Diffeomorphisms Groups and Pattern Matching in Image Analysis

摘要

In a previous paper, it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group. We show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images. Using Lie group ideas, we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations. Then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub-optimal gradient pattern matching. Its links with fluid models are established.