3D Texture Synthesis算法

Use 3D functions to define texture properties of objects
• Non‐trivial programming
• Flexibility
• Parametric control
• Unlimited resolution, antialiasing possible
• Low memory requirements
• Low‐cost visual complexity
• Adapts to arbitrary geometry

第一步：构造纹理特征

Analytic scalar function of world coordinates (x, y, z)
Texturing: evaluation of function on object surface
- Ray tracing: 3D intersection point with surface
Textures of natural objects
- Similarity between different patches
  - Repetitiveness, coherence
- Similarity on different resolution scales
  - Self-similarity
- But never completely identical
  - Additional disturbances, turbulence, noise
Procedural texture function
- Mimics statistical properties of natural textures
- Purely empirical approach
  - Looks convincing, but has nothing to do with material's physics

第二步：Perlin’s Noise生成随机纹理

[Perlin, Siggraph 1985]

Noise (x,y,z)
- Statistical invariance under rotation
- Statistical invariance under translation
- Narrow bandpass limit in frequency
Integer lattice (i, j,k)
- Random number at each lattice point (i, j,k)
  - Look-up table or hashing function
- Gradient lattice noise
  - Random gradient vectors
Evaluation at (x,y,z)
- Tri-linear interpolation
- Cubic interpolation (Hermite spline \(\to\) later)
Unlimited domain
- Lattice replicated to fill entire space
Fixed fundamental frequency of \(\sim\) 1 Hz over lattice
Smooth interpolation of interim values

噪声转化为纹理

Noise function
- “White” frequency spectrum
Natural textures
- Decreasing power spectrum towards high frequencies
Turbulence from noise
- Turbulence \((x)=\sum_{i=0}^{k}\) abs ( noise \((2^i x ) / 2^{i}\))
- Summation truncation
  - \(1 / 2^{k+1}\) < size of one pixel (band limit)
- 1. Term: noise (x)
- 1. Term: noise (2 x) / 2
- \(\dots\)
- Power spectrum: 1 / f
- (Brownian motion: \(1/f^2\))

应用

Reaction Diffusion Based Method
[Turk, Siggraph 1991]

Solid Textures

[Peachey, Siggraph 1985]

Solid texture functions in 3D space
Nonhomogeneous materials
• wood and stone

切开之后里面的体素也有纹理

Sample‐based texture synthesis

Methodology

Synthesize a surface texture by coloring mesh vertices
Extensions from 2D texture synthesis
Key issues
- Resampling
- 邻域信息：Size、Orientation

纹理只定义在mesh顶点上，这种算法常于mesh加密的情况

Vertex colors on three levels in the mesh hierarchy

例子

以下是mesh上某个点的邻域信息

第一步：把点的邻域参数化

第二步：采样

Recap: Texture Synthesis by Neighborhood Search

用多分辨率的方法实现上面过程，可以同时捕捉不同大小的特征

Differences between 2D and 3D

Texture Orientation

Methodology中提到这类算法需要使用某点邻域的方向，获取方向的方法有：

user‐specified
random (for isotropic textures)
smooth or symmetric (for anisotropic textures)
- by relaxation

不同orientation对纹理结果的影响：

Patch‐based Synthesis

[Praun et al., Siggraph 2001]

每贴一块就是这一块的参数化

大块贴完没贴满的部分，用周边的颜色产生一个patch

一个patch一般不是整块，而是基于基本元素的边界，这样是为了保证纹理特征的完整性

如果没有结构，可以随机设置边界

Patch Growth

Results: Splotches

(completely automatic: no direction field)

Controlling Direction and Scale

各向同性可以随机nomral，各向异性必须定义normal

Controlling Direction and Scale

各向同性	各向异性

Limitations

Feature‐aligned Texture Synthesis

[Xu et al., Siggraph Asia 2009]

第一步：提取边界特性和方向，把起点集中到一个不显眼的地方

结果对比：

不基于特征	基于特征

Progressively‐Variant Texture Synthesis

[Zhang et al., Siggraph 2003]

BTF Synthesis

[Tong et al., Siggraph 2002]

纹理效果与光照方向有关，这样合成效果更有立体感

Bidirectional Texture Functions (BTF): A collection of images of the same surface under different lighting and viewing directions.
✅ 6D Function ( \(x, y, l_θ, l_φ, v_θ, v_φ\) )
✅ Dense Sampling in Viewing/Lighting Directions
✅ Capturing Appearance of Real World Surface