An efficient iterative method for reconstructing surface from point clouds

• URL: http://arxiv.org/abs/2005.11864v1
• Date: Mon, 25 May 2020 00:01:53 GMT
• Title: An efficient iterative method for reconstructing surface from point clouds
• Authors: Dong Wang
• Abstract summary: We develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration.
• Score: 7.581956025432869
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The surface is implicitly represented by indicator functions and the energy functional is then approximated based on such representations using heat kernel convolutions. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration. We then use asymptotic expansion to give a connection between the proposed algorithm and active contour models. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.

Related papers

• Point Cloud Resampling with Learnable Heat Diffusion [58.050130177241186]
  We propose a learnable heat diffusion framework for point cloud resampling. Unlike previous diffusion models with a fixed prior, the adaptive conditional prior selectively preserves geometric features of the point cloud.
  arXiv  Detail & Related papers  (2024-11-21T13:44:18Z)
• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• 3D Reconstruction with Fast Dipole Sums [12.865206085308728]
  We introduce a method for high-quality 3D reconstruction from multiview images. We represent implicit geometry and radiance fields as per-point attributes of a dense point cloud. These queries facilitate the use of ray tracing to efficiently and differentiably render images.
  arXiv  Detail & Related papers  (2024-05-27T03:23:25Z)
• Optimizing Implicit Neural Representations from Point Clouds via Energy-Based Models [1.573038298640368]
  We propose a method to optimize implicit neural representations (INRs) using energy-based models (EBMs) Our experiments confirmed that the proposed method is more robust against point cloud noise than conventional surface reconstruction methods.
  arXiv  Detail & Related papers  (2023-11-05T08:57:22Z)
• Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian [44.28251558359345]
  We propose a new approach for reconstructing surfaces from point clouds. Our 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.
  arXiv  Detail & Related papers  (2023-09-04T20:10:38Z)
• $PC^2$: Projection-Conditioned Point Cloud Diffusion for Single-Image 3D Reconstruction [97.06927852165464]
  Reconstructing the 3D shape of an object from a single RGB image is a long-standing and highly challenging problem in computer vision. We propose a novel method for single-image 3D reconstruction which generates a sparse point cloud via a conditional denoising diffusion process.
  arXiv  Detail & Related papers  (2023-02-21T13:37:07Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Learning Modified Indicator Functions for Surface Reconstruction [10.413340575612233]
  We propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in potential energy theory, which gives an explicit integral formula for the indicator functions. We design a novel deep neural network to perform surface integral and learn the modified indicator functions from un-oriented and noisy point clouds.
  arXiv  Detail & Related papers  (2021-11-18T05:30:35Z)
• Deep Implicit Surface Point Prediction Networks [49.286550880464866]
  Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation.
  arXiv  Detail & Related papers  (2021-06-10T14:31:54Z)
• Shape As Points: A Differentiable Poisson Solver [118.12466580918172]
  In this paper, we introduce a differentiable point-to-mesh layer using a differentiable formulation of Poisson Surface Reconstruction (PSR) The differentiable PSR layer allows us to efficiently and differentiably bridge the explicit 3D point representation with the 3D mesh via the implicit indicator field. Compared to neural implicit representations, our Shape-As-Points (SAP) model is more interpretable, lightweight, and accelerates inference time by one order of magnitude.
  arXiv  Detail & Related papers  (2021-06-07T09:28:38Z)
• Learning Occupancy Function from Point Clouds for Surface Reconstruction [6.85316573653194]
  Implicit function based surface reconstruction has been studied for a long time to recover 3D shapes from point clouds sampled from surfaces. This paper proposes a novel method for learning occupancy functions from sparse point clouds and achieves better performance on challenging surface reconstruction tasks.
  arXiv  Detail & Related papers  (2020-10-22T02:07:29Z)

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.