基于对数极坐标及对称循环矩阵的形状特征描述
摘要
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.