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

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 ?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 Nystrom 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.