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Implicit Neural Representation of Tileable Material Textures

Hallison Paz, Tiago Novello, Luiz Velho

TL;DR

This work addresses the challenge of representing seamless tileable textures with a compact, coordinate-based model. It introduces sinusoidal implicit neural representations (INRs) whose first layer is initialized with angular frequencies aligned to a period $P$, and proves that the network remains periodic with period $P$. A Poisson-based regularization on the torus enforces seamless boundaries while enabling high-fidelity, high-resolution reconstruction. The approach is extended to multiresolution networks (MRnet) to support continuous level-of-detail, and experiments demonstrate strong texture reconstruction and practical texture-mapping capabilities suitable for graphics pipelines.

Abstract

We explore sinusoidal neural networks to represent periodic tileable textures. Our approach leverages the Fourier series by initializing the first layer of a sinusoidal neural network with integer frequencies with a period $P$. We prove that the compositions of sinusoidal layers generate only integer frequencies with period $P$. As a result, our network learns a continuous representation of a periodic pattern, enabling direct evaluation at any spatial coordinate without the need for interpolation. To enforce the resulting pattern to be tileable, we add a regularization term, based on the Poisson equation, to the loss function. Our proposed neural implicit representation is compact and enables efficient reconstruction of high-resolution textures with high visual fidelity and sharpness across multiple levels of detail. We present applications of our approach in the domain of anti-aliased surface.

Implicit Neural Representation of Tileable Material Textures

TL;DR

This work addresses the challenge of representing seamless tileable textures with a compact, coordinate-based model. It introduces sinusoidal implicit neural representations (INRs) whose first layer is initialized with angular frequencies aligned to a period , and proves that the network remains periodic with period . A Poisson-based regularization on the torus enforces seamless boundaries while enabling high-fidelity, high-resolution reconstruction. The approach is extended to multiresolution networks (MRnet) to support continuous level-of-detail, and experiments demonstrate strong texture reconstruction and practical texture-mapping capabilities suitable for graphics pipelines.

Abstract

We explore sinusoidal neural networks to represent periodic tileable textures. Our approach leverages the Fourier series by initializing the first layer of a sinusoidal neural network with integer frequencies with a period . We prove that the compositions of sinusoidal layers generate only integer frequencies with period . As a result, our network learns a continuous representation of a periodic pattern, enabling direct evaluation at any spatial coordinate without the need for interpolation. To enforce the resulting pattern to be tileable, we add a regularization term, based on the Poisson equation, to the loss function. Our proposed neural implicit representation is compact and enables efficient reconstruction of high-resolution textures with high visual fidelity and sharpness across multiple levels of detail. We present applications of our approach in the domain of anti-aliased surface.
Paper Structure (20 sections, 1 theorem, 11 equations, 11 figures, 1 table)

This paper contains 20 sections, 1 theorem, 11 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and related methods
  3. Texture representations
  4. Tileable Textures
  5. Neural Textures
  6. Implicit neural representations
  7. Periodic Neural Networks
  8. Shallow Sinusoidal networks
  9. Deep sinusoidal networks
  10. Multiresolution sinusoidal networks
  11. Frequency initialization
  12. Network training
  13. Experiments
  14. Seamless Tileable Materials
  15. Repeating Patterns in Sample
  16. ...and 5 more sections

Key Result

Theorem 1

If the first layer of a sinusoidal MLP $f$ is periodic with period $P$, then $f$ is also periodic with period $P$.

Figures (11)

  • Figure 1: Original image (left); reconstruction of the network (right)
  • Figure 2: Reconstructed multiresolution levels extrapolation. Top left: level 2; bottom left: level 4; right: level 6.
  • Figure 3: (a) Full training data. (b) Network reconstruction from full data. (c) Masked training data; black pixels were not provided in training. (d) Network reconstruction from masked data.
  • Figure 4: From left to right: training data, network reconstruction in $[0, 3]^2$, and zoom in one tile to highlight the reconstruction artifact.
  • Figure 5: On the left, the masked input data, where the black pixels were removed from training. On the right, the network reconstruction.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Theorem 1