基于有向点和有向线段的图像匹配算法研究
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摘要
图像匹配是集成电路制造装备研发的关键技术之一，为了满足集成电路制造的高密度、微尺度、大批量的要求，视觉自动对准系统成为其必不可少的组成部分，而图像匹配算法又是对准软件的核心所在。传统的基于灰度的图像匹配算法计算量大而且对光照变化敏感，为了提高匹配的速度、精度以及稳定性，本论文详细地研究了基于有向点和有向线段的图像匹配算法，并且使用C++实现了一个完整的图像匹配程序，可以快速精确地匹配模板图像和目标图像，主要研究内容和成果如下：
1)把边缘点的坐标和梯度方向联合起来构成了有向点特征，并且推广到直线段，把直线段的端点坐标和直线段的梯度方向联合起来构成了有向线段特征。提出了一种几何滤波算法，利用直线拟合对亚像素级有向点进行滤波除噪，使得亚像素级有向点的坐标和方向更加稳定。对有向线段也进行了几何滤波，使得有向线段不受边缘链段中离群点的影响。
2)以像素级有向点为特征定义了一种稳定的相似性度量，在搜索变换参数的过程中，利用相似性度量阈值和图像金字塔提高计算效率，并且提出了一种基于掩模的加速方法，根据目标图像中的有向点建立掩模，排除了不可能匹配的搜索区域，避免了在图像金字塔最顶层进行耗时的穷尽搜索，实现了模板图像和目标图像的快速粗略匹配。
3)以亚像素级有向点为特征构造了一个新的匹配目标函数，不仅把斜切变换矩阵和缩放变换矩阵引入其中，扩展了适用范围，而且使用点-线距离作为误差度量，提高了匹配精度。为了快速求解目标函数，提出了一种点-线距离与点-点距离的等效转化方法，成功地将复杂的非线性优化问题转化为简单的线性优化问题，从而能够利用最小二乘法获得准确的解析解，实现了模板图像和目标图像的快速精确匹配。
4)提出了一种基于点线对偶的图像匹配算法（Point-Line Duality，PLD），以有向线段为特征，利用点线对偶将其从(x-y)图像空间转换到(-)对偶空间，从而将直线匹配问题转化为点集匹配问题。提出了一种点融合的方法来处理原本属于同一条直线段的多条断开的直线段，增强了对偶点的稳定性，提高了对偶点集的匹配效率。提出了一种基于投票的点集匹配算法，能够快速地求解变换参数，并且定义了一种相似性度量来寻找所有对应的直线段，实现了模板图像和目标图像的快速粗略匹配。
Image matching is one of crucial techniques in the Integrated Circuit (IC)manufacturing equipments. As IC fabrication and packaging tend to be smaller, highlyintegrated, three-dimensional and massive, the vision based high precision alignmentsub-system is indispensable. However, the traditional area based image matching methodsare computationally expensive and sensitive to illumination changes. For the purpose ofimproving the performance of the alignment sub-system, the dissertation investigates theimage matching methods based on oriented point and oriented line segment systematically.And we develop a program for matching images fast and accurately using C++. The maincontributions are as follows:
1) The coordinates and the gradient direction of an edge point are used to describe anew geometric feature named oriented point. And similarly, The coordinates ofendpoints and the gradient direction of a line segment are used to describe anothernew geometric feature named oriented line segment. A geometric denoisingmethod is proposed to make the oriented point more stable and to eliminate theinfluence of outliers on the oriented line segment.
2) A robust similarity measure is defined by using the pixel level oriented points.During the search for transformation parameters, methods based on similaritymeasure threshold and image pyramids are used for computational efficiency. Amethod based on mask is proposed to avoid exhaustive search in the highest levelof image pyramid, where a mask is built according to the oriented points in thetarget image. The oriented point based image matching algorithm is able toquickly achieve coarse matching between images.
3) A new objective function is built by using the subpixel level oriented points,which contains shearing matrix and scaling matrix. Also, the point to line error measure is used for better accuracy. However, the new objective function isnonlinear equation and this optimization problem is very time consuming. Toobtain the closed-form solution efficiently, the point to line error is equivalentlycomputed as the point to line error. The minimum point to line error based imagematching algorithm is able to quickly achieve fine matching between images.
4) A Point-Line Duality (PLD) based method is proposed for image matching byusing the oriented line segments as feature. According to the fact that a linesegment in the image (x-y) space corresponds to a point in the dual (-) space,the line matching problem is converted to a point matching problem. For thepurpose of matching stability and computational efficiency, a point mergingalgorithm is proposed to deal with the fragmentary line segments that shouldbelong to a single line. A point pattern matching algorithm is proposed todetermine the transformation parameters, and the matched line pairs can also bereadily determined. The PLD image matching algorithm is able to quickly achievecoarse matching between images.
1)把边缘点的坐标和梯度方向联合起来构成了有向点特征，并且推广到直线段，把直线段的端点坐标和直线段的梯度方向联合起来构成了有向线段特征。提出了一种几何滤波算法，利用直线拟合对亚像素级有向点进行滤波除噪，使得亚像素级有向点的坐标和方向更加稳定。对有向线段也进行了几何滤波，使得有向线段不受边缘链段中离群点的影响。
2)以像素级有向点为特征定义了一种稳定的相似性度量，在搜索变换参数的过程中，利用相似性度量阈值和图像金字塔提高计算效率，并且提出了一种基于掩模的加速方法，根据目标图像中的有向点建立掩模，排除了不可能匹配的搜索区域，避免了在图像金字塔最顶层进行耗时的穷尽搜索，实现了模板图像和目标图像的快速粗略匹配。
3)以亚像素级有向点为特征构造了一个新的匹配目标函数，不仅把斜切变换矩阵和缩放变换矩阵引入其中，扩展了适用范围，而且使用点-线距离作为误差度量，提高了匹配精度。为了快速求解目标函数，提出了一种点-线距离与点-点距离的等效转化方法，成功地将复杂的非线性优化问题转化为简单的线性优化问题，从而能够利用最小二乘法获得准确的解析解，实现了模板图像和目标图像的快速精确匹配。
4)提出了一种基于点线对偶的图像匹配算法（Point-Line Duality，PLD），以有向线段为特征，利用点线对偶将其从(x-y)图像空间转换到(-)对偶空间，从而将直线匹配问题转化为点集匹配问题。提出了一种点融合的方法来处理原本属于同一条直线段的多条断开的直线段，增强了对偶点的稳定性，提高了对偶点集的匹配效率。提出了一种基于投票的点集匹配算法，能够快速地求解变换参数，并且定义了一种相似性度量来寻找所有对应的直线段，实现了模板图像和目标图像的快速粗略匹配。
Image matching is one of crucial techniques in the Integrated Circuit (IC)manufacturing equipments. As IC fabrication and packaging tend to be smaller, highlyintegrated, three-dimensional and massive, the vision based high precision alignmentsub-system is indispensable. However, the traditional area based image matching methodsare computationally expensive and sensitive to illumination changes. For the purpose ofimproving the performance of the alignment sub-system, the dissertation investigates theimage matching methods based on oriented point and oriented line segment systematically.And we develop a program for matching images fast and accurately using C++. The maincontributions are as follows:
1) The coordinates and the gradient direction of an edge point are used to describe anew geometric feature named oriented point. And similarly, The coordinates ofendpoints and the gradient direction of a line segment are used to describe anothernew geometric feature named oriented line segment. A geometric denoisingmethod is proposed to make the oriented point more stable and to eliminate theinfluence of outliers on the oriented line segment.
2) A robust similarity measure is defined by using the pixel level oriented points.During the search for transformation parameters, methods based on similaritymeasure threshold and image pyramids are used for computational efficiency. Amethod based on mask is proposed to avoid exhaustive search in the highest levelof image pyramid, where a mask is built according to the oriented points in thetarget image. The oriented point based image matching algorithm is able toquickly achieve coarse matching between images.
3) A new objective function is built by using the subpixel level oriented points,which contains shearing matrix and scaling matrix. Also, the point to line error measure is used for better accuracy. However, the new objective function isnonlinear equation and this optimization problem is very time consuming. Toobtain the closed-form solution efficiently, the point to line error is equivalentlycomputed as the point to line error. The minimum point to line error based imagematching algorithm is able to quickly achieve fine matching between images.
4) A Point-Line Duality (PLD) based method is proposed for image matching byusing the oriented line segments as feature. According to the fact that a linesegment in the image (x-y) space corresponds to a point in the dual (-) space,the line matching problem is converted to a point matching problem. For thepurpose of matching stability and computational efficiency, a point mergingalgorithm is proposed to deal with the fragmentary line segments that shouldbelong to a single line. A point pattern matching algorithm is proposed todetermine the transformation parameters, and the matched line pairs can also bereadily determined. The PLD image matching algorithm is able to quickly achievecoarse matching between images.
引文
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