轮廓匹配的有限差分法

Contour matching using finite-difference method

本文提出一种匹配相似轮廓线的有限差分法,这个方法是在Duncan方法的基础上开发的。Duncan的方法是通过优化一个二次指标函数来匹配两条轮廓线的。这个指标函数由一个与弯曲能量有关的曲率差项和一个弹性约束项组成。Cohen指出Duncan的方法可能造成两条轮廓线上点不是按顺序一一对应。他提出用有限元法来解这个问题。本文采用新的弹性约束项,得到的优化方程不但容易计算而且有明确的物理意义,本文讨论了用有限差分法解这个方程的方法,对于复杂形状的轮廓匹配可以用多尺度法来解决。

A Multiresolution method to match deformed contours was presented. Our approach was inspired by the Duncan method, who proposed a scheme for matching two contours based on the minimization of a quadratic fitting criterion. Cohen improved this method by ensuring that the resulting displacement vectors actually map points belonging to the two contours, which is not the case in Duncan. The innovation of our work is in the incorporation of a new smoothness term in the elastic fitting criterion. As a result, the computational complexity is reduced and the equation corresponding to the minimization of the fitting criterion has a simple interpretation. The solution method is based on a finite difference approach, for which we present convergence characteristics. A multi-smoothing scheme is proposed to improve the convergence of the matching process.