一种新的平面开曲线形状距离的度量

平面曲线形状识别是最基本的模式识别问题，然而这个问题至今仍然未能很好地解决。其困难在于难以给出两条曲线的形状差别的定量描述。本文为基于曲率表示的两条平面开曲线的等形下了严格的数学定义，从而找到了一种新的形状距离度量，并且证明了这种形状距离的计算问题可以转化为一个泛函的极值问题，同时给出了求解形状距离的微分方程。由于解这个微分方程是困难的，实验中采用粗略的分段匹配法。本文还介绍了算法的程序实现，尤其是离散情况下的曲线的曲率表示，并且用基于动量守恒的高斯滤波解决了曲率法表示曲线的噪声敏感性问题。实验表明本文提出的形状距离度量方法是有效的。

A New Kind of Shape Distance between Two Open Planar Curves

Shape recognition of planar curves is a fundamental problem of pattern recognition. But it has not been well resolved by now. It is difficult to value the shape difference between two curves. This paper gives a mathematical definition to that two open planar curves have the same shape based on curvature representation, therefore, a new kind of shape distance is proposed. It is concluded that the problem of computing the shape distance between two open planar curves can be changed to the problem of a functional extremum, and the differential equation is given, which can be used to figure out the shape distance. However, it is very difficult to solve that equation. Since there is no better means at hand, a rude method of fragmentation matching is used in experiments. It is also presented in this paper how to implement the algorithm step by step, especially how to represent an open planar curve in the discrete case. A constant momentum based Gaussian filtering is applied to reduce the noise sensitivity of curvature based representation. The experimental results show that this kind of shape distance is effective.