Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis

TL;DR

This paper introduces a novel unsupervised clustering-based framework for non-rigid point set registration that ensures smooth, robust deformations, reduces computational complexity, and outperforms existing methods in accuracy across diverse scenarios.

Contribution

It develops a holistic clustering-based registration framework with closed-form solutions, theoretical guarantees, and a new Nyström method for efficient large-scale processing.

Findings

Achieves high accuracy in various registration scenarios

Surpasses existing methods significantly in handling large deformations

Effective in shape transfer and medical registration tasks

Abstract

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an $\ell_1$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nystr\"om method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration.