Shuangmin Chen

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.

Zihan Zhao, Pengfei Wang, Minfeng Xu et al.

Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let $R$ denote the radius function defined on the base surface $S$. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on $S$ and their corresponding off-surface points, displaced along $R$-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of $S$. Moreover, our method mitigates the misalignment issues commonly seen in crust-based approaches through a lightweight fine-tuning procedure. We validate the accuracy and efficiency of OffsetCrust through extensive experiments, and demonstrate its practical utility in applications such as reconstructing original boundary surfaces from medial axis transform (MAT) representations.

Junjie Gao, Qiujie Dong, Ruian Wang et al.

In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received substantial attention owing to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. Nonetheless, this paradigm exhibits two notable limitations.Firstly, the utilization of the Dual Softmax operation has the potential to promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. This propensity arises from the fact that a source superpoint typically maintains associations with multiple target superpoints. Secondly, it is imperative to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Based on these considerations, we propose {\em OAAFormer} to enhance correspondence quality. On one hand, we introduce a soft matching mechanism, facilitating the propagation of potentially valuable correspondences from coarse to fine levels. Additionally, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7\% in the inlier ratio, as well as an enhancement of 2-4\% in registration recall. =

Qiujie Dong, Xiaoran Gong, Rui Xu et al.

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.

Zixiong Wang, Pengfei Wang, Pengshuai Wang et al.

Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns the noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised fashion. We use the IMLS to regularize the distance values reported by the MLP while using the MLP to regularize the normals of the data points for running the IMLS. We also prove that at the convergence, our neural network, benefiting from the mutual learning mechanism between the MLP and the IMLS, produces a faithful SDF whose zero-level set approximates the underlying surface. We conducted extensive experiments on various benchmarks, including synthetic scans and real scans. The experimental results show that {\em Neural-IMLS} can reconstruct faithful shapes on various benchmarks with noise and missing parts. The source code can be found at~\url{https://github.com/bearprin/Neural-IMLS}.

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.

Qiujie Dong, Huibiao Wen, Rui Xu et al.

Quadrilateral mesh generation plays a crucial role in numerical simulations within Computer-Aided Design and Engineering (CAD/E). Producing high-quality quadrangulation typically requires satisfying four key criteria. First, the quadrilateral mesh should closely align with principal curvature directions. Second, singular points should be strategically placed and effectively minimized. Third, the mesh should accurately conform to sharp feature edges. Lastly, quadrangulation results should exhibit robustness against noise and minor geometric variations. Existing methods generally involve first computing a regular cross field to represent quad element orientations across the surface, followed by extracting a quadrilateral mesh aligned closely with this cross field. A primary challenge with this approach is balancing the smoothness of the cross field with its alignment to pre-computed principal curvature directions, which are sensitive to small surface perturbations and often ill-defined in spherical or planar regions. To tackle this challenge, we propose NeurCross, a novel framework that simultaneously optimizes a cross field and a neural signed distance function (SDF), whose zero-level set serves as a proxy of the input shape. Our joint optimization is guided by three factors: faithful approximation of the optimized SDF surface to the input surface, alignment between the cross field and the principal curvature field derived from the SDF surface, and smoothness of the cross field. Acting as an intermediary, the neural SDF contributes in two essential ways. First, it provides an alternative, optimizable base surface exhibiting more regular principal curvature directions for guiding the cross field. Second, we leverage the Hessian matrix of the neural SDF to implicitly enforce cross field alignment with principal curvature directions...

Qiujie Dong, Zixiong Wang, Manyi Li et al.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.