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Optimizing 3D Geometry Reconstruction from Implicit Neural Representations

Shen Fan, Przemyslaw Musialski

TL;DR

This method integrates periodic activation functions, positional encodings, and normals into the neural network architecture, which significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

Abstract

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary as the zero-level set of the learned continuous function and learns a mapping from a low-dimensional latent space to the space of all possible shapes represented by its signed distance function. However, most INRs struggle to retain high-frequency details, which are crucial for accurate geometric depiction, and they are computationally expensive. To address these limitations, we present a novel approach that both reduces computational expenses and enhances the capture of fine details. Our method integrates periodic activation functions, positional encodings, and normals into the neural network architecture. This integration significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

Optimizing 3D Geometry Reconstruction from Implicit Neural Representations

TL;DR

This method integrates periodic activation functions, positional encodings, and normals into the neural network architecture, which significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

Abstract

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary as the zero-level set of the learned continuous function and learns a mapping from a low-dimensional latent space to the space of all possible shapes represented by its signed distance function. However, most INRs struggle to retain high-frequency details, which are crucial for accurate geometric depiction, and they are computationally expensive. To address these limitations, we present a novel approach that both reduces computational expenses and enhances the capture of fine details. Our method integrates periodic activation functions, positional encodings, and normals into the neural network architecture. This integration significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

Paper Structure

This paper contains 15 sections, 11 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Learning with Explicit Representations
  4. Implicit Neural Representations
  5. Methodology
  6. Formulation
  7. Activation Functions
  8. Positional Encoding
  9. Normals
  10. Evaluation Method
  11. Results
  12. Dataset
  13. Qualitative Results
  14. Quantitative Results
  15. Conclusion and Future Work

Figures (5)

  • Figure 1: Reconstruction comparison between DeepSDF and our model.'GT' denotes the ground truth.
  • Figure 2: Reconstruction results using activation function from HOSC and SIREN, respectively.
  • Figure 3: Reconstruction results using activation function from HOSC and SIREN, respectively..
  • Figure 4: Reconstruction results with or without normals
  • Figure 5: Reconstruction of test shapes. From left to right alternating: ground truth shape and our reconstruction. The right most column show failure case. This failure are likely due to lack of training data and failure of minimization convergence.