Differentiable Convex Polyhedra Optimization from Multi-view Images

• URL: http://arxiv.org/abs/2407.15686v1
• Date: Mon, 22 Jul 2024 14:53:29 GMT
• Title: Differentiable Convex Polyhedra Optimization from Multi-view Images
• Authors: Daxuan Ren, Haiyi Mei, Hezi Shi, Jianmin Zheng, Jianfei Cai, Lei Yang,
• Abstract summary: This paper presents a novel approach for the differentiable rendering of convex polyhedra. It addresses the limitations of recent methods that rely on implicit field supervision.
• Score: 29.653374825428614
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines non-differentiable computation of hyperplane intersection through duality transform with differentiable optimization for vertex positioning with three-plane intersection, enabling gradient-based optimization without the need for 3D implicit fields. This allows for efficient shape representation across a range of applications, from shape parsing to compact mesh reconstruction. This work not only overcomes the challenges of previous approaches but also sets a new standard for representing shapes with convex polyhedra.

Related papers

• Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation [50.376243444909136]
  We present a unified framework to predict both point-wise correspondences and shape between 3D shapes. We combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains.
  arXiv  Detail & Related papers  (2024-02-29T07:26:23Z)
• DeFormer: Integrating Transformers with Deformable Models for 3D Shape Abstraction from a Single Image [31.154786931081087]
  We propose a novel bi-channel Transformer architecture, integrated with parameterized deformable models, to simultaneously estimate the global and local deformations of primitives. DeFormer achieves better reconstruction accuracy over the state-of-the-art, and visualizes with consistent semantic correspondences for improved interpretability.
  arXiv  Detail & Related papers  (2023-09-22T02:46:43Z)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• IKOL: Inverse kinematics optimization layer for 3D human pose and shape estimation via Gauss-Newton differentiation [44.00115413716392]
  This paper presents an inverse kinematic layer (IKOL) for 3D human pose shape estimation. IKOL has a much over over than most existing regression-based methods. It provides a more accurate range of 3D human pose estimation.
  arXiv  Detail & Related papers  (2023-02-02T12:43:29Z)
• A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching [69.14632473279651]
  We present a scalable algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We propose a novel primal coupled with a Lagrange dual problem that is several orders of magnitudes faster than previous solvers.
  arXiv  Detail & Related papers  (2022-04-27T09:47:47Z)
• 3D Equivariant Graph Implicit Functions [51.5559264447605]
  We introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details. Our method improves over the existing rotation-equivariant implicit function from 0.69 to 0.89 on the ShapeNet reconstruction task.
  arXiv  Detail & Related papers  (2022-03-31T16:51:25Z)
• Representing 3D Shapes with Probabilistic Directed Distance Fields [7.528141488548544]
  We develop a novel shape representation that allows fast differentiable rendering within an implicit architecture. We show how to model inherent discontinuities in the underlying field. We also apply our method to fitting single shapes, unpaired 3D-aware generative image modelling, and single-image 3D reconstruction tasks.
  arXiv  Detail & Related papers  (2021-12-10T02:15:47Z)
• Differentiable Surface Triangulation [40.13834693745158]
  We present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably weighted Delaunay triangulation. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints.
  arXiv  Detail & Related papers  (2021-09-22T12:42:43Z)
• H3D-Net: Few-Shot High-Fidelity 3D Head Reconstruction [27.66008315400462]
  Recent learning approaches that implicitly represent surface geometry have shown impressive results in the problem of multi-view 3D reconstruction. We tackle these limitations for the specific problem of few-shot full 3D head reconstruction. We learn a shape model of 3D heads from thousands of incomplete raw scans using implicit representations.
  arXiv  Detail & Related papers  (2021-07-26T23:04:18Z)
• Isometric Multi-Shape Matching [50.86135294068138]
  Finding correspondences between shapes is a fundamental problem in computer vision and graphics. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis.
  arXiv  Detail & Related papers  (2020-12-04T15:58:34Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)

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.