Rui Xu

Zixiong Wang, Yunxiao Zhang, Rui Xu et al.

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods.

Zimeng Wang, Zhiyang Dou, Rui Xu et al.

We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input or suffer from substantial computational costs, thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.

Jionghao Wang, Cheng Lin, Yuan Liu et al.

Point-based representations have consistently played a vital role in geometric data structures. Most point cloud learning and processing methods typically leverage the unordered and unconstrained nature to represent the underlying geometry of 3D shapes. However, how to extract meaningful structural information from unstructured point cloud distributions and transform them into semantically meaningful point distributions remains an under-explored problem. We present PDT, a novel framework for point distribution transformation with diffusion models. Given a set of input points, PDT learns to transform the point set from its original geometric distribution into a target distribution that is semantically meaningful. Our method utilizes diffusion models with novel architecture and learning strategy, which effectively correlates the source and the target distribution through a denoising process. Through extensive experiments, we show that our method successfully transforms input point clouds into various forms of structured outputs - ranging from surface-aligned keypoints, and inner sparse joints to continuous feature lines. The results showcase our framework's ability to capture both geometric and semantic features, offering a powerful tool for various 3D geometry processing tasks where structured point distributions are desired. Code will be available at this link: https://github.com/shanemankiw/PDT.

Qiujie Dong, Rui Xu, Pengfei Wang et al.

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

Rui Xu, Wenyue Chen, Jiepeng Wang et al.

Gaussian Splattings demonstrate impressive results in multi-view reconstruction based on Gaussian explicit representations. However, the current Gaussian primitives only have a single view-dependent color and an opacity to represent the appearance and geometry of the scene, resulting in a non-compact representation. In this paper, we introduce a new method called SuperGaussians that utilizes spatially varying colors and opacity in a single Gaussian primitive to improve its representation ability. We have implemented bilinear interpolation, movable kernels, and even tiny neural networks as spatially varying functions. Quantitative and qualitative experimental results demonstrate that all three functions outperform the baseline, with the best movable kernels achieving superior novel view synthesis performance on multiple datasets, highlighting the strong potential of spatially varying functions.

Chao Chen, Chenghua Guo, Rui Xu et al.

Graphical models have demonstrated their exceptional capabilities across numerous applications, such as social networks, citation networks, and online recommendation systems. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data and the challenges of accurately modeling real-world complexities. There has been increased interest in developing uncertainty quantification (UQ) techniques tailored to graphical models. In this survey, we comprehensively examine existing works on UQ for graphical models, focusing on key aspects such as the sources, representation, handling, and evaluation of uncertainty. This survey distinguishes itself from most existing UQ surveys by specifically concentrating on UQ in graphical models, including probabilistic graphical models (PGMs) and graph neural networks (GNNs). After reviewing sources of uncertainty, we organize the work using two high-level dimensions: uncertainty representation and uncertainty handling. By offering a comprehensive overview of the current landscape, including both established methodologies and emerging trends, we aim to bridge gaps in understanding key challenges and opportunities in UQ for graphical models, hoping to inspire researchers working on graphical models or uncertainty quantification to make further advancements at the cross of the two fields.