【作者】 王洪星；

【导师】 杨丹； 张小洪；

【作者基本信息】 重庆大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 图像的局部特征在保留图像重要信息的同时,又有效地减少了图像处理的数据量,极大地提高了运算速度。因此特征提取成为模式识别与计算机视觉等图像处理相关领域的基础性研究内容。在众多图像特征中,角点不仅具有最少的数据量,而且稳定性极高,这使角点检测成为特征提取的重要分支。然而目前的角点检测算法更多的是在实验层面得到解释,缺乏系统的数学理论论证。基于此,本文在轮廓尺度空间中研究角点的演化行为,为角点描述提供一种有效的表达方式。本文的研究工作如下:①将二阶微分算子Laplacian应用到轮廓曲线上,利用角点为曲线上的不光滑点这一性质,定义曲线Laplacian变换的2-范数为角点响应(简称为Laplacian角点响应),指出该角点响应与流行的曲率角点响应能够导出相同的角点位置,定义具有一致性。②在不同尺度下通过与Gaussian函数卷积来演化轮廓生成轮廓的Gaussian尺度空间,并定义演化轮廓的Laplacian角点响应为角点的LoG (Laplacian of Gaussian)响应。之后系统地分析了LoG角点的行为特征,以解析形式描述了单角点模型与双角点模型在尺度空间中的形态。③首先根据LoG角点行为理论提出LoG角点检测算法,然后通过LoG算子的逼近形式DoG (Difference of Gaussian)算子构造DoG角点检测算法。最后与经典的CSS (Curvature Scale Space)角点检测算法进行对比,实验结果表明LoG与DoG算法具有更好的角点检测性能,以及更强的对噪声的鲁棒性。更多还原

【Abstract】 Image local features retain important information, which reduce the data quantity of image processing effectively, and improve the operation speed greatly. Thus, feature extraction has become the basic research of the related areas of image processing such as pattern recognition and computer vision. Among the many image features, not only do the corners have the least amount of data, but also they are quite stable, which makes corner detection as an important branch of feature extraction. However, most of the corner detection algorithms are merely implemented in the experimental level, lacking of mathematical demonstration. Based on above, this paper will investigate the evolution behavior of corners in the contour scale space, which will provide an excellent corner description. Specifically, this research work is as follows:①The Laplacian differential operator is applied to the contour curves. According to the property that a corner is non-smooth in the curve, the corner response is defined as the 2-norm of Laplacian of the curve (referred to as the Laplacian corner response). These responses are able to locate the same corners as the popular curvature corner response. Therefore, the definition is consistent with previous.②The evolved contours is obtained by convolving the original contour with Gaussian function at different scales, which consist of the Gaussian scale space of contours. And the Laplacian corner reponse of the evolved contours is defined as the Laplacian of Gaussian (LoG) scale space of corners. Afterwards, the behavior of LoG corners is investigated in the form of analytical solution via single and double corner models.③The LoG corner detection algorithm is proposed on the basis of the behavior of LoG corners. In addition, the Difference of Gaussian (DoG) operator that is the approximation of LoG operator is used to construct the DoG corner detection algorithm. Eventually, both the LoG and DoG algorithm are proved to process more superior detection performance and stronger robustness against to noise than the classic CSS(Curvature Scale Space) algorithm.更多还原