Probabilistic Matching of Planar Regions

TL;DR

This paper presents a probabilistic algorithm for matching planar shapes under transformations, efficiently finding near-optimal overlaps with high probability, especially for polygons where runtime is less dependent on vertices.

Contribution

It introduces a probabilistic method for shape matching that is efficient for polygons, with bounds independent of the number of vertices.

Findings

Algorithm achieves high-probability near-maximal overlap

Runtime for polygons is less dependent on vertices

Effective under translations and rigid motions

Abstract

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes $A$ and $B$, the algorithm computes a transformation $t$ such that with high probability the area of overlap of $t(A)$ and $B$ is close to maximal. In the case of polygons, we give a time bound that does not depend significantly on the number of vertices.