基于对数极坐标及对称循环矩阵的形状特征描述  

Shape feature description based on log-polar coordinates and symmetric circulant matrix

作　　者：宋瑞霞[1] 李成华[1] 王也娜 徐燕青[1] 齐东旭[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《中国科学：数学》2014年第7期815-822,共8页Scientia Sinica：Mathematica

基　　金：国家重点基础研究发展计划(973)(批准号:2011CB302400);国家自然科学基金(批准号:61272026);北京市自然科学基金(批准号:KZ201210009011)资助项目

摘　　要：在形状检索算法中,满足尺度和旋转不变是基本要求.本文将形状的边界用对数极坐标表示,使得形状的放缩和旋转化为简单的平移.由于计算机读取形状边界信息时与起点有关,当形状旋转时会带来边界点列的循环,影响旋转不变性.为消除边界点列循环带来的影响,本文首先证明"奇数阶对称循环矩阵,当生成元循环时,所得循环矩阵的特征值不变",在这个数学理论基础上,把形状边界点数插值到奇数,构造相应的对称循环矩阵,通过这个循环矩阵的特征值来描述形状特征,由此得到一种具有放缩旋转不变的形状检索新算法.实验表明,本文算法对运动目标和非刚性形变的形状检索具有良好的鲁棒性和快捷的运行速度,这在目标跟踪方面将发挥作用.A fundamental requirement in shape retrieval algorithms is that the shape descriptor should be invariant to geometric transformations, such as scaling and rotation. In this paper, the shape boundary is represented in log-polar coordinate system, so that the shape scaling and rotation is translated into translation, which is a much simpler geometric transformation. As the boundary information is related to the starting point, the shape rotation makes the boundary point sequence circulate, which will affect rotational invariance. To eliminate the effect brought by boundary point sequence circulation, we first propose a theorem： for a circulant matrix of odd order, when the generator vector, which forms the first row of the matrix, is shifted circularly, the new formed circulant matrix has the same eigenvector. Based on this theorem, we first get odd number of boundary points using interpolation method, and then construct a corresponding symmetric circulant matrix, whose eigenvectors are used to describe the shape features. Based on the obtained features, we present a new retrieval algorithm that is invariant to translation, scale, and rotation. Experiment results show that the new algorithm is robust for retrieving moving target and non-rigid shapes, and it is also a time saving method and feasible in a real-time system, hence the new algorithm could effetely be applied on target detection and tracking.

关 键 词：对数极坐标 对称循环矩阵 特征值 特征提取 形状检索 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]