The goal of this thesis is to provide a texture generation approach that works on cellular textures and enables structural modifications when generating a new output exemplar.
In the field of computer graphics, two-dimensional textures are an efficient tool to make a virtual scene richer in detail and therefore visually more appealing. Consequently, the perceived quality of a rendered image highly depends on the quality of the used textures.
Unfortunately, creating textures by hand is a time-consuming task, which in extreme cases can only be performed by professional artists. On the other hand, the use of real photographs often requires post-processing steps, e.g. to make them tileable so that there are no visual transitions between multiple texture copies covering a large surface.
Approaches exist that automatically create new texture variants with different sizes based on a given input sample. However, most of these methods focus on generating output textures that are as similar to the original input as possible, while not allowing for further modifications.
Table of Contents
1 Introduction
2 Related Work
2.1 Texture Perception
2.2 Stochastic Texture Synthesis
2.3 Non-parametric Texture Synthesis
2.4 Pixel-based Non-parametric Texture Synthesis
2.5 Patch-based Synthesis
2.6 Multi-Exemplar Synthesis
2.7 Synthesis Output Manipulation
2.8 Implications for this Thesis
3 Fundamentals
3.1 Textures
3.1.1 Texture Types
3.1.2 Texture Mapping
3.2 Image Filters
3.3 Image Pyramids
3.3.1 Gaussian Pyramids
3.3.2 Laplacian Pyramids
3.3.3 Steerable Pyramids
3.4 Worley-Noise
3.5 Voronoi Diagrams
3.6 Principal Component Analysis
3.7 Gradient Descent
4 Methods and Implementation
4.1 Cellular Textures
4.2 Parameters
4.3 Analysis
4.3.1 Cell Segmentation
4.3.2 Initial Parameter Generation
4.3.3 Parameter Optimization
4.4 Generation
4.4.1 Cell Structure Generation
4.4.2 Statistical Seed Placement
4.4.3 Placement based on binary Input
4.4.4 Storing Individual Cells
4.5 Synthesis
4.5.1 Filling Cells with Color
4.5.2 Texture Refinement
4.5.3 Multi-Exemplar Synthesis
5 Evaluation
5.1 Parameter Analysis
5.2 Generated Results
5.2.1 Tileable Input
5.2.2 Parameter Preservation
5.2.3 Parameter Modification
5.2.4 Multi-Input Synthesis
5.3 Limitations
6 Conclusion and Future Work
6.1 Conclusion
6.2 Future Work
A Gradient Descent Derivations
A.1 Norm Derivations
A.2 Seed Point Optimization
A.3 Simplified Optimization
A.4 Including Vector Transformations
B Texture Comparison
Research Objectives and Key Themes
The primary objective of this thesis is to develop a novel texture generation framework specifically for cellular textures. The research addresses the current limitation in texture synthesis where traditional methods focus on reproducing visual similarity without offering the user control over the underlying structural characteristics. The thesis proposes a methodology that analyzes a given input sample to extract parameters defining its cellular structure—such as cell distribution, orientation, and expansion—enabling users to modify these parameters to generate new, custom-tailored output exemplars while preserving the original visual quality.
- Analysis of cellular structures using Voronoi diagrams and Worley noise.
- Implementation of user-driven parameter optimization via Gradient Descent.
- Generation of customized cellular textures through statistical and structural control.
- Synthesis techniques for high-quality, pixel-refined output based on input exemplars.
- Evaluation of synthesis results including tileability and multi-exemplar blending.
Excerpt from the Book
4.3.3 Parameter Optimization
When considering a perfect Voronoi diagram, the seed point of each cell is not necessarily identical to the center of gravity of the same cell. Even small changes in the seeds position can lead to significant change in the location of cell boundaries which can be seen in Figure 4.4. For that reason, a false underlying structure would be generated by using the calculated centroids as seeds for a Voronoi grid that should represent the cellular characteristics of an input image (see Figure 4.5).
In contrast, if the borders of the actual cells are known, the correct seed positions can be calculated. Due to the definition of Worley noise or Voronoi diagrams in Euclidean space (see Chapter 3), it holds that for each border separating two cells: ||S0 - x||2 = ||S1 - x||2, ∀x ∈ P (4.2) where S0 and S1 are the seed points of cell 0 and cell 1, respectively, and P is the set of all points on the border between these two cells.
Summary of Chapters
1 Introduction: Provides context on computer-generated imagery, the importance of textures, and the motivation for developing user-controllable texture synthesis.
2 Related Work: Reviews existing literature on texture perception, stochastic and non-parametric synthesis, and previous approaches to structural modification.
3 Fundamentals: Establishes background knowledge on texture mapping, image filters, pyramids, noise functions, Voronoi diagrams, PCA, and Gradient Descent.
4 Methods and Implementation: Details the core methodology, including input analysis, parameter extraction, cellular structure generation, and the synthesis pipeline.
5 Evaluation: Assesses the efficacy of the parameter analysis, shows various synthesized results, and discusses the limitations of the proposed approach.
6 Conclusion and Future Work: Summarizes the contributions of the thesis and outlines potential improvements and extensions, such as 3D implementation.
Key Terms
Texture synthesis, cellular textures, Voronoi structure, image analysis, parameter optimization, Gradient Descent, Niblack algorithm, Voronoi diagrams, Worley noise, image pyramids, mesh relaxation, PCA, texture refinement, tileability, feature-based blending.
Frequently Asked Questions
What is the core focus of this research?
The research focuses on the analysis and synthesis of cellular textures, allowing users to modify the underlying structure of a texture while maintaining its visual properties.
What is the primary objective of this thesis?
The goal is to provide a texture generation approach that enables structural modifications when synthesizing new output, bridging the gap between traditional reproduction and user-guided design.
Which scientific methods are primarily employed?
The approach utilizes image processing techniques such as cell segmentation, Worley noise generation, Voronoi diagrams for structural modeling, and Gradient Descent for parameter optimization.
What are the central thematic areas?
The themes include texture analysis, cellular structure modeling, parameter-based synthesis, and refinement techniques to ensure visual quality.
What does the main body of the work cover?
The main body covers the theoretical fundamentals, the implementation of the analysis and synthesis pipeline, and a comprehensive evaluation of the results on various texture types.
Which keywords characterize this work?
Key terms include texture synthesis, cellular textures, Voronoi structure, optimization, and image processing.
How is the seed point optimization performed for cellular structures?
Optimization is achieved by minimizing the energy function between cell borders and seed points using the Gradient Descent algorithm, ensuring that seed points are equidistant to the cell boundaries.
Why are standard pixel-based synthesis methods often insufficient for this task?
Traditional methods primarily aim for visual similarity to a source image and do not account for the underlying structural components of cellular images, making them unsuitable for interactive structural modifications.
- Arbeit zitieren
- Thomas Conraths (Autor:in), 2018, Parameter Analysis and Synthesis of Cellular Textures, München, GRIN Verlag, https://www.grin.com/document/1194367
