一种基于梯度算子的图像匹配算法

An Image Gradient Based Matching

在图像处理中常需要找出一幅图像与其对应的样板图像间的位移（ 变形） 量．本文比较了几种常用的图像匹配方法，并对一种基于梯度算子的弹性匹配方法进行了研究．这种方法首先构造一个二次误差指标函数．此指标函数由两项组成：匹配误差项和平滑约束项．此指标函数不同于Ｈｏｒｎ 和Ｓｃｈｕｎｃｋ 的光流法之处在于：其中的匹配误差项和平滑约束项直接定义于位移矢量场而不是光流场．利用变分法可以从这个二次误差指标函数导出一组椭圆形偏微分方程泊松方程（Ｐｏｉｓｓｏｎ ｅｑｕａｔｉｏｎ），这类方程有相当成熟的数值解法．采用有限差分法，对多组图像进行计算，证明此算法是有效的，并具有收敛速度快。

In image processing and video image compression,it is important to estimate the displacement between deformed image and its template.In this paper,we discuss some related methods and introduce an elastic matching,which is an image gradient based approach.First,a new quadratic error functional is proposed.The functional consists of two terms:one is matching error;the other is a smoothness constraint.Being different from Horn and Schunck' optical flow method,the matching errors and smoothness constraint are explicitly defined on the displacement vector field instead of “flow field”.The functional by variational calculus leads to a set of elliptic partial differential equations,in particular,Poisson equations,which is possibly solved by numerical methods.Using finite difference method,our algorithm is effective for matching deformed image planes.It quickly converges to good estimates of displacement vector field,and is insensitive to additive noise.