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Occupancy-Based Dual Contouring

Jisung Hwang, Minhyuk Sung

TL;DR

This work addresses the challenge of converting neural occupancy functions into high-fidelity meshes. It introduces Occupancy-Based Dual Contouring (ODC), a learning-free method that replaces distance-based MDC components with GPU-accelerated 1D, 2D, and 3D point searches and an auxiliary 2D-point plane estimation, enabling accurate surface extraction from occupancy fields. By combining a robust line-binary search, local flat-plane modeling via 2D points, and quad-splitting polygonization, ODC achieves state-of-the-art fidelity, manifold meshes, and low self-intersection rates across multiple occupanc y models (e.g., SALAD, 3DShape2VecSet, Michelangelo, IM-NET) and a Myles mesh dataset, typically within a few seconds on modern GPUs. The approach demonstrates strong generalization to varied occupancy nets and SDF-based inputs while maintaining efficient parallelizable computation, highlighting its practical impact for 3D reconstruction and generation from implicit representations.

Abstract

We introduce a dual contouring method that provides state-of-the-art performance for occupancy functions while achieving computation times of a few seconds. Our method is learning-free and carefully designed to maximize the use of GPU parallelization. The recent surge of implicit neural representations has led to significant attention to occupancy fields, resulting in a wide range of 3D reconstruction and generation methods based on them. However, the outputs of such methods have been underestimated due to the bottleneck in converting the resulting occupancy function to a mesh. Marching Cubes tends to produce staircase-like artifacts, and most subsequent works focusing on exploiting signed distance functions as input also yield suboptimal results for occupancy functions. Based on Manifold Dual Contouring (MDC), we propose Occupancy-Based Dual Contouring (ODC), which mainly modifies the computation of grid edge points (1D points) and grid cell points (3D points) to not use any distance information. We introduce auxiliary 2D points that are used to compute local surface normals along with the 1D points, helping identify 3D points via the quadric error function. To search the 1D, 2D, and 3D points, we develop fast algorithms that are parallelizable across all grid edges, faces, and cells. Our experiments with several 3D neural generative models and a 3D mesh dataset demonstrate that our method achieves the best fidelity compared to prior works.

Occupancy-Based Dual Contouring

TL;DR

This work addresses the challenge of converting neural occupancy functions into high-fidelity meshes. It introduces Occupancy-Based Dual Contouring (ODC), a learning-free method that replaces distance-based MDC components with GPU-accelerated 1D, 2D, and 3D point searches and an auxiliary 2D-point plane estimation, enabling accurate surface extraction from occupancy fields. By combining a robust line-binary search, local flat-plane modeling via 2D points, and quad-splitting polygonization, ODC achieves state-of-the-art fidelity, manifold meshes, and low self-intersection rates across multiple occupanc y models (e.g., SALAD, 3DShape2VecSet, Michelangelo, IM-NET) and a Myles mesh dataset, typically within a few seconds on modern GPUs. The approach demonstrates strong generalization to varied occupancy nets and SDF-based inputs while maintaining efficient parallelizable computation, highlighting its practical impact for 3D reconstruction and generation from implicit representations.

Abstract

We introduce a dual contouring method that provides state-of-the-art performance for occupancy functions while achieving computation times of a few seconds. Our method is learning-free and carefully designed to maximize the use of GPU parallelization. The recent surge of implicit neural representations has led to significant attention to occupancy fields, resulting in a wide range of 3D reconstruction and generation methods based on them. However, the outputs of such methods have been underestimated due to the bottleneck in converting the resulting occupancy function to a mesh. Marching Cubes tends to produce staircase-like artifacts, and most subsequent works focusing on exploiting signed distance functions as input also yield suboptimal results for occupancy functions. Based on Manifold Dual Contouring (MDC), we propose Occupancy-Based Dual Contouring (ODC), which mainly modifies the computation of grid edge points (1D points) and grid cell points (3D points) to not use any distance information. We introduce auxiliary 2D points that are used to compute local surface normals along with the 1D points, helping identify 3D points via the quadric error function. To search the 1D, 2D, and 3D points, we develop fast algorithms that are parallelizable across all grid edges, faces, and cells. Our experiments with several 3D neural generative models and a 3D mesh dataset demonstrate that our method achieves the best fidelity compared to prior works.
Paper Structure (42 sections, 2 theorems, 4 equations, 19 figures, 11 tables)

This paper contains 42 sections, 2 theorems, 4 equations, 19 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Occupancy Function Polygonization
  4. Neural Mesh Construction
  5. Problem Definition and Notations
  6. Background: Manifold Dual Contouring
  7. 1D Point Identification
  8. 3D Point Identification
  9. Polygonization
  10. Challenges of MDC on Occupancy Fields
  11. Occupancy-Based Dual Contouring
  12. 1D Point Search
  13. 2D Point Search
  14. 3D Point Identification
  15. Polygonization
  16. ...and 27 more sections

Key Result

lemma 1

Let $l_1$ and $l_2$ be lines that pass distinct 1D points $\mathbf{p}_{e_1}$ and $\mathbf{p}_{e_2}$, respectively. $l_1$ and $l_2$ are identical or meet at a unique point $\mathbf{u}$ which is neither $\mathbf{p}_{e_1}$ nor $\mathbf{p}_{e_2}$. Then, the 2D point $\mathbf{p}_f$ is chosen as either th

Figures (19)

  • Figure 1: Sharp feature preservation of occupancy-based models (from left to right): Smoothing method (LMC) lempitsky2010surface, Contouring DIF (CDIF) manson2011contouring, MISE occupancenetworks, and ODC (ours). ODC effectively captures sharp features.
  • Figure 2: 2D illustration comparing local planes derived from gradients and 2D points. The QEF identifies a point where local flat planes (thick dashed lines) passing through the 1D points (gray dots with green boundaries) meet. On the left, gradients are used as normals for the local flat planes. Although these planes fit the surface of infinitesimal regions, they do not represent larger surface areas within voxels, causing their intersections to fall outside the actual surface. In contrast, the right side shows local planes formed using 2D points (green dots with black boundaries). Since 2D points are determined by searching within a grid face, the resulting local planes align more closely with the actual surface inside the voxel, leading to improved QEF results. Refer to Section \ref{['sec:method_2d_search']} for more details on the 2D point search.
  • Figure 3: Overview of Occupancy-Based Dual Contouring (ODC). Dots with blue, red, and green boundaries represent grid vertices that are outside, inside, and 1D points, respectively. Dots with black boundaries, colored green and orange, represent 2D points and 3D points, respectively. Refer to Section \ref{['sec:method']} for details.
  • Figure 4: Illustration of the 2D point search. The orange line denotes the ground truth isocurve in 2D, and the dots with blue, red and green boundary denotes grid vertices outside, inside and 1D points, respectively. Please refer to the explanation on Section \ref{['sec:method_2d_search']}.
  • Figure 5: Qualitative results with SALAD. (a) Reach for the Spheres sellan2023reach: inflation and shrinkwrap method, (b) PoNQ maruani2024ponq: learning-based method, and (c) ODC (ours). Recent SDF-based methods fail to construct meshes with occupancy functions.
  • ...and 14 more figures

Theorems & Definitions (2)

  • lemma 1
  • lemma 2