Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation

• URL: http://arxiv.org/abs/2209.15619v3
• Date: Sun, 30 Apr 2023 14:01:45 GMT
• Title: Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation
• Authors: Dong Xiao, Zuoqiang Shi, Siyu Li, Bailin Deng, Bin Wang
• Abstract summary: Oriented normals are common pre-requisites for many geometric algorithms based on point clouds. We propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation. Our method can achieve high performance in non-uniform and noisy data.
• Score: 16.467735758073363
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and reconstruction in the implicit space and propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation. In implicit surface reconstruction, the reconstructed shape is represented as an isosurface of an implicit function defined in the ambient space. Therefore, when such a surface is reconstructed from a set of sample points, the implicit function values at the points should be close to the isovalue corresponding to the surface. Based on this observation and the Poisson equation, we propose an optimization formulation that combines isovalue constraints with local consistency requirements for normals. We optimize normals and implicit functions simultaneously and solve for a globally consistent orientation. Thanks to the sparsity of the linear system, our method can work on an average laptop with reasonable computational time. Experiments show that our method can achieve high performance in non-uniform and noisy data and manage varying sampling densities, artifacts, multiple connected components, and nested surfaces. The source code is available at \url{https://github.com/Submanifold/IsoConstraints}.

Related papers

• Extracting Manifold Information from Point Clouds [0.0]
  A kernel based method is proposed for the construction of signature functions of subsets of $mathbbRd$. The analytical and analysis of point clouds are the main application.
  arXiv  Detail & Related papers  (2024-03-30T17:21:07Z)
• $p$-Poisson surface reconstruction in curl-free flow from point clouds [5.330266804358638]
  Implicit neural representations (INRs) have emerged as a promising approach to surface reconstruction. In this paper, we show that proper supervision of partial differential equations and fundamental properties of differential vector fields are sufficient to robustly reconstruct high-quality surfaces.
  arXiv  Detail & Related papers  (2023-10-31T00:20:24Z)
• GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation [73.77505964222632]
  We present a learning-based method, namely GeoUDF, to tackle the problem of reconstructing a discrete surface from a sparse point cloud. To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation. To extract triangle meshes from the predicted UDF, we propose a customized edge-based marching cube module.
  arXiv  Detail & Related papers  (2022-11-30T06:02:01Z)
• HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces [54.77683371400133]
  We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Experimental results show that our HSurf-Net achieves the state-of-the-art performance on the synthetic shape dataset.
  arXiv  Detail & Related papers  (2022-10-13T16:39:53Z)
• Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion [71.52576837870166]
  We present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. Our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.
  arXiv  Detail & Related papers  (2022-07-29T16:55:06Z)
• A Level Set Theory for Neural Implicit Evolution under Explicit Flows [102.18622466770114]
  Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. We present a framework that allows applying deformation operations defined for triangle meshes onto such implicit surfaces. We show that our approach exhibits improvements for applications like surface smoothing, mean-curvature flow, inverse rendering and user-defined editing on implicit geometry.
  arXiv  Detail & Related papers  (2022-04-14T17:59:39Z)
• Temporally-Consistent Surface Reconstruction using Metrically-Consistent Atlases [131.50372468579067]
  We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. We represent the reconstructed surfaces as atlases computed by a neural network, which enables us to establish correspondences between frames. Our approach outperforms state-of-the-art ones on several challenging datasets.
  arXiv  Detail & Related papers  (2021-11-12T17:48:25Z)
• PU-Flow: a Point Cloud Upsampling Networkwith Normalizing Flows [58.96306192736593]
  We present PU-Flow, which incorporates normalizing flows and feature techniques to produce dense points uniformly distributed on the underlying surface. Specifically, we formulate the upsampling process as point in a latent space, where the weights are adaptively learned from local geometric context. We show that our method outperforms state-of-the-art deep learning-based approaches in terms of reconstruction quality, proximity-to-surface accuracy, and computation efficiency.
  arXiv  Detail & Related papers  (2021-07-13T07:45:48Z)
• DiGS : Divergence guided shape implicit neural representation for unoriented point clouds [36.60407995156801]
  Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. We propose a divergence guided shape representation learning approach that does not require normal vectors as input.
  arXiv  Detail & Related papers  (2021-06-21T02:10:03Z)
• Least squares surface reconstruction on arbitrary domains [30.354512876068085]
  We propose a new method for computing numerical derivatives based on 2D Savitzky-Golay filters and K-nearest neighbour kernels. We show how to write both orthographic or perspective height-from-normals as a linear least squares problem using the same formulation. We demonstrate improved performance relative to state-of-the-art on both synthetic and real data.
  arXiv  Detail & Related papers  (2020-07-16T21:33:39Z)
• Curvature Regularized Surface Reconstruction from Point Cloud [4.389913383268497]
  We propose a variational functional and fast algorithms to reconstruct implicit surface from point cloud data with a curvature constraint. The proposed method shows against noise, and recovers concave features and sharp corners better compared to models without curvature constraint.
  arXiv  Detail & Related papers  (2020-01-22T05:34:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.