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Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields

Haotian Yin, Przemyslaw Musialski

TL;DR

This work proposes a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces that achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

Abstract

We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields

TL;DR

This work proposes a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces that achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

Abstract

We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.
Paper Structure (31 sections, 10 equations, 4 figures, 2 tables)

This paper contains 31 sections, 10 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Implicit Neural Representations (INRs)
  4. Signed Distance Fields
  5. Surface Reconstruction
  6. Spatial Decomposition
  7. Surface Tracking
  8. Shrink Wrapping
  9. Surface Parameterization
  10. Methodology
  11. Shape representation
  12. Shape Shrinking
  13. Shrink Wrapping
  14. Iterative Shrinking by Scaled Gradient
  15. Shrinking Parameterization in 3D
  16. ...and 16 more sections

Figures (4)

  • Figure 1: We introduce a shrinking method, iteratively morphing a parameterized sphere to extract an implicitly represented surface, maintaining surface parameterization. From left to right, it show the shrinking process through iteration through the Spot geometry model.
  • Figure 2: Sketch map for anchor points base on spherical coordinates, we then get a initial parameterized sphere
  • Figure 3: From left to right is the sketch map of shrinking in a 2D scenario. The signed distance field implicitly encodes the target shape in the 2D plane, with blue indicating positive signed distances and red indicating negative. The process begins with an initial circle, which morphs into the target shape. Parameterized anchor points are set on the circle and gradually shrink by following the scaled gradient of the signed distance field until they conform to the target shape. Momentum processing is also incorporated in the 2D scenario when shrinking.
  • Figure 4: Qualitative comparisons of 3D surface reconstruction on Spot, Bunny and Duck model with MC and our shrinking parameterization method. Please note, we intentionally use a low-resolution volume discretization for the MC result in order to match the size of the resulting triangles to that of our results (cf. Section \ref{['sec:evaluation']}).