【Basic】Image Texture Analysis in MATLAB: Using Gray Level Co-occurrence Matrices

# 2.1 Definition and Calculation of the Gray-Level Co-occurrence Matrix (GLCM)

The Gray-Level Co-occurrence Matrix (GLCM) is a statistical tool used to describe the spatial relationships of pixel pairs within an image. It records the frequency at which a pair of pixels with a specific gray-level value occurs at a given distance and direction in the image.

Given an image I, with dimensions M×N, the GLCM G(i, j; d, θ) is defined as:

G(i, j; d, θ) = #{ (x, y), (x', y') ∈ I | I(x, y) = i, I(x', y') = j, |x - x'| = d, θ = arctan((y' - y) / (x' - x)) }

where:

* i and j are gray-level values
* d is the distance between pixel pairs
* θ is the direction between pixel pairs (usually 0°, 45°, 90°, and 135°)

# 2. GLCM Theory

### 2.1 Definition and Calculation of the Gray-Level Co-occurrence Matrix (GLCM)

The Gray-Level Co-occurrence Matrix (GLCM) is a commonly used statistical feature in image texture analysis. It describes the gray-level value relationships of adjacent pixel pairs within an image.

**Definition:**

For a given image I, its GLCM G(i, j; d, θ) is defined as:

G(i, j; d, θ) = #{ (p, q) ∈ I | I(p) = i, I(q) = j, ||p - q|| = d, θ = ∠(p - q) }

where:

* i and j are gray-level values
* d is the distance between pixel pairs
* θ is the angle between pixel pairs

**Calculation:**

The GLCM can be calculated using the following steps:

1. Convert the image to grayscale.
2. For each pixel in the image, calculate its distance and angle with surrounding pixels.
3. Assign pixel pairs to the corresponding GLCM cells based on distance and angle.
4. Count the number of pixel pairs in each cell.

### 2.2 Feature Extraction from the Gray-Level Co-occurrence Matrix

The GLCM provides rich texture information, which can be quantified by extracting its features. These features can be categorized into three classes:

#### 2.2.1 Statistical Features

***Energy:** Measures the closeness of gray-level values in the GLCM.
***Entropy:** Measures the uniformity of gray-level value distribution in the GLCM.
***Contrast:** Measures the magnitude of gray-level value differences in the GLCM.
***Correlation:** Measures the correlation between gray-level values in the GLCM.

#### 2.2.2 Structural Features

***Homogeneity:** Measures the equality of gray-level values in the GLCM.
***Heterogeneity:** Measures the difference of gray-level values in the GLCM.
***Max Probability:** The most frequent gray-level value of pixel pairs in the GLCM.
***Inertia:** Measures the extent to which gray-level values in the GLCM are distributed along the diagonals.

#### 2.2.3 Information Theoretic Features

***Information Measure 1:** Measures the entropy of gray-level value distribution in the GLCM.
***Information Measure 2:** Measures the uniformity of gray-level value distribution in the GLCM.
***Correlation:** Measures the correlation between gray-level values in the GLCM.

### Code Example

% Calculate Gray-Level Co-occurrence Matrix
glcm = graycomatrix(I, 'Offset', [2 0]);

% Extract Statistical Features
contrast = graycoprops(glcm, 'Contrast');
correlation = graycoprops(glcm, 'Correlation');
energy = graycoprops(glcm, 'Energy');
homogeneity = graycoprops(glcm, 'Homogeneity');

% Extract Structural Features
inertia = graycoprops(glcm, 'Inertia');
maxprob = graycoprops(glcm, 'MaxProbability');

% Extract Information Theoretic Features
entropy = graycoprops(glcm, 'Entropy');
info1 = graycoprops(glcm, 'InfoMeasure_1');
info2 = graycoprops(glcm, 'InfoMeasure_2');

**Code Logic:**

* The `graycomatrix` function calculates the GLCM.
* The `graycoprops` function extracts GLCM features.
* Each feature extraction function returns a struct containing the values of the corresponding features.

# 3 Practical Applications of the Gray-Level Co-occurrence Matrix

### 3.1 Image Texture Classification

The Gray-Level Co-occurrence Matrix plays a crucial role in image texture classification. By extracting features from the GLCM, the statistical, structural, and information-theoretic characteristics of image texture can be effectively represented, thus achieving image texture classification.

**Steps:**

1. **Calculate the Gray-Level Co-occurrence Matrix:** Calculate the GLCM of the image based on specified distance and angle.
2. **Feature Extraction:** Extract statistical features (such as mean, standard deviation, energy), structural features (such as correlation, contrast, entropy), and information-theoretic features (such as mutual information, correlation) from the GLCM.
3. **Feature Selection:** Select distinctive features to reduce the dimensionality of the feature space and improve classification accuracy.
4. **Classification:** Classify the extracted features using machine learning algorithms (such