Feature-preserving point cloud filtering via mixture family manifold

Filtering noisy point cloud of complex models while effectively preserving geometric features, especially fine-scale features, presents the main challenge. In this paper, we propose a non-learning, feature-preserving point cloud filtering method from the novel perspective of mixture family manifold, which does not require normal estimation and does not depend on the distribution of the input data. Our novel perspective refers to formulate a potential function regularization term, related to Shannon entropy, within the mixture family manifold parameterized by the mixture weights. This regularization constrains the parameter estimation in the point cloud filtering model inspired by the Gaussian Mixture Model (GMM), avoiding the use of purely distance-based isotropic weights. Our method effectively removes noise while preserving geometric details. Experimental results on both synthetic and scanned data demonstrate that our approach outperforms the selected state-of-the-art methods, including those that roughly utilize normal information for point cloud filtering.