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Deep Level Sets: Implicit Surface Representations for 3D Shape Inference

Mateusz Michalkiewicz, Jhony K. Pontes, Dominic Jack, Mahsa Baktashmotlagh, Anders Eriksson

TL;DR

This work addresses the boundary accuracy limitations of voxel-based 3D reconstructions by introducing an end-to-end model that predicts implicit surfaces as oriented level sets of a continuous embedding function. A variational loss combines data fidelity with geometric priors, enabling arbitrary topology and improved surface detail. Empirical results on ShapeNet show that the implicit level-set representation yields more accurate and richly detailed 3D shapes than voxel-based approaches, with performance improving at higher resolutions. The method provides a flexible framework that integrates level-set theory with deep learning and can be extended to higher-resolution inference and segmentation tasks.

Abstract

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract 3D surface meshes. To overcome this limitation, we propose an end-to-end trainable model that directly predicts implicit surface representations of arbitrary topology by optimising a novel geometric loss function. Specifically, we propose to represent the output as an oriented level set of a continuous embedding function, and incorporate this in a deep end-to-end learning framework by introducing a variational shape inference formulation. We investigate the benefits of our approach on the task of 3D surface prediction and demonstrate its ability to produce a more accurate reconstruction compared to voxel-based representations. We further show that our model is flexible and can be applied to a variety of shape inference problems.

Deep Level Sets: Implicit Surface Representations for 3D Shape Inference

TL;DR

This work addresses the boundary accuracy limitations of voxel-based 3D reconstructions by introducing an end-to-end model that predicts implicit surfaces as oriented level sets of a continuous embedding function. A variational loss combines data fidelity with geometric priors, enabling arbitrary topology and improved surface detail. Empirical results on ShapeNet show that the implicit level-set representation yields more accurate and richly detailed 3D shapes than voxel-based approaches, with performance improving at higher resolutions. The method provides a flexible framework that integrates level-set theory with deep learning and can be extended to higher-resolution inference and segmentation tasks.

Abstract

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract 3D surface meshes. To overcome this limitation, we propose an end-to-end trainable model that directly predicts implicit surface representations of arbitrary topology by optimising a novel geometric loss function. Specifically, we propose to represent the output as an oriented level set of a continuous embedding function, and incorporate this in a deep end-to-end learning framework by introducing a variational shape inference formulation. We investigate the benefits of our approach on the task of 3D surface prediction and demonstrate its ability to produce a more accurate reconstruction compared to voxel-based representations. We further show that our model is flexible and can be applied to a variety of shape inference problems.

Paper Structure

This paper contains 8 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. A Variational Loss Function for Shape Inference
  5. Experimental Validation
  6. Implementation Details
  7. Results
  8. Conclusion and Future Work

Figures (4)

  • Figure 1: 3D shape inference from a single image. (top left) Input image, (top right) ground-truth, (bottom left) predicted shape using a volumetric representation, (bottom right) predicted shape using our proposed implicit shape representation. Both representations have a resolution of $20^3$.
  • Figure 2: Four common representations of 3D shape along with their advantages and disadvantages.
  • Figure 3: An overview of the network architecture used.
  • Figure 4: 3D shape inference from a single 2D image. The columns are (a) ground-truth shape, (b) input image, (c) predicted shape, level set, $20^3$, (d) predicted shape, voxels, $20^3$, (e) predicted shape, level set, $30^3$, (f) predicted shape, voxels, $30^3$.