【作者】 张征；

【导师】 杨明强；

【作者基本信息】 山东大学 ， 信号与信息处理， 2013， 硕士

【摘要】 随着现代技术的发展,图像以其对目标特性的全面客观描述性,被越来越多的作为传递信息的媒介来使用,所以近些年来研究者将自己的目光更多的聚焦在计算机视觉以及图像处理领域的研究,如图像特征提取算法研究、目标识别算法研究、图像检索技术的研究等。在这些研究中基于图像形状的特征提取吸引了更多研究者的目光,因为图像的形状最能反映目标的直观性质,具有很高的区分度。近些年来针对形状特征提取算法以及相对应的相似性测量算法研究,涌现出大量优秀论文,提出了大量优秀算法,其中很多算法已得到广泛应用。在基于图像形状的特征提取和相似性测量的研究中,使算法能够抵抗形状的几何变换以及退化形变是研究的重点。这些特征提取算法可以被分为两类：基于形状区域的特征提取算法(如基于形状矩的算法、通用傅里叶描述符等),这些算法使用的是形状的区域信息作为特征提取的基础；还有一类是基于形状轮廓的特征提取算法(如傅里叶描述符、链码算法、曲率尺度空间算法等),这些算法是使用形状轮廓信息作为特征提取的基础。其中,傅里叶描述符算法不仅简单易于实现,而且具有很好的效果,是常用的形状特征提取算法。在本文中,提出了一种新的用于傅里叶描述的形状签名算法,叫做基于形状区域分割的面积函数。算法首先提取形状的封闭轮廓,再对该轮廓进行等面积重采样。而后选择轮廓上的任意一点作为分割起点,将进行轮廓等点数间隔的分割。分割起点和各个分割点连线将形状分成了一些子区域,计算这些子区域的面积。同时轮廓上的每个点都可以作为分割起点将轮廓分割,并计算分割区域的面积。轮廓上的所有点作为分割起点,分别得到分割区域的面积可以组成一个矩阵,这个矩阵就是形状签名矩阵。该矩阵的行数表示分割区域的数目,列数表述形状轮廓点数,其中的值是子区域的面积值。最后对形状签名矩阵的每一行应用傅里叶变换,选取前二十个归一化后的傅里叶系数组成的矩阵为最后的形状特征矩阵(傅里叶描述符)。在本文中,算法的相似性测度定义为欧式距离。本文的算法具有平移、旋转、尺度不变性,更重要的是该算法对于形状的仿射变换具有很强的鲁棒性。在本文中,通过数学推导我们详细证明了算法所具有的各项性质,并通过具体的实验验证了结论的正确性。同时分析了算法的计算复杂度,以及算法中关键参数选取对算法性能影响的分析,并确定合适的算法参数。最后选取MPEG-7CE-Shape-1下面的几个图像数据库作为实验数据库,选取了其它六种傅里叶描述符(包括中心距离函数、复坐标函数、累积角函数、面积函数、最远点距离函数、多级弦长函数)进行对比实验,同时还选择了两种优秀的非傅里叶描述算法(包括Zernike矩算法、曲率尺度空间算法)进行对比实验,详细分析本文算法的优劣。最终的实验结果显示,本文算法在各个方面均要好于其它类型的算法。本文算法的平均检索率为79.60%,这个数值比中心函数算法要高十个百分点,而中心函数算法被D.S.Zhang证明是现今傅里叶算法中最优秀的算法。本文所提出的算法不但使用了形状的全局轮廓信息,同时使用了分割后局部的区域信息,因而算法具有更强的对形状特征的描述能力。更多还原

【Abstract】 With the development of modern technology, more and more images have been used to transport information. So now researchers focus on computer vision such as object recognition and image retrieval. For object recognition and image retrieval, object shape features are powerful because shape is usually strongly linked to object functionality and identity. In recent years, a wide range of shape-based feature extraction and similarity measures methods are proposed in literatures, moreover various applications are likely to use shape features.For shape-based feature extraction and similarity measure, geometric invariance and deformation resistibility are important issues. Nowadays, many approaches have been proposed which are divided into two classes:region-based and contour-based. Geometric moment, Hu invariant moment, Zernike moment, generic Fourier descriptors and so on are all region-based approaches, and Fourier descriptors, chain codes, curvature scale space and so on are all contour-based approaches. Especially, Fourier descriptors are classical approaches and realized easily.In this paper we proposed a novel shape signature for Fourier descriptors. The shape signature is called contour split-based area function. We extract the closed contour of the shape, and resample the contour with the method of iso-area normalization. Different from the traditional methods like centroid distance and farthest point distance which use distance as the functions, the proposed approach use area as the shape signature function. The contour of shape is split by equal number of points, so we can get the area of each region surrounded by the chord of linking start point and split point and the corresponding arc. All points on the contour can build a matrix to save the areas, and this matrix is the proposed shape signature. Assuming that the rows of the matrix represent the number of the split regions and the columns represent the number of points on the contour. Then we apply Fourier transform on every row of the matrix, and only select the first20normalized Fourier coefficients to build a new matrix. This matrix is the Fourier descriptors feature matrix. According to the proposed approach, we define a new approach of similarity measure based on Euclidean distance.The proposed approach has the qualities of translation, scale, and rotation invariance, and the great advantage of it is invariant to affine transform, because of the method of resample and using area as the shape signature function. In the paper we not only prove the affine invariance through mathematical deduction, but also do experiment to show the correctness of the conclusion. At last, we select the MPEG-7CE-Shape-1part B as the image database for retrieval. We select another six kinds of Fourier descriptors which are centroid distance, complex coordinates, cumulative angle function, area function, farthest point distance and multi-level chord length function descriptor to compare with the proposed approach. At the same time, we select two non-Fourier descriptors which are Zernike moments and curvature scale space to compare with the proposed approach.The result of the comparative experiment shows that the performance of proposed approach is much better than other compared approaches. And the bull’s eye of the proposed approach is79.60%which is more than ten percentage points higher than centroid distance which is proved as the best Fourier descriptors by D.S. Zhang. The novel approach for shape signature proposed based on contour split and using the split region areas as function describes shape not only with reference location of points on contour, but also with shape regions referenced, so it can represent shape more completely than other shape signature approaches. The proposed approach is affine invariance, and the experiments on image database show the approach’s advantage.更多还原