Shape Matching Through Particle Dynamics Warping

Abstract

Shape matching is fundamental to numerous computer vision algorithms and may be used for similarity determination and registration. Establishing correspondence and measuring similarity between shapes is of great importance. Shape matching often involves simultaneous estimation of both a correspondence and an alignment transformation. Such an estimate is particularly difficult when the alignment transformation is non-linear and so contains a large number of degrees of freedom. We describe a novel approach for shape matching that is based on shape contexts and uses particle dynamics warping to maximize the similarity of shapes while satisfying structural constraints. The approach is based on an iterative solution of a system of first order ordinary differential equations. The main advantage of the proposed approach is its ability to incorporate shape constraints into the matching process. Furthermore, the proposed approach does not require a solution of an optimal assignment problem which is sensitive to outliers, and does not require thin-plate spline warping which is computationally expensive. To illustrate the applicability of our approach we address the problem of offline signature recognition which in contrast to online signature recognition does not provide for a simple parametrization of the signature curves. The proposed approach is evaluated by measuring the precision and recall rates of documents based on signature similarity. To facilitate a realistic evaluation, the signature data we use was collected from real world documents spanning a period of several decades.