Matching contours in images through the use of curvature, distance to centroid and global optimization with order-preserving constraint

Abstract

This paper presents a new methodology to establish the best global match of objects' contours in images. The first step is the extraction of the sets of ordered points that define the objects' contours. Then, by using the curvature value and its distance to the corresponded centroid for each point, an affinity matrix is built. This matrix contains information of the cost for all possible matches between the two sets of ordered points. Then, to determine the desired one-to-one global matching, an assignment algorithm based on dynamic programming is used. This algorithm establishes the global matching of the minimum global cost that preserves the circular order of the contours' points. Additionally, a methodology to estimate the similarity transformation that best aligns the matched contours is also presented. This methodology uses the matching information which was previously obtained, in addition to a statistical process to estimate the parameters of the similarity transformation in question. In order to validate the proposed matching methodology, its results are compared to those obtained by the geometric modeling approach proposed by Shapiro and Brady who are well known in this domain.