纹理分析

纹理分析

@(Major Study)

纹理（Texture）

局部不规则而宏观有规律。

1. 纹理基元
2. 纹理基元的排列组合

统计法（Statistical approches）

利用纹理在空间上的灰度分布特性，从纹理图像中计算出一些在某个区域内或区域间边界处保持相对平稳的特征值，以此特征值来表示区域内的一致性以及区域间的相异性。

灰度分布统计

\(z\) : a random variable denoting intensity

\(p(z_i), i = 0,1,2,...,L - 1\) : the corresponding histogram 第 \(i\) 个灰度值 \(z_i\) 出现的频度

• the \(p\)s have values in the range [0,1]
• sum equals 1

\(L\) : the number of distinct intensity levels 图像的灰度级

the \(n\)th moment of \(z\) about the mean:
\[ \mu_n(z) = \sum_{i=0}^{L - 1}(z_i - m)^n p(z_i)\\ \mu_0 = 1\\ \mu_1 = 0 \]

1. 均值(mean value of \(z\), the average intensity) : \(m = \sum_{i=0}^{L-1} z_{i} p(z_i)\)
2. 标准差(the variance) : \(\sigma^2 = \mu_2(z)\)
   • important in texture description
   • a measure of intensity contrast
   • establish descriptors of relative smoothness
3. 平滑度(normalized) : \(R(z) = 1 - \frac{1}{1 + \sigma^2(z)}\)
4. 三阶矩(the third moment) : \(\mu_3= \sum_{i=0}^{L - 1} p^2(z_i)\)
   • a measure of the skewness of the histogram
5. 一致性(uniformity) : \(U = \sum_{i=0}^{L - 1} p^2(z_i)\)
   • maximum for an image which all intensity levels are equal (maximally uniform), and decreases from there
6. 熵(average entropy) : \(e(z) = - \sum_{i=0}^{L - 1} p(z_i) \log_{2} p(z_i)\)
   • a measure of variability
   • 0 for a constant image

clear;
close all; %清除MATLAB所有变量

灰度共生矩阵(Co-occurrence matrix)

\(\mathcal{Q}\) : an operator that defines the position of two pixels relative to each other

\(f\) : an image

\(L\) : possible intensity levels

\(G\) : a matrix whose element \(g_{ij}\) is the number of times that pixel pairs with intensities \(z_i\) and \(z_j\) occur in \(f\) in the position specified by \(Q\), where \(i \leq i, j \leq L\).

• gray-level (or intensity) co-occurrence matrix
• G : co-oocurrence matrix

自相关函数

结构法（Structural methods）