Alternately denoising and reconstructing unoriented point sets

We propose a new strategy to bridge point cloud denoising and surface reconstruction by alternately updating the denoised point clouds and the reconstructed surfaces. In Poisson surface reconstruction, the implicit function is generated by a set of smooth basis functions centered at the octnodes. When the octree depth is properly selected, the reconstructed surface is a good smooth approximation of the noisy point set. Our method projects the noisy points onto the surface and alternately reconstructs and projects the point set. We use the iterative Poisson surface reconstruction (iPSR) to support unoriented surface reconstruction. Our method iteratively performs iPSR and acts as an outer loop of iPSR. Considering that the octree depth significantly affects the reconstruction results, we propose an adaptive depth selection strategy to ensure an appropriate depth choice. To manage the oversmoothing phenomenon near the sharp features, we propose a $\lambda$-projection method, which means to project the noisy points onto the surface with an individual control coefficient $\lambda_{i}$ for each point. The coefficients are determined through a Voronoi-based feature detection method. Experimental results show that our method achieves high performance in point cloud denoising and unoriented surface reconstruction within different noise scales, and exhibits well-rounded performance in various types of inputs. The source code is available at~\url{https://github.com/Submanifold/AlterUpdate}.Comment: Accepted by Computers & Graphics from CAD/Graphics 202

Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction

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}

Neural Gradient Learning and Optimization for Oriented Point Normal Estimation

We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying geometry of the data. We utilize a simple neural network to parameterize the objective function to produce gradients at points using a global implicit representation. However, the derived gradients usually drift away from the ground-truth oriented normals due to the lack of local detail descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to learn an angular distance field based on local plane geometry to refine the coarse gradient vectors. Finally, we formulate our method with a two-phase pipeline of coarse estimation followed by refinement. Moreover, we integrate two weighting functions, i.e., anisotropic kernel and inlier score, into the optimization to improve the robust and detail-preserving performance. Our method efficiently conducts global gradient approximation while achieving better accuracy and generalization ability of local feature description. This leads to a state-of-the-art normal estimator that is robust to noise, outliers and point density variations. Extensive evaluations show that our method outperforms previous works in both unoriented and oriented normal estimation on widely used benchmarks. The source code and pre-trained models are available at https://github.com/LeoQLi/NGLO.Comment: accepted by SIGGRAPH Asia 202

Learning Graph-Convolutional Representations for Point Cloud Denoising

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by learning-based point cloud processing methods. The network is fully-convolutional and can build complex hierarchies of features by dynamically constructing neighborhood graphs from similarity among the high-dimensional feature representations of the points. When coupled with a loss promoting proximity to the ideal surface, the proposed approach significantly outperforms state-of-the-art methods on a variety of metrics. In particular, it is able to improve in terms of Chamfer measure and of quality of the surface normals that can be estimated from the denoised data. We also show that it is especially robust both at high noise levels and in presence of structured noise such as the one encountered in real LiDAR scans.Comment: European Conference on Computer Vision (ECCV) 202

Learning robust and efficient point cloud representations

L'abstract è presente nell'allegato / the abstract is in the attachmen

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

DiGS : Divergence guided shape implicit neural representation for unoriented point clouds

Neural shape representations have recently shown to be effective in shape analysis and reconstruction tasks. Existing neural network methods require point coordinates and corresponding normal vectors to learn the implicit level sets of the shape. Normal vectors are often not provided as raw data, therefore, approximation and reorientation are required as pre-processing stages, both of which can introduce noise. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal shape representation networks that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and show state-of-the-art performance compared to other unoriented methods and on-par performance compared to oriented methods