An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matching

TL;DR

This paper introduces an integer linear programming method for partial-partial 3D shape matching that leverages geometric consistency, providing robust, smooth, and scalable correspondences in realistic partial observation scenarios.

Contribution

It is the first ILP-based approach specifically designed for partial-partial shape matching, addressing the challenges of unknown overlaps and geometric consistency.

Findings

Achieves high-quality matching with low error and smoothness.

Demonstrates superior scalability over previous methods.

Effectively estimates overlapping regions in partial shapes.

Abstract

The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the partial-partial setting, very likely due to its unique challenges: we must compute accurate correspondences while at the same time find the unknown overlapping region. Nevertheless, partial-partial 3D shape matching reflects the most realistic setting, as in many real-world cases, such as 3D scanning, shapes are only partially observable. In this work, we introduce the first integer linear programming approach specifically designed to address the distinctive challenges of partial-partial shape matching. Our method leverages geometric consistency as a strong prior, enabling both robust estimation of the overlapping region and computation of neighbourhood-preserving correspondences. We empirically demonstrate that our approach achieves high-quality matching results both in terms of matching error and smoothness. Moreover, we show that our method is more scalable than previous formalisms.