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Global Parameterization-based Texture Space Optimization

Wei Chen, Yuxue Ren, Na Lei, Zhongxuan Luo, Xianfeng Gu

TL;DR

The paper tackles wasted texture space and inefficient GPU addressing in texture mapping by introducing a global parameterization-based optimization that avoids NP-hard atlas packing. It employs a robust pipeline: data preparation, harmonic-map-based global parameterization, and a scan-line texture-image generation to produce tight, non-redundant textures. The approach leverages topological denoising and cotangent-weighted harmonic energy, with theoretical support through Radó's theorem for existence and uniqueness. Experiments demonstrate dense texture utilization and storage/rendering benefits, though area distortion from harmonic maps is a noted limitation. Overall, the work offers a practical pathway to compact texture spaces with improved rendering efficiency, while indicating avenues for improved parameterization in future work.

Abstract

Texture mapping is a common technology in the area of computer graphics, it maps the 3D surface space onto the 2D texture space. However, the loose texture space will reduce the efficiency of data storage and GPU memory addressing in the rendering process. Many of the existing methods focus on repacking given textures, but they still suffer from high computational cost and hardly produce a wholly tight texture space. In this paper, we propose a method to optimize the texture space and produce a new texture mapping which is compact based on global parameterization. The proposed method is computationally robust and efficient. Experiments show the effectiveness of the proposed method and the potency in improving the storage and rendering efficiency.

Global Parameterization-based Texture Space Optimization

TL;DR

The paper tackles wasted texture space and inefficient GPU addressing in texture mapping by introducing a global parameterization-based optimization that avoids NP-hard atlas packing. It employs a robust pipeline: data preparation, harmonic-map-based global parameterization, and a scan-line texture-image generation to produce tight, non-redundant textures. The approach leverages topological denoising and cotangent-weighted harmonic energy, with theoretical support through Radó's theorem for existence and uniqueness. Experiments demonstrate dense texture utilization and storage/rendering benefits, though area distortion from harmonic maps is a noted limitation. Overall, the work offers a practical pathway to compact texture spaces with improved rendering efficiency, while indicating avenues for improved parameterization in future work.

Abstract

Texture mapping is a common technology in the area of computer graphics, it maps the 3D surface space onto the 2D texture space. However, the loose texture space will reduce the efficiency of data storage and GPU memory addressing in the rendering process. Many of the existing methods focus on repacking given textures, but they still suffer from high computational cost and hardly produce a wholly tight texture space. In this paper, we propose a method to optimize the texture space and produce a new texture mapping which is compact based on global parameterization. The proposed method is computationally robust and efficient. Experiments show the effectiveness of the proposed method and the potency in improving the storage and rendering efficiency.
Paper Structure (9 sections, 1 theorem, 7 equations, 12 figures, 3 algorithms)

This paper contains 9 sections, 1 theorem, 7 equations, 12 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Theoretic Background
  4. Proposed Method and Algorithm
  5. Data Preparation
  6. Global Parameterization Based on Harmonic Map
  7. Texture Image Generating
  8. Experiments
  9. Conclusions

Key Result

Theorem 1

For any connected closed surface $S \hookrightarrow \mathbb{S}^3$ embedded in the three-dimensional sphere $\mathbb{S}^3$ of genus $g$, there exists $g$ handle loops $\{h_1, h_2, ..., h_g\}$ forming a basis for $H_1(O_S)$ and $g$ tunnel loops $\{t_1, t_2, ..., t_g\}$ forming a basis for $H_1(I_S)$.

Figures (12)

  • Figure 1: Smooth surface and its discretization: \ref{['fig:surface']} a smooth surface of a girl, \ref{['fig:mesh']} a discretization version of the surface which is a polygon mesh here.
  • Figure 2: Surfaces with different genus: \ref{['fig:genus_zero']} genus zero surfaces, \ref{['fig:genus_one']} genus one surfaces, and \ref{['fig:genus_two']} genus two surfaces. The two surfaces in each picture have the same genus.
  • Figure 3: Cut graph of a mesh: \ref{['fig:cg_eight']} an input mesh, \ref{['fig:cg_slice']} the fundamental domain produced by slicing along the cut graph in red.
  • Figure 4: Handle and tunnel loops: \ref{['fig:genus3']} a closed surface of genus three, \ref{['fig:genus3_loops']} the green lines show the handle loops, and the red lines show the tunnel loops.
  • Figure 5: Topological denoising based on homology detection, the green loops are the handle or tunnel loops, which their number is equal to the genus of the surface. \ref{['fig:eight']} a simple surface with genus $2$, \ref{['fig:clifford']} a complicated surface with genus $25$.
  • ...and 7 more figures

Theorems & Definitions (7)

  • definition 1: Genus
  • definition 2: Boundary
  • definition 3: Cut Graph
  • definition 4: Handle Loop
  • definition 5: Tunnel Loop
  • Theorem 1: Handle and Tunel Loops
  • definition 6: Parameterized Surface