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Texture Analysis

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Texture Analysis: Step-by-Step Guide with Examples

1. Introduction to Texture in Images

Texture refers to the spatial arrangement of intensity or color patterns in an image.
It is widely used for classification, segmentation, and pattern recognition.

Common approaches for texture analysis:

  • Statistical methods (GLCM, LBP)
  • Filter-based methods (Gabor filters, Laws’ texture energy)
  • Texture-based segmentation

2. Statistical Texture Analysis

2.1 Gray Level Co-occurrence Matrix (GLCM)

GLCM captures how often pixel pairs with specific intensities occur at a given offset.

Example 4×4 patch:

0 1 1 2
2 0 1 1
0 2 2 1
1 0 1 2

Step 1: Decide direction & distance → Horizontal neighbor, distance = 1.

Step 2: List all horizontal pixel pairs row by row:
(0,1), (1,1), (1,2), (2,0), (0,1), (1,1), (0,2), (2,2), (2,1), (1,0), (0,1), (1,2)

Step 3: Count occurrences of each pair (i,j) → form raw GLCM:

0 1 2
0 0 3 2
1 1 2 2
2 1 1 1

Step 4: Normalize GLCM (divide each entry by total pairs = 12):

0 1 2
0 0 0.25 0.1667
1 0.0833 0.1667 0.1667
2 0.0833 0.0833 0.0833

Step 5: Compute features from normalized GLCM:

5a. Contrast

Formula: Contrast = Σ |i-j|² * P(i,j)

    • Contribution of each pair:
      • |0-0|²*0 = 0
      • |0-1|²*0.25 = 1*0.25 = 0.25
      • |0-2|²*0.1667 = 4*0.1667 ≈ 0.6668
      • |1-0|²*0.0833 = 1*0.0833 ≈ 0.0833
      • |1-1|²*0.1667 = 0
      • |1-2|²*0.1667 = 1*0.1667 ≈ 0.1667
      • |2-0|²*0.0833 = 4*0.0833 ≈ 0.3332
      • |2-1|²*0.0833 = 1*0.0833 ≈ 0.0833
      • |2-2|²*0.0833 = 0

Contrast ≈ 1.583

5b. Energy

Formula: Energy = Σ P(i,j)²

      • 0² + 0.25² + 0.1667² + 0.0833² + 0.1667² + 0.1667² + 0.0833² + 0.0833² + 0.0833²
      • = 0 + 0.0625 + 0.0278 + 0.0069 + 0.0278 + 0.0278 + 0.0069 + 0.0069 + 0.0069 ≈ 0.1515

Energy ≈ 0.1515

5c. Homogeneity

Formula: Homogeneity = Σ P(i,j) / (1 + |i-j|)

      • (0/(1+0)) + (0.25/2) + (0.1667/3) + (0.0833/2) + (0.1667/1) + (0.1667/2) + (0.0833/3) + (0.0833/2) + (0.0833/1)
      • = 0 + 0.125 + 0.0556 + 0.0417 + 0.1667 + 0.0833 + 0.0278 + 0.0417 + 0.0833 ≈ 0.625

Homogeneity ≈ 0.625

5d. Correlation

Formula: Correlation = Σ [(i-μi)(j-μj)P(i,j)] / (σi * σj)

Using μi ≈ 1.083, μj ≈ 1.083, σi ≈ 0.745, σj ≈ 0.745

Correlation ≈ 0.0417

Result: Features computed step-by-step from normalized GLCM:

    • Contrast ≈ 1.583
    • Energy ≈ 0.1515
    • Homogeneity ≈ 0.625
    • Correlation ≈ 0.0417

2.2 Local Binary Patterns (LBP)

LBP encodes the neighborhood of each pixel into a binary number based on whether neighbors are greater or smaller than the center pixel.

Example 3×3 patch:

52 55 61
62 59 55
63 65 66

Step 1: Center pixel = 59

Step 2: Compare neighbors ≥ center → 1, else 0

Neighbor Value Comparison
Top-left 52 0
Top-center 55 0
Top-right 61 1
Left 62 1
Right 55 0
Bottom-left 63 1
Bottom-center 65 1
Bottom-right 66 1

Step 3: Arrange clockwise from top-left → Binary pattern = 00110111

Step 4: Convert binary to decimal

Step 4a: Assign powers of 2
Bit position 7 6 5 4 3 2 1 0
Binary 0 0 1 1 0 1 1 1
Weight (2^n) 128 64 32 16 8 4 2 1
Step 4b: Multiply each bit by its weight
  • 0*128=0
  • 0*64=0
  • 1*32=32
  • 1*16=16
  • 0*8=0
  • 1*4=4
  • 1*2=2
  • 1*1=1
Step 4c: Sum all values

0+0+32+16+0+4+2+1 = 55

✅ Result: LBP value for center pixel = 55

3. Filter-based Texture Analysis

3.1 Gabor Filters

Gabor filters analyze texture by frequency and orientation.

G(x,y) = exp(-(x'^2 + γ^2*y'^2)/2σ^2) * cos(2π*x'/λ + φ)
x' = x cosθ + y sinθ
y' = -x sinθ + y cosθ

Example 3×3 patch, θ=0°, λ=4, σ=1:

0.8 0.9 1.0
0.7 0.85 0.95
0.6 0.75 0.9

Step 1: Convolve patch with Gabor kernel

Step 2: Sum results → Filtered response highlights horizontal texture patterns

3.2 Laws’ Texture Energy Measures

Step 1: Apply Laws’ 1D kernels:

  • L5 = [1 4 6 4 1]
  • E5 = [-1 -2 0 2 1]
  • S5 = [-1 0 2 0 -1]

Step 2: Convolve kernel with 5×5 patch → square → sum → Texture energy

Example: L5*E5 response squared & summed → Texture energy = 2025

4. Texture-based Segmentation

Step 1: Divide image into windows (e.g., 3×3)

Step 2: Compute texture features for each window (GLCM contrast, LBP, etc.)

Step 3: Apply segmentation rule:

  • Contrast > 10 → Region 1
  • Contrast ≤ 10 → Region 2

Example:

Contrast=12 Contrast=2
Contrast=11 Contrast=3

Segmented Regions:

Region 1 Region 2
Region 1 Region 2

5. Summary Table

Method Step-by-Step Computation Result / Feature
GLCM Compute horizontal neighbor co-occurrence, then Contrast, Energy, Homogeneity, Correlation Contrast=12, Energy=0.34, Homogeneity=0.62, Correlation≈0.21
LBP Compare neighbors with center, binary → decimal Decimal LBP = 55
Gabor Filter Convolve patch with kernel (θ=0°) Filtered response highlights horizontal patterns
Laws’ Energy Convolve with L5*E5, square, sum Texture energy=2025
Texture-based Segmentation Cluster pixels by GLCM/contrast or LBP Contrast>10 → Region 1, else Region 2
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