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

Fuente: arXiv
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Autori principali: Zhao, Mingyang, Jiang, Jingen, Ma, Lei, Xin, Shiqing, Meng, Gaofeng, Yan, Dong-Ming
Natura: Preprint
Pubblicazione: 2024
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author Zhao, Mingyang
Jiang, Jingen
Ma, Lei
Xin, Shiqing
Meng, Gaofeng
Yan, Dong-Ming
author_facet Zhao, Mingyang
Jiang, Jingen
Ma, Lei
Xin, Shiqing
Meng, Gaofeng
Yan, Dong-Ming
contents 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 Nyström 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_18817
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
Zhao, Mingyang
Jiang, Jingen
Ma, Lei
Xin, Shiqing
Meng, Gaofeng
Yan, Dong-Ming
Computer Vision and Pattern Recognition
Artificial Intelligence
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 Nyström 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.
title Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
topic Computer Vision and Pattern Recognition
Artificial Intelligence
url https://arxiv.org/abs/2406.18817