Three-dimensional co-occurrence matrices

1
Three-dimensional co-occurrence matrices Gabor
filtersCurrent progress

• Gray-level co-occurrence matrices
• Carl Philips
• Gabor filters
• Daniel Li
• Supervisor Jacob D. Furst, Ph.D.

2
Goals

• Comparison of co-occurrence matrices and Gabor
  filters
• 2D GLCM vs. 3D GLCM
• 2D Gabor vs. 3D Gabor
• Linear Discriminate Analysis vs. Decision Tree

3
3D image
4
Co-occurrence matrices

• Co-occurrence Matrix

• Distance 2
• Angle 0

1 2 3 4 5 6
1 0 1 1 0 0 0
2 1 0 0 1 0 0
3 1 2 0 0 0 0
4 0 0 1 0 0 1
5 1 1 0 1 0 0
6 1 1 0 1 0 0

• Original Image

1 6 3 4 2
5 6 5 1 5
2 4 4 3 5
4 3 6 2 2
1 3 2 1 1
5
Co-occurrence matrices

• Output 13 Haralick texture descriptors

• Energy
• Entropy
• Correlation
• Contrast
• Inverse Difference Moment
• Variance
• Sum Mean

• Inertia
• Cluster Shade
• Cluster Prominence
• Max Probability
• Inverse Variance
• Mode Probability

6
Co-occurrence matrices

• Global
• Features extracted are for the entire cube
• 13 Directions
• Four original 2D directions
• Nine new 3D directions
• 4 Distances
• 1, 2, 4, and 8 pixels
• 13 features extracted per distance per direction
• 13413676 features per cube

7
Principle Component Analysis

• 676 is far to many features
• Computers unable to perform LDA
• Retain 1.0000 variability with 5 component
• Main variable within each component is Cluster
  Tendency

8
Linear Discriminate Analysis
9
Decision Tree
10
Linear Discriminate Analysis results

• Classification of cubes using 2D Co-Occurrence
  Matrices and Linear Discriminate Analysis

• 57.6 of the training set correctly classified
• 58.2 of the testing set correctly classified

11
Linear Discriminate Analysis results

• Classification of cubes using 3D Co-Occurrence
  Matrices and Linear Discriminate Analysis

• 57.9 of the training set correctly classified
• 51.2 of the testing set correctly classified

12
Decision Tree results

• Classification of cubes using 2D Co-Occurrence
  Matrices and Decision Tree

• 93.4 of the training set correctly classified
• 88.8 of the testing set correctly classified

13
Decision Tree results

• Classification of cubes using 3D Co-Occurrence
  Matrices and Decision Tree

• 91.7 of the training set correctly classified
• 89.1 of the testing set correctly classified

14
Gabor filters, introduction

Sinusoid
Gaussian
Gabor
15
Gabor filters, a 2D example
16
Gabor filters, a 2D example
17
Gabor filters, a 2D example
18
Gabor filter Construction
Sinusoid1In2D Sinusoid2In2D
Gabor1In2D Gabor2In2D
Gaussian2 Gaussian3
Sinusoid1In3D Sinusoid2In3D Sinusoid3In3D
Gabor1In3D Gabor2In3D Gabor3In3D
19
Gabor filters The five filters
2D 1-dir and 2-dir
3D 1-dir, 2-dir, 3-dir
20
Gabor filters Our tests
x 3710
Liver cube
x 3710
Non-liver cube
21
Results for Gabor filters
22
Results for Gabor filters
23
Hypotheses for results

• 2D data sets were 20x / 60x larger than 3D data
  sets
• Scans were not isotropic, and distance in
  Z-direction not uniform across patients

24
Future work

• Reduce cases of 2D to be same as 3D and compare
  results
• Complete 3in3D testing
• Use isotropic data if possible

25
Questions

• Any questions?

26
Co-occurrence matrices

• Output 13 Haralick texture descriptors

• Inertia
• Contrast
• Energy

• Sum Mean
• Entropy
• Correlation
• Variance

27
Co-occurrence matrices

• Output 13 Haralick texture descriptors

• Max Probability
• Inverse Variance
• Mode Probability

• Homogeneity
• Cluster Shade
• Cluster Prominence