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

2026-02-06

AI Summary

This work addresses the challenge in partial-to-partial 3D shape matching where the overlapping region is unknown and correspondences are difficult to estimate accurately and simultaneously. We propose the first joint optimization framework based on integer linear programming (ILP) that unifies the discovery of the overlapping region and the establishment of neighborhood-preserving correspondences through geometric consistency priors. Both components are solved concurrently within a single optimization process. As the first approach to introduce ILP to this task, our method achieves significantly higher matching accuracy and smoothness compared to existing techniques, while also demonstrating superior scalability.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• partial-partial shape matching
• 3D shape correspondence
• overlapping region estimation
• geometric consistency
• 3D scanning

Innovation

• Integer Linear Programming
• Partial-Partial Shape Matching
• Geometric Consistency
• 3D Shape Correspondence
• Overlapping Region Estimation