Current novel view synthesis methods are typically designed for high-quality and clean input images. However, in foggy scenes, scattering and attenuation can significantly degrade the quality of rendering. Although NeRF-based dehazing approaches have been developed, their reliance on deep fully connected neural networks and per-ray sampling strategies leads to high computational costs. Furthermore, NeRF's implicit representation limits its ability to recover fine-grained details from hazy scenes. To overcome these limitations, we propose DehazeGS, the first physics-driven 3D Gaussian Splatting (3DGS) framework for dehazing. We adopt an explicit Gaussian representation to model fog formation via a physically consistent forward rendering process, enabling reconstruction and rendering of fog-free scenes using only multi-view foggy images as input. Specifically, based on the atmospheric scattering model, we simulate the formation of fog by establishing the transmission function directly on Gaussian primitives via depth-to-transmission mapping. During training, we jointly learn the atmospheric light and scattering coefficients while optimizing the Gaussian representation of foggy scenes. At inference time, we remove the effects of scattering and attenuation in Gaussian distributions and directly render the scene to obtain dehazed views. Experiments on both real-world and synthetic foggy datasets demonstrate that DehazeGS achieves state-of-the-art performance.

To improve learning on irregular 3D shapes, such as meshes with varying discretizations and point clouds with different samplings, we propose L 2 -GNN, a new graph neural network that approximates the spectral filters using twice linear parameterization. First, we parameterize the spectral filters using wavelet filter basis functions. The parameterization allows for an enlarged receptive field of graph convolutions, which can simultaneously capture low-frequency and high-frequency information. Second, we parameterize the wavelet filter basis functions using Chebyshev polynomial basis functions. This parameterization reduces the computational complexity of graph convolutions while maintaining robustness to the change of mesh discretization and point cloud sampling. Our L 2 -GNN based on the fast spectral filter can be used for shape correspondence, classification, and segmentation tasks on non-regular mesh or point cloud data. Experimental results show that our method outperforms the current state of the art in terms of both quality and efficiency.

Point cloud registration is a basic task in computer vision and computer graphics. Recently, deep learning-based end-to-end methods have made great progress in this field. One of the challenges of these methods is to deal with partial-to-partial registration tasks. In this work, we propose a novel end-to-end framework called MCLNet that makes full use of multi-level consistency for point cloud registration. First, the point-level consistency is exploited to prune points located outside overlapping regions. Second, we propose a multi-scale attention module to perform consistency learning at the correspondence-level for obtaining reliable correspondences. To further improve the accuracy of our method, we propose a novel scheme to estimate the transformation based on geometric consistency between correspondences. Compared to baseline methods, experimental results show that our method performs well on smaller-scale data, especially with exact matches. The reference time and memory footprint of our method are relatively balanced, which is more beneficial for practical applications.

Abstract For rigid point cloud data registration, algorithms based on soft correspondences are more robust than the traditional ICP method and its variants. However, point clouds with severe outliers and missing data may lead to imprecise many‐to‐many correspondences and consequently inaccurate registration. In this study, we propose a point cloud registration algorithm based on partial optimal transport via a hard marginal constraint. The hard marginal constraint provides an explicit parameter to adjust the ratio of points that should be accurately matched, and helps avoid incorrect many‐to‐many correspondences. Experiments show that the proposed method achieves state‐of‐the‐art registration results when dealing with point clouds with significant amount of outliers and missing points (see https://www.acm.org/publications/class‐2012 ).

Abstract A 3D human skeleton plays important roles in human shape reconstruction and human animation. Remarkable advances have been achieved recently in 3D human skeleton estimation from color and depth images via a powerful deep convolutional neural network. However, applying deep learning frameworks to 3D human skeleton extraction from point clouds remains challenging because of the sparsity of point clouds and the high nonlinearity of human skeleton regression. In this study, we develop a deep learning‐based approach for 3D human skeleton extraction from point clouds. We convert 3D human skeleton extraction into offset vector regression and human body segmentation via deep learning‐based point cloud contraction. Furthermore, a disambiguation strategy is adopted to improve the robustness of joint points regression. Experiments on the public human pose dataset UBC3V and the human point cloud skeleton dataset 3DHumanSkeleton compiled by the authors show that the proposed approach outperforms the state‐of‐the‐art methods.

We introduce a mass-driven curve skeleton as a curve skeleton representation for 3D point cloud data. The mass-driven curve skeleton presents geometric properties and mass distribution of a curve skeleton simultaneously. The computation of the mass-driven curve skeleton is formulated as a minimization of Wasserstein distance, with an entropic regularization term, between mass distributions of point clouds and curve skeletons. Assuming that the mass of one sampling point should be transported to a line-like structure, a topology-aware rough curve skeleton is extracted via the optimal transport plan. A Dirichlet energy regularization term is then used to obtain a smooth curve skeleton via geometric optimization. Given that rough curve skeleton extraction does not depend on complete point clouds, our algorithm can be directly applied to curve skeleton extraction from incomplete point clouds. We demonstrate that a mass-driven curve skeleton can be directly applied to an unoriented raw point scan with significant noise, outliers and large areas of missing data. In comparison with state-of-the-art methods on curve skeleton extraction, the performance of the proposed mass-driven curve skeleton is more robust in terms of extracting a correct topology.

Abstract The symmetrizable and converged Laplace–Beltrami operator ( ) is an indispensable tool for spectral geometrical analysis of point clouds. The , introduced by Liu et al. [LPG12] is guaranteed to be symmetrizable, but its convergence degrades when it is applied to models with sharp features. In this paper, we propose a novel , which is not only symmetrizable but also can handle the point‐sampled surface containing significant sharp features. By constructing the anisotropic Voronoi diagram in the local tangential space, the can be well constructed for any given point. To compute the area of anisotropic Voronoi cell, we introduce an efficient approximation by projecting the cell to the local tangent plane and have proved its convergence. We present numerical experiments that clearly demonstrate the robustness and efficiency of the proposed for point clouds that may contain noise, outliers, and non‐uniformities in thickness and spacing. Moreover, we can show that its spectrum is more accurate than the ones from existing for scan points or surfaces with sharp features.

In this article, we present a multi-class blue noise sampling algorithm by throwing samples as the constrained Wasserstein barycenter of multiple density distributions. Using an entropic regularization term, a constrained transport plan in the optimal transport problem is provided to break the partition required by the previous Capacity-Constrained Voronoi Tessellation method. The entropic regularization term cannot only control spatial regularity of blue noise sampling, but it also reduces conflicts between the desired centroids of Vornoi cells for multi-class sampling. Moreover, the adaptive blue noise property is guaranteed for each individual class, as well as their combined class. Our method can be easily extended to multi-class sampling on a point set surface. We also demonstrate applications in object distribution and color stippling.

Efficient visualization of large volumetric data is a challenge for image processing community. In this paper, we present a novel volume rendering algorithm based on the concept of fractal. It consists of dividing the volumetric data set into sub-blocks, calculating the 3D fractal coefficients of each sub-block, projecting them to 2D image plane, and generating sub-images through 2D inverse fractal transform. The final rendered image is then obtained by simply summing the sub-images. Compared to the conventional ray casting technique, the proposed fractal volume rendering (FVR) method presents the advantage of reducing time complexity as well as memory complexity while maintaining good rendering quality. Moreover, the progressive refinement is supported owing to the iterative convergent process of sub-image generation