"name":"xref","data":{"text":"图3","type":"fig","rid":"F3","data":[{"name":"text","data":"图3"}]}},{"name":"text","data":"可以得出，Lab颜色空间的输出强度变化波动明显要弱于RGB，即Lab某一颜色通道的输入值变化时，其余两个颜色通道输入值为定值所对应的输出值跟RGB相比受变化输入值影响较小。"}]},{"name":"p","data":[{"name":"text","data":"Lab与RGB的输出变化波动比较结果如"},{"name":"xref","data":{"text":"表1","type":"table","rid":"T1","data":[{"name":"text","data":"表1"}]}},{"name":"text","data":"所示。"}]},{"name":"table","data":{"id":"T1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"Lab与RGB的输出变化波动比较结果"}]},{"lang":"en","label":[{"name":"text","data":"Tab.1"}],"title":[{"name":"text","data":"The output fluctuation of Lab and RGB is compared"}]}],"note":[],"table":[{"head":[[{"rowspan":"2","align":"center","style":"border-top:solid;border-bottom:solid;","data":[{"name":"text","data":"颜色空间"}]},{"colspan":"2","align":"center","style":"border-top:solid;border-bottom:solid;","data":[{"name":"text","data":"输入颜色通道"}]},{"colspan":"2","align":"center","style":"border-top:solid;border-bottom:solid;","data":[{"name":"text","data":"输出颜色强度的变化波动"}]}],[{"align":"center","style":"border-bottom:solid;","data":[{"name":"text","data":"输入值变化的通道"}]},{"align":"center","style":"border-bottom:solid;","data":[{"name":"text","data":"输入值固定的通道"}]},{"align":"center","style":"border-bottom:solid;","data":[{"name":"text","data":"最大相差绝对值"}]},{"align":"center","style":"border-bottom:solid;","data":[{"name":"text","data":"样本标准差"}]}]],"body":[[{"rowspan":"6","align":"center","data":[{"name":"text","data":"RGB"}]},{"rowspan":"2","align":"center","data":[{"name":"text","data":"R"}]},{"align":"center","data":[{"name":"text","data":"G"}]},{"align":"center","data":[{"name":"text","data":"45.178 6"}]},{"align":"center","data":[{"name":"text","data":"16.023 2"}]}],[{"align":"center","data":[{"name":"text","data":"B"}]},{"align":"center","data":[{"name":"text","data":"9.498 36"}]},{"align":"center","data":[{"name":"text","data":"2.899 38"}]}],[{"rowspan":"2","align":"center","data":[{"name":"text","data":"G"}]},{"align":"center","data":[{"name":"text","data":"R"}]},{"align":"center","data":[{"name":"text","data":"73.106 2"}]},{"align":"center","data":[{"name":"text","data":"26.834 5"}]}],[{"align":"center","data":[{"name":"text","data":"B"}]},{"align":"center","data":[{"name":"text","data":"25.387 11"}]},{"align":"center","data":[{"name":"text","data":"10.359 7"}]}],[{"rowspan":"2","align":"center","data":[{"name":"text","data":"B"}]},{"align":"center","data":[{"name":"text","data":"R"}]},{"align":"center","data":[{"name":"text","data":"30.830 64"}]},{"align":"center","data":[{"name":"text","data":"11.189 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结　论"}],"level":"1","id":"s5"}},{"name":"p","data":[{"name":"text","data":"针对投影图像在RGB颜色空间颜色校正与边缘亮度调节的过程中亮度与色度相互干扰的问题，提出基于Lab的多投影颜色校正及亮度融合技术。在颜色校正的过程中，将L（亮度）、a（色度）、b（色度）单独提取出来，分别用B样条曲线模型建立起各投影仪原图像与投影画面的亮度、色度转换关系，以消除各投影仪投影画面之间颜色差异，避免亮度与色度相互干扰。在边缘亮度调节的过程中，Lab只需把L通道的颜色强度提取出即可，不必像RGB三通道进行各自的调节，而且，B样条曲线与伽马校正融合使每个颜色强度对应各自的伽马系数，跟RGB空间的伽马校正相比，准确性更高。"}]},{"name":"p","data":[{"name":"text","data":"相对于RGB颜色空间，在Lab空间进行颜色校正使两个投影显示画面的颜色强度差异在R通道减少了5.75，在G通道减少了4.82，在B通道减少了7.02，在L通道减少了4.14，在a通道减少了2.41，在b通道减少了2.44；相对于RGB颜色空间的伽马校正，在Lab空间将伽马校正与B样条曲线融合进行亮度调节使投影显示画面重叠区域与非重叠区域的颜色强度在R通道减少了5.48，在G通道减少了8.02，在B通道减少了6.74，在L通道减少了6.12，在a通道减少了4.64，在b通道减少了3.47。基于Lab的多投影颜色校正及亮度融合技术可对投影显示画面亮度与色度进行更准确的校正，并且可对不同颜色强度采用对应的融合系数进行校正。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"R1","label":"1","citation":[{"lang":"en","text":[{"name":"text","data":"MAHDI A T"},{"name":"text","data":"， "},{"name":"text","data":"GOPI M"},{"name":"text","data":"， "},{"name":"text","data":"ADITI 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