Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
This addresses registration problems in fields like computer vision and medical imaging, offering a novel method for handling large deformations without correspondences.
The paper tackles non-rigid point set registration by using unsupervised clustering to treat source and target points as centroids and members, achieving high accuracy and surpassing competitors, especially for large deformations.
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.