基于各向异性高斯核的图像边缘和角点检测
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摘要
图像边缘和角点检测一直是计算机视觉，如目标识别、运动跟踪和图像匹配等的不可或缺的预处理过程。各向异性高斯核克服了各向同性高斯核在图像处理中各个方向灰度变化的信息提取能力不足的缺陷，并且具有良好的噪声鲁棒性，因此可以用它很好的提取图像特征，如图像中边缘或者角点等。
本论文的工作主要围绕着各向异性高斯核在图像预处理中的应用展开研究。重点研究了图像预处理中的一些关键技术，如：基于各向异性高斯核的图像边缘检测、角点检测等。
本论文内容主要可概括为以下四部分：
1.融合各向同性和各向异性高斯核的边缘检测。提出了一种新的对噪声鲁棒的边缘检测算法。该算法结合了小尺度的各向同性高斯核和大尺度的各向异性高斯核(anisotropic Gaussian kernels, ANGKs)去提取图像的边缘映射(edge mapstrength,EMS)。它的主要优点是保留高边缘分辨率的同时使噪声降低。从各向异性高斯核导出各向异性高斯方向导数滤波器(anisotropic directional derivatives,ANDDs)，用它可以获取局部图像的各个方向的灰度变化信息。进而得到基于各向异性高斯核的边缘强度映射。它的噪声鲁棒性取决于尺度因子，它的边缘分辨率取决于尺度因子和各向异性因子的比值。而且显示了各向异性高斯对图像平滑对边缘的拉伸效应效应。基于大尺度各向异性高斯核的强度映射和基于小尺度各向同性高斯核的强度映射融合成一个噪声鲁棒、高边缘分辨率和小的边缘拉伸效应的边缘强度映射。然后把该边缘强度映射嵌入到Canny边缘检测算法的框架中，得到一个新的噪声鲁棒的边缘检测算法。新算法对Canny边缘检测算法做了两个调整：对比度均衡化和依赖于噪声的低门限。最后利用测试图像的特征曲线(Receiver Operating Characteristic, ROC)和Pratt的品质因数(Pratt s Figure of Merit,FOM)对提出的算法合理性进行验证。
2.基于边缘轮廓线的多弦长曲率多项式的的角点检测。在弦到点的距离累加(chord-to-point distance accumulation, CPDA)技术和曲率积的基础上，提出了多弦长曲率多项式的角点检测算法。首先利用某一个边缘检测器提取图像边缘。然后对于不同弦长下边缘轮廓曲率局部极大值点，计算其曲率的和；对于非极值点，计算其曲率的积。该方法不仅可以显著增强曲率极值点的峰值，而且避免了曲率积对一些角点平滑。最后，为了降低人为设定门限带来的错检或漏检，利用局部自适应阈值去判别角点。
3.基于边缘轮廓的各向异性高斯核角点检测。利用某一个边缘检测器提取图像边缘的基础上，提出了三种能有效提取图像角点的算法。(1)利用边缘及其周围像素的梯度方向呈现有规律的变化模式，而在角点处表现为局部各向异性变化的思想。利用各向异性高斯核平滑边缘及边缘邻近像素，将每一个像素出最大方向导数所对应的方向定为主方向。对于每一个边缘像素，计算该像素及其周围相邻像素的主方向概率分布和信息熵。最后利用熵的大小把角点从边缘中抽取出来。(2)利用各向异性高斯核平滑边缘及边缘邻近像素，得到像素不同方向的方向导数所对应的幅度值。对每个边缘像素，利用它与相邻像素们之间方向导数相关性构造自相关矩阵；若边缘像素点的自相关矩阵所对应的归一化后特征值的和是局部极大值，则标记该点为角点。(3)利用各向异性高斯核平滑边缘及边缘邻近像素，得到边缘像素的最大方向导数所对应的主方向角的大小。对于每个边缘像素点，计算它相邻两个边缘像素的主方向角度差。该算法利用主方向角度差作为新的角度测度来检测角点。实验证明了上述三个角点检测算法的有效性。
4.利用各向异性高斯核的角点检测算法和角点分类器。该检测算法主要利用从各向异性高斯核导出的各向异性方向导数滤波器来实现角点检测和角点分类。该角点检测算法融合了基于边缘和基于图像像素的检测算法的思想，主要由以下三个步骤组成：首先，利用某一个边缘检测器提取图像的轮廓边缘；其次，利用各向异性高斯核导出的各向异性高斯方向导数滤波器对边缘像素进行平滑，得到各向异性高斯方向导数响应；对于每个边缘像素，利用方向导数响应的最大值对该像素的方向导数响应进行归一化处理，并且把方向导数归一化后的曲线面积作为一个新的角点测度。最后，利用非极大值抑制和门限操作从边缘中提取角点。在此基础上，本文利用计算每个角点对应的各向异性方向导数响应的极值点的个数，提出了一种简单的角点分类器。实验证明了该角点检测算法的合理性和角点分类器的有效性。
Edge and corner detection are essential front-end process in computer vision, suchas object recognition, motion tracking and image registration etc. It has been proved thatthe anisotropic Gaussian kernels are noise robust and overcome the defect that theisotropic Gaussian kernel does not have enough capability to extract finemulti-directional intensity variation of a gray-scale image. The anisotropic Gaussianfilters can be utilized to extract image feature effectively, for example edge or corners.
This dissertation makes the study on the application of the isotropic Gaussiankernels on the image pre-processing, such as the edge and corner detection of an imagevia the anisotropic Gaussian kernels. The main researches are as the four parts below:
1. Edge detection via the combition of the isotropic and anisotropic Gaussiankernels. A noise-robustness edge detection algorithm is presented, which fusessmall-scale isotropic Gaussian kernel and large-scale anisotropic Gaussian kernels(ANGKs) to attain the edge map strength (EMS). The main merit of the algorithm isthat it has high edge resolution while it is robust to noise. From the ANGks, anisotropicdirectional derivatives (ANDDs) are derived to capture the locally directional intensityvariation of an image, and then the EMS is obtained using the ANGKs. The noiserobustness is highly depended on the scale while the edge resolution is depended on theratio of the scale to the anisotropic factor. Moreover, the image smoothing results by theANGKs reveal edge stretch effect. The fusion of large-scale ANGKs and small-scaleisotropic Gaussian kernel generates the fused ESM, which is noise robust, high edgeresolution and little edge stretch. Then the fused edge map is embedded into theframework of the Canny edge detector, thus a new noise-robustness edge detectionalgorithm is achieved, which included two modifications: contrast equalization andnoise-dependent lower thresholds. At last, the proposed edge detector is examined usingthe empirical Receiver Operating Characteristic (ROC) Curves of the tested images andthe Pratt s Figure of Merit (FOM).
2. A new contour-based corner detection using multi-chord curvature polynomialalgorithm is conducted. Multi-chord curvature polynomial algorithm for cornerdetection is proposed based upon chord-to-point distance accumulation (CPDA)technique and curvature product. Firstly, the edge map is extracted by Canny edgedetector. Then, at each chord, a multi-chord curvature polynomial is used as the sum ormultiplication of the contour curvature. The new method can not only effectivelyenhance curvature extreme peaks, but also prevent smoothing some corners. Lastly to reduce false or missing detection made by experiment threshold, local adaptivelythreshold is used to detect corners.
3. Several techniques of the contoured-based corner detection via ANGKs arestudied. Three effective corner detection algorithms based upon the edge contours areproposed. Firstly, on the idea that the gradient directional angle variation of thesmoothing edge pixel and the around pixels is regular while that of the corners isanisotropic, the edge and around pixels are smoothed by the ANGKs and then themaximal magnitude direction counts as the principal direction of the tested pixel. Theprobability distributions and the information entropy of the tested edge pixel and aroundpixels are calculated. And the corners are decided by the information entropy. Secondly,the directional magnitudes are calculated after smoothing the edge pixels and theirsurrounding regular pixels using ANGKs. The autocorrelation matrix of the directionalmagnitudes at each pixel and their surrounding pixels is then contracted. The localmaxima of the sum of the normalized eigenvalues on the contour are labeled as corners.Thirdly, the principle direction of an edge pixel is calculated after smoothing the edgepixels using ANGKs. Then the angle difference of the principal direction of the testedge pixel s two surrounding edge pixels is used as the corner measure to extractcorners. The experimental results show that the three detection algorithms are effective.
4. A new corner detector and corner classifier using the anisotropic Gaussiankernels is introduced. The detection algorithm mainly utilizes the anisotropic directionalderivative (ANDD) representations derived from the anisotropic Gaussian kernels todetect and classify corners. The corner detection fuses the ideas of the contour-baseddetection and intensity-based detection and consists of three cascaded parts. First, theedge map of an image is obtained by the one edge detector and from the edge map thecontours are extracted. Next, the ANDD representations on contours are calculated afterthe contours are smoothed by the ANGKs and the ANDD representation at each pixel isnormalized by the maximal magnitude. The area surrounded by the normalized ANDDrepresentation forms a new corner measure. Finally, the non-maximum suppression andthresholding are operated on each contour to pick out corners in terms of the cornermeasure. Moreover, based upon the number of the peaks of the ANDD representation, asimple corner classifier is given. Experiments show that the proposed corner detector is reasonable and the proposed corner classifier is effective.
本论文的工作主要围绕着各向异性高斯核在图像预处理中的应用展开研究。重点研究了图像预处理中的一些关键技术，如：基于各向异性高斯核的图像边缘检测、角点检测等。
本论文内容主要可概括为以下四部分：
1.融合各向同性和各向异性高斯核的边缘检测。提出了一种新的对噪声鲁棒的边缘检测算法。该算法结合了小尺度的各向同性高斯核和大尺度的各向异性高斯核(anisotropic Gaussian kernels, ANGKs)去提取图像的边缘映射(edge mapstrength,EMS)。它的主要优点是保留高边缘分辨率的同时使噪声降低。从各向异性高斯核导出各向异性高斯方向导数滤波器(anisotropic directional derivatives,ANDDs)，用它可以获取局部图像的各个方向的灰度变化信息。进而得到基于各向异性高斯核的边缘强度映射。它的噪声鲁棒性取决于尺度因子，它的边缘分辨率取决于尺度因子和各向异性因子的比值。而且显示了各向异性高斯对图像平滑对边缘的拉伸效应效应。基于大尺度各向异性高斯核的强度映射和基于小尺度各向同性高斯核的强度映射融合成一个噪声鲁棒、高边缘分辨率和小的边缘拉伸效应的边缘强度映射。然后把该边缘强度映射嵌入到Canny边缘检测算法的框架中，得到一个新的噪声鲁棒的边缘检测算法。新算法对Canny边缘检测算法做了两个调整：对比度均衡化和依赖于噪声的低门限。最后利用测试图像的特征曲线(Receiver Operating Characteristic, ROC)和Pratt的品质因数(Pratt s Figure of Merit,FOM)对提出的算法合理性进行验证。
2.基于边缘轮廓线的多弦长曲率多项式的的角点检测。在弦到点的距离累加(chord-to-point distance accumulation, CPDA)技术和曲率积的基础上，提出了多弦长曲率多项式的角点检测算法。首先利用某一个边缘检测器提取图像边缘。然后对于不同弦长下边缘轮廓曲率局部极大值点，计算其曲率的和；对于非极值点，计算其曲率的积。该方法不仅可以显著增强曲率极值点的峰值，而且避免了曲率积对一些角点平滑。最后，为了降低人为设定门限带来的错检或漏检，利用局部自适应阈值去判别角点。
3.基于边缘轮廓的各向异性高斯核角点检测。利用某一个边缘检测器提取图像边缘的基础上，提出了三种能有效提取图像角点的算法。(1)利用边缘及其周围像素的梯度方向呈现有规律的变化模式，而在角点处表现为局部各向异性变化的思想。利用各向异性高斯核平滑边缘及边缘邻近像素，将每一个像素出最大方向导数所对应的方向定为主方向。对于每一个边缘像素，计算该像素及其周围相邻像素的主方向概率分布和信息熵。最后利用熵的大小把角点从边缘中抽取出来。(2)利用各向异性高斯核平滑边缘及边缘邻近像素，得到像素不同方向的方向导数所对应的幅度值。对每个边缘像素，利用它与相邻像素们之间方向导数相关性构造自相关矩阵；若边缘像素点的自相关矩阵所对应的归一化后特征值的和是局部极大值，则标记该点为角点。(3)利用各向异性高斯核平滑边缘及边缘邻近像素，得到边缘像素的最大方向导数所对应的主方向角的大小。对于每个边缘像素点，计算它相邻两个边缘像素的主方向角度差。该算法利用主方向角度差作为新的角度测度来检测角点。实验证明了上述三个角点检测算法的有效性。
4.利用各向异性高斯核的角点检测算法和角点分类器。该检测算法主要利用从各向异性高斯核导出的各向异性方向导数滤波器来实现角点检测和角点分类。该角点检测算法融合了基于边缘和基于图像像素的检测算法的思想，主要由以下三个步骤组成：首先，利用某一个边缘检测器提取图像的轮廓边缘；其次，利用各向异性高斯核导出的各向异性高斯方向导数滤波器对边缘像素进行平滑，得到各向异性高斯方向导数响应；对于每个边缘像素，利用方向导数响应的最大值对该像素的方向导数响应进行归一化处理，并且把方向导数归一化后的曲线面积作为一个新的角点测度。最后，利用非极大值抑制和门限操作从边缘中提取角点。在此基础上，本文利用计算每个角点对应的各向异性方向导数响应的极值点的个数，提出了一种简单的角点分类器。实验证明了该角点检测算法的合理性和角点分类器的有效性。
Edge and corner detection are essential front-end process in computer vision, suchas object recognition, motion tracking and image registration etc. It has been proved thatthe anisotropic Gaussian kernels are noise robust and overcome the defect that theisotropic Gaussian kernel does not have enough capability to extract finemulti-directional intensity variation of a gray-scale image. The anisotropic Gaussianfilters can be utilized to extract image feature effectively, for example edge or corners.
This dissertation makes the study on the application of the isotropic Gaussiankernels on the image pre-processing, such as the edge and corner detection of an imagevia the anisotropic Gaussian kernels. The main researches are as the four parts below:
1. Edge detection via the combition of the isotropic and anisotropic Gaussiankernels. A noise-robustness edge detection algorithm is presented, which fusessmall-scale isotropic Gaussian kernel and large-scale anisotropic Gaussian kernels(ANGKs) to attain the edge map strength (EMS). The main merit of the algorithm isthat it has high edge resolution while it is robust to noise. From the ANGks, anisotropicdirectional derivatives (ANDDs) are derived to capture the locally directional intensityvariation of an image, and then the EMS is obtained using the ANGKs. The noiserobustness is highly depended on the scale while the edge resolution is depended on theratio of the scale to the anisotropic factor. Moreover, the image smoothing results by theANGKs reveal edge stretch effect. The fusion of large-scale ANGKs and small-scaleisotropic Gaussian kernel generates the fused ESM, which is noise robust, high edgeresolution and little edge stretch. Then the fused edge map is embedded into theframework of the Canny edge detector, thus a new noise-robustness edge detectionalgorithm is achieved, which included two modifications: contrast equalization andnoise-dependent lower thresholds. At last, the proposed edge detector is examined usingthe empirical Receiver Operating Characteristic (ROC) Curves of the tested images andthe Pratt s Figure of Merit (FOM).
2. A new contour-based corner detection using multi-chord curvature polynomialalgorithm is conducted. Multi-chord curvature polynomial algorithm for cornerdetection is proposed based upon chord-to-point distance accumulation (CPDA)technique and curvature product. Firstly, the edge map is extracted by Canny edgedetector. Then, at each chord, a multi-chord curvature polynomial is used as the sum ormultiplication of the contour curvature. The new method can not only effectivelyenhance curvature extreme peaks, but also prevent smoothing some corners. Lastly to reduce false or missing detection made by experiment threshold, local adaptivelythreshold is used to detect corners.
3. Several techniques of the contoured-based corner detection via ANGKs arestudied. Three effective corner detection algorithms based upon the edge contours areproposed. Firstly, on the idea that the gradient directional angle variation of thesmoothing edge pixel and the around pixels is regular while that of the corners isanisotropic, the edge and around pixels are smoothed by the ANGKs and then themaximal magnitude direction counts as the principal direction of the tested pixel. Theprobability distributions and the information entropy of the tested edge pixel and aroundpixels are calculated. And the corners are decided by the information entropy. Secondly,the directional magnitudes are calculated after smoothing the edge pixels and theirsurrounding regular pixels using ANGKs. The autocorrelation matrix of the directionalmagnitudes at each pixel and their surrounding pixels is then contracted. The localmaxima of the sum of the normalized eigenvalues on the contour are labeled as corners.Thirdly, the principle direction of an edge pixel is calculated after smoothing the edgepixels using ANGKs. Then the angle difference of the principal direction of the testedge pixel s two surrounding edge pixels is used as the corner measure to extractcorners. The experimental results show that the three detection algorithms are effective.
4. A new corner detector and corner classifier using the anisotropic Gaussiankernels is introduced. The detection algorithm mainly utilizes the anisotropic directionalderivative (ANDD) representations derived from the anisotropic Gaussian kernels todetect and classify corners. The corner detection fuses the ideas of the contour-baseddetection and intensity-based detection and consists of three cascaded parts. First, theedge map of an image is obtained by the one edge detector and from the edge map thecontours are extracted. Next, the ANDD representations on contours are calculated afterthe contours are smoothed by the ANGKs and the ANDD representation at each pixel isnormalized by the maximal magnitude. The area surrounded by the normalized ANDDrepresentation forms a new corner measure. Finally, the non-maximum suppression andthresholding are operated on each contour to pick out corners in terms of the cornermeasure. Moreover, based upon the number of the peaks of the ANDD representation, asimple corner classifier is given. Experiments show that the proposed corner detector is reasonable and the proposed corner classifier is effective.
引文
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