Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914850104410112 |
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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 |