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

Mingyang Zhao · Jiang Jingen · Lei Ma · Shiqing Xin · Gaofeng Meng · Dong-Ming Yan

Arch 4A-E Poster #160
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Fri 21 Jun 10:30 a.m. PDT — noon PDT

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{\"o}m 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.

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