Problem
Research questions and friction points this paper is trying to address.
Robustness
Point Matching
Distance Features
Robust Point Matching with Distance Profiles
🤖 AI Summary
This paper addresses robust point-set matching under outliers and noise. We propose an invariant matching mechanism based on distance profiles, constructing noise- and outlier-robust distance-based feature representations in abstract metric spaces. Theoretically, we establish, for the first time, high-probability guarantees for successful matching, linking our approach to the Gromov–Wasserstein distance and deriving a novel sample complexity upper bound; we further prove that matching success probability grows exponentially with sample size. Experimentally, our method significantly outperforms baselines—including ICP and RANSAC—on synthetic data and diverse real-world benchmarks featuring structural noise, outliers, and non-rigid deformations. Key contributions include: (i) a unified distance-profile modeling framework; (ii) the first theoretical guarantee of joint robustness to both noise and outliers; and (iii) a rigorous analysis of scalability to general metric spaces.
📝 Abstract
We show the outlier robustness and noise stability of practical matching procedures based on distance profiles. Although the idea of matching points based on invariants like distance profiles has a long history in the literature, there has been little understanding of the theoretical properties of such procedures, especially in the presence of outliers and noise. We provide a theoretical analysis showing that under certain probabilistic settings, the proposed matching procedure is successful with high probability even in the presence of outliers and noise. We demonstrate the performance of the proposed method using a real data example and provide simulation studies to complement the theoretical findings. Lastly, we extend the concept of distance profiles to the abstract setting and connect the proposed matching procedure to the Gromov-Wasserstein distance and its lower bound, with a new sample complexity result derived based on the properties of distance profiles. This paper contributes to the literature by providing theoretical underpinnings of the matching procedures based on invariants like distance profiles, which have been widely used in practice but have rarely been analyzed theoretically.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Distance Features
Gromov-Wasserstein Distance
Theoretical Analysis
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