Three-dimensional co-occurrence matrices & Gabor filters: Current progress Gray-level co-occurrence matrices Carl Philips Gabor filters Daniel Li Supervisor: Jacob D. Furst, Ph.D.

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

3D image

Co-occurrence matrices  Original Image o Co-occurrence MatrixDistance =2 Angle = 0°

 Energy  Entropy  Correlation  Contrast  Inverse Difference Moment  Variance  Sum Mean Co-occurrence matrices Output: 13 Haralick texture descriptors  Inertia  Cluster Shade  Cluster Prominence  Max Probability  Inverse Variance  Mode Probability

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  13*4*13=676 features per cube

Principle Component Analysis  676 is far to many features Computers unable to perform LDA  Retain % variability with 5 component Main variable within each component is Cluster Tendency

Linear Discriminate Analysis

Decision Tree

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

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

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

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

Gabor filters, introduction × SinusoidGaussian Gabor

Gabor filters, a 2D example

Gabor filter: Construction Gaussian2 Gaussian3 Sinusoid1In2D Sinusoid2In2D Sinusoid1In3D Sinusoid2In3D Sinusoid3In3D Gabor1In2D Gabor2In2D Gabor1In3D Gabor2In3D Gabor3In3D

Gabor filters: The five filters 2D: 1-dir and 2-dir 3D: 1-dir, 2-dir, 3-dir

Gabor filters: Our tests x 3710 Liver cube x 3710 Non-liver cube

Results for Gabor filters

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

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

Questions Any questions?

Sum Mean  Entropy  Correlation  Variance Co-occurrence matrices Output: 13 Haralick texture descriptors  Inertia  Contrast  Energy

Co-occurrence matrices Output: 13 Haralick texture descriptors  Homogeneity  Cluster Shade  Cluster Prominence  Max Probability  Inverse Variance  Mode Probability