基于图理论的图像结构化描述与匹配方法研究
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摘要
图像描述与图像匹配是图像工程中的两个基础性任务，也是计算机视觉、模式识别等领域的研究热点。图像的结构是图像中相对稳定的信息特征，由图像中的基元及其相互关系组成，反映了图像本质内容，而图作为一种描述工具可以描述图像基元之间的关系，是一个有效的结构特征信息的表示方式，因此，采用图来描述图像的结构特征并应用图匹配技术来研究图像特征之间的匹配问题受到越来越多的关注。本文采用图的方式来描述图像的结构，围绕着基于图的图像结构化描述和匹配展开研究，主要工作与创新成果如下：
（1）提出了基于最小生成树的图像结构化描述方法。基于图像中提取的结构基元构造最小生成树，最小生成树如同图像的“骨架”支撑着整幅图像，较好地反映了图像的结构。利用最小生成树定义了三个评价指标，用来衡量一组结构基元在图像中的分布均匀性、独特性和覆盖范围。该指标可以用来分析图像的结构信息，也可以用来评价一组结构基元对图像结构的描述能力。
（2）研究了基于特征点的图像结构化描述。针对广义特征点，提出了一种新的二进制串描述符，与传统的高维浮点数向量描述符相比，该描述符在保证匹配性能的同时，显著提高了匹配速度，并降低了存储空间需求；基于特征点构造最小生成树，利用上述三个指标来分析特征点在图像中的分布情况和图像中的重复模式情况，从而反映了图像的结构信息；利用上述三个指标作为评价准则，提出了一种基于最小生成树删减的特征点选取方法，结果表明，该方法能够选取出在上述准则下取得准最优的一组特征点来描述图像的结构。
（3）研究了基于特征曲线的图像结构化描述。针对传统边缘算子的检测结果中含有大量干扰边缘的不足，提出了一种基于非经典感受野自适应调制的轮廓检测方法，该方法通过模拟非经典感受野的兴奋与抑制作用来处理边缘算子的梯度图像，提高有意义的轮廓边缘的边缘强度，降低干扰纹理边缘的边缘强度，从而提高了传统边缘算子的轮廓检测性能；针对传统的边缘算子在检测屋脊型边缘时给出双边缘的现象，提出了一种改进的基于USAN（Univalue Segment AssimilatingNucleus）区域的宽线检测算子—M-USAN宽线算子，该方法将屋脊型边缘当做宽线处理，能够有效检测宽线的中心线；针对USAN宽线算子和M-USAN宽线算子中存在冗余计算的不足，提出了两种加速算法——自适应步长宽线检测算子和随机宽线检测算子，在保证USAN算子检测性能的同时，有效地消除了冗余计算量，提高了算子的运算速度。
（4）提出了基于联合图与路径相似性的图匹配方法。该方法首先通过比较图的节点属性信息提取潜在匹配节点对作为联合图的节点，然后通过比较相应节点之间的最短路径的相似性建立联合图的亲和性矩阵，最后通过求解亲和性矩阵的主特征向量获得节点之间的对应关系。针对特征点和直线段特征构造的图，分别构造相似不变量和仿射不变量来建立最短路径的描述向量，并通过仿真图像实验和实际图像实验验证了算法的有效性。
Image description and image matching are two fundamental tasks in imageengineering and hot research topics in the field of computer vision and patternrecognition. The structure of an image which consists of image elements and theirrelationships is one of the most stable features in the image and reflects the essentialcontent of the image. And graph, which is an important and effective way to representthe structural information, can describe the relationships of image elements well.Therefore, it is receiving more and more attention to represent the image structure usinggraph and to solve the image feature matching problem by graph matching. In this thesis,we use graph to represent the structural information of images and investigate theproblem of structural description and matching of images in detail. The main researchworks and achievements are outlined as follows:
(1)A method for structural description of images based on MST(MinimumSpanning Tree) is proposed. The MST constructed from the structural elements extractfrom the image support the image like the skeleton of the image, which reflects thestructure of image. Three indexes for evaluating the distribution uniformity, thedistinctiveness and the spanning degree of a set of image structural elements are definedbased on the MST. The evaluating indexes can be used to analyze the structuralinformation of an image and can also be used to evaluate the capability of a set ofstructural elements to describe the structure of an image.
(2)The structural description of an image using feature points as structuralelements is studied. Firstly, a new binary descriptor for feature point is proposed.Comparing to the traditional floating-point descriptors of high-dimension vector, thisdescriptor yields comparable matching performance while running very fast andrequiring comparatively smaller amounts of memory. Then, the MST is constructedusing the points extracted from the image and the evaluating indexes are computed toanalyze the distribution of the points in the image and the repetitive pattern in the image,which reflect the structural information of the image. Taking the indexes as evaluatingprinciple, a method for choosing a set of points based on the pruning of MST isproposed. Experimental results show that the method can selecting a set of points whichare optimal or suboptimal in principle to describe the structure of the image.
(3)The structural description of an image using feature lines as structural elementsis discussed. Since the detection results of standard edge detectors contain a lot ofspurious edges, an contour edge detection algorithm based on the adaptive facilitationand suppression mechanism of NCRF(Non-Classical Receptive Field) is presented. Bysimulating the facilitation and inhibition mechanism of NCRF, the algorithm strengthenthe gradient magnitudes of contour edges and decrease the gradient magnitudes of spurious edges, which simplifies the post-processing and improves the contour detectionperformance of standard edge detectors. Aiming at the phenomenon of double edgesgiven by traditional edge detectors when processing the ridge-type edges, a modifiedwide-line detector based on USAN(Univalue Segment AssimilatingNucleus)—M-USAN detector is presented, which treat the ridge-type edges aswide-lines and can extract the center-line of the wide lines. Moreove, in order to removethe redundant computation in the implementation of USAN wide-line detector andM-USAN wide-line detector, two acceleration algorithms—ASM-USAN detector(Adaptive Step Moving USAN detector) and R-USAN detector (Randomized USANdetector) are proposed, which successfully improve the speed of the USAN detectorwhile keeping its detection performance almost unspoiled.
(4)A graph matching method based on association graph and path similarity isproposed. Firstly, the association graph whose nodes are the potential correspondencesof the two matching graphs is constructed, then its affinity matrix is computed bycomparing the corresponding shortest path in the two matching graphs, and finally thecorrect assignments are recovered by using the principal eigenvector of the affinitymatrix. For the graph constructed from different features, such as feature points andstraight lines, different similarity transformation invariants and affine transformationinvariants are used to construct the descriptive vector of shortest path between twovertexes in the graph. Experiments results on both the simulated images and real imagesdemonstrate the effectiveness of the method.
（1）提出了基于最小生成树的图像结构化描述方法。基于图像中提取的结构基元构造最小生成树，最小生成树如同图像的“骨架”支撑着整幅图像，较好地反映了图像的结构。利用最小生成树定义了三个评价指标，用来衡量一组结构基元在图像中的分布均匀性、独特性和覆盖范围。该指标可以用来分析图像的结构信息，也可以用来评价一组结构基元对图像结构的描述能力。
（2）研究了基于特征点的图像结构化描述。针对广义特征点，提出了一种新的二进制串描述符，与传统的高维浮点数向量描述符相比，该描述符在保证匹配性能的同时，显著提高了匹配速度，并降低了存储空间需求；基于特征点构造最小生成树，利用上述三个指标来分析特征点在图像中的分布情况和图像中的重复模式情况，从而反映了图像的结构信息；利用上述三个指标作为评价准则，提出了一种基于最小生成树删减的特征点选取方法，结果表明，该方法能够选取出在上述准则下取得准最优的一组特征点来描述图像的结构。
（3）研究了基于特征曲线的图像结构化描述。针对传统边缘算子的检测结果中含有大量干扰边缘的不足，提出了一种基于非经典感受野自适应调制的轮廓检测方法，该方法通过模拟非经典感受野的兴奋与抑制作用来处理边缘算子的梯度图像，提高有意义的轮廓边缘的边缘强度，降低干扰纹理边缘的边缘强度，从而提高了传统边缘算子的轮廓检测性能；针对传统的边缘算子在检测屋脊型边缘时给出双边缘的现象，提出了一种改进的基于USAN（Univalue Segment AssimilatingNucleus）区域的宽线检测算子—M-USAN宽线算子，该方法将屋脊型边缘当做宽线处理，能够有效检测宽线的中心线；针对USAN宽线算子和M-USAN宽线算子中存在冗余计算的不足，提出了两种加速算法——自适应步长宽线检测算子和随机宽线检测算子，在保证USAN算子检测性能的同时，有效地消除了冗余计算量，提高了算子的运算速度。
（4）提出了基于联合图与路径相似性的图匹配方法。该方法首先通过比较图的节点属性信息提取潜在匹配节点对作为联合图的节点，然后通过比较相应节点之间的最短路径的相似性建立联合图的亲和性矩阵，最后通过求解亲和性矩阵的主特征向量获得节点之间的对应关系。针对特征点和直线段特征构造的图，分别构造相似不变量和仿射不变量来建立最短路径的描述向量，并通过仿真图像实验和实际图像实验验证了算法的有效性。
Image description and image matching are two fundamental tasks in imageengineering and hot research topics in the field of computer vision and patternrecognition. The structure of an image which consists of image elements and theirrelationships is one of the most stable features in the image and reflects the essentialcontent of the image. And graph, which is an important and effective way to representthe structural information, can describe the relationships of image elements well.Therefore, it is receiving more and more attention to represent the image structure usinggraph and to solve the image feature matching problem by graph matching. In this thesis,we use graph to represent the structural information of images and investigate theproblem of structural description and matching of images in detail. The main researchworks and achievements are outlined as follows:
(1)A method for structural description of images based on MST(MinimumSpanning Tree) is proposed. The MST constructed from the structural elements extractfrom the image support the image like the skeleton of the image, which reflects thestructure of image. Three indexes for evaluating the distribution uniformity, thedistinctiveness and the spanning degree of a set of image structural elements are definedbased on the MST. The evaluating indexes can be used to analyze the structuralinformation of an image and can also be used to evaluate the capability of a set ofstructural elements to describe the structure of an image.
(2)The structural description of an image using feature points as structuralelements is studied. Firstly, a new binary descriptor for feature point is proposed.Comparing to the traditional floating-point descriptors of high-dimension vector, thisdescriptor yields comparable matching performance while running very fast andrequiring comparatively smaller amounts of memory. Then, the MST is constructedusing the points extracted from the image and the evaluating indexes are computed toanalyze the distribution of the points in the image and the repetitive pattern in the image,which reflect the structural information of the image. Taking the indexes as evaluatingprinciple, a method for choosing a set of points based on the pruning of MST isproposed. Experimental results show that the method can selecting a set of points whichare optimal or suboptimal in principle to describe the structure of the image.
(3)The structural description of an image using feature lines as structural elementsis discussed. Since the detection results of standard edge detectors contain a lot ofspurious edges, an contour edge detection algorithm based on the adaptive facilitationand suppression mechanism of NCRF(Non-Classical Receptive Field) is presented. Bysimulating the facilitation and inhibition mechanism of NCRF, the algorithm strengthenthe gradient magnitudes of contour edges and decrease the gradient magnitudes of spurious edges, which simplifies the post-processing and improves the contour detectionperformance of standard edge detectors. Aiming at the phenomenon of double edgesgiven by traditional edge detectors when processing the ridge-type edges, a modifiedwide-line detector based on USAN(Univalue Segment AssimilatingNucleus)—M-USAN detector is presented, which treat the ridge-type edges aswide-lines and can extract the center-line of the wide lines. Moreove, in order to removethe redundant computation in the implementation of USAN wide-line detector andM-USAN wide-line detector, two acceleration algorithms—ASM-USAN detector(Adaptive Step Moving USAN detector) and R-USAN detector (Randomized USANdetector) are proposed, which successfully improve the speed of the USAN detectorwhile keeping its detection performance almost unspoiled.
(4)A graph matching method based on association graph and path similarity isproposed. Firstly, the association graph whose nodes are the potential correspondencesof the two matching graphs is constructed, then its affinity matrix is computed bycomparing the corresponding shortest path in the two matching graphs, and finally thecorrect assignments are recovered by using the principal eigenvector of the affinitymatrix. For the graph constructed from different features, such as feature points andstraight lines, different similarity transformation invariants and affine transformationinvariants are used to construct the descriptive vector of shortest path between twovertexes in the graph. Experiments results on both the simulated images and real imagesdemonstrate the effectiveness of the method.
引文
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