Texture Classification Using QMF Bank-Based Sub-band Decomposition A. Kundu J.L. Chen

1. Texture Classification Using QMF Bank-Based Sub-band DecompositionA. Kundu J.L. Chen Carole Bakhos Evan Kastner Dave Abrams Tommy Keane Rochester Institute of Technology Pattern Recognition May 6th, 2008

2. Overview • Theory of QMF banks • Design considerations • Feature measures proposed by Haralick and QMF features • Experimental Environment • Results • Conclusions

3. Introduction

4. Co-occurrence Matrices and QMF • Texture provides important information. • Co-occurrence matrices: • Proposed by Haralick. • Based on second-order distribution of gray levels. • Spatial relationship between pairs of gray levels of pixels. • Quadrature Mirror Filter (QMF): • Efficient information extraction and parallel implementation • Perfect reconstruction capability • Used as a set of localized filters to extract the information • Reduced amount of computations

5. Quadrature Mirror Filter Bank

6. QMF features: Haralick features in the low-low band Zero-crossing features in the other bands QMF Banks composed of: Decimators: partition the signal into several consecutive frequency bands. Interpolators: combine the partitioned signals back to the original signal without loss of information. QMF Filter Bank

7. Perfect Reconstruction • Decimators: • Sub-band filters have mirror-image conjugate symmetry about their mutual boundaries • Separable filters: • Interpolators:

8. The two responses are picked to be the same. Error due to distortion Stop Band error: Optimal H(w) obtained by minimizing the linear combination of both errors. Tree Structure of Separable 2D QMF

9. Feature Measures and System Description

10. Haralick Features • Spatial domains Nx={1,2,…,nx}, Ny={1,2,…,ny} • Gray level values G={0,1,2,…,L-1} • Image I assigns a G to each pair of Nx, Ny • I: Nx x Ny  G • Co-occurrence matrix gives us probabilities • Taken at θ =0, 45, 90, and 135 • 0: |x1-x2|=d; y1=y2 • 45: ((x1-x2=d) && (y1-y2=-d)) || ((x1-x2=-d) && (y1-y2=d)) • Similar for 90 and 135

11. Haralick Features • Measurement features use pθ to calculate necessary calculations • Visual texture characteristic features: contrast, angular second moment, correlation • Statistical features: inverse different moment, variance, sum average, sum variance, different variance • Information theory features: entropy, sum entropy, different entropy • Correlation features: information measures of correlation, maximal correlation coefficient • For example • Contrast = ΣiΣj(i-j)2 pθ(i,j) • Angular second momentum = ΣiΣj pθ2(i,j)

12. QMF Features • Low-low band (LPF in x and y) • Contrast, angular second momentum, entropy, inverse different moment, and information measures of correlation • High-low, low-high, and high-high (HPF’ed in x or y) • Quantize to G = {0, 255} • Co-occurrence matrices becomes 2x2 • Calculate zero-crossing feature: • ZC= pθ (0,255) + pθ (255,0) = 2 pθ (0,255)

13. System Scheme Linear Scaling Random Sample Selection Histogram Equalization QMF Haralick Features Extraction Classifier LL Gray Level Quantization Zero-crossing Features Extraction LH, HL, HH

14. Experimental Results

15. Experimental Overview • Objective: to compare QMF features and Haralick features • 10 Natural Textures from Brodatz’s texture album • 512x512, 8-bit, grayscale images • 6 Synthetic Textures • 256x256, 2-6 gray levels • L = 16 1-D Linear-Phase FIR used as Quadrature Mirror Filter

16. Natural Texture Setup • Each texture rotated +/- 10 degrees • Original and two rotations form a texture class • 16 nonoverlapped sub images extracted from each texture rotation • 8 of the 16 selected at random • 6 additional samples created by contrast adjustment of random selections • Total of 24 training samples and 30 test samples per class (3x8 for training, 3x the other 8 + 6 for testing)

17. Synthetic Texture Setup • Each texture rotated +/- 10 degrees • Four degrees of fineness • Original and two rotations at each level of fineness form a texture class (12 variants) • Extract four non-overlapped sub-images • Two of four randomly chosen as training samples. The other as test samples • Contrast adjustments made similar to natural texture setup • Total of 24 training samples and 30 test samples per class (3x8 for training, 3x the other 8 + 6 for testing)

18. Experiment • Haralick features with four dimensions computed for d = 1,2,3,4 separately, and those with 16 dimensions computed jointly for d = 1,2,3,4 • QMF features with 16 dimensions computed for d = 1,2,3,4 separately • Fischer Linear Discriminant used to classify features. • The majority vote of the five feature measures ultimately determines class membership

19. Experiment Descriptions • Goal: Haralick Features and QMF System Comparison • Motivation: Confirm that extensions made to Haralick feature selection are valid and at least as accurate, if not more so. • 2 Types of Experiments: • Test Data (images) very similar to Training Set • Test Data Qualitatively Different from Training Set • Contrast Issue: Desire similar lighting situation, but that is not a reasonable assumption. Therefore, use histogram equalization and assume texture primitives are robust against illumination variations. • Testing Sets: • Same Contrast as Training Set (Histogram Equalization • Different Contrast as Training Set (Use Linear Histogram Scaling)

20. Experiment Descriptions Cont’ • Haralick Features: • Using 4 Dimensions, Calculate With [d = 1 , 2 , 3 , 4] • Separately Using 16 Dimensions, Calculate With [d = 1 , 2 , 3 , 4] Jointly • QMF Features: • Using 16 Dimensions, Calculate With [d = 1 , 2 , 3 , 4] Separately Tables 1 – 2 Compare The Haralick Features To The QMF Features for the Varied Testing Sets As Described Above.

21. QMF Bank Succeeds in Finding Better Features in Non-Synthetic Images since the Texture of a Non-Synthetic Image is Described by More Than Co-Occurrence Matrices Feature Point Maps [Fig. 6] Represent The Spread of the Feature Distributions For The Textures, A Means of Visually Understanding The Classification. The Maps From Fig. 6 Show Good Separability Between Features, Allowing for Good Classification, Given A Well-Designed Classifier. Results and Analysis Comparison

22. Computational Consideration • Since the QMF bank works on subband images that are 25% of the size of the original image, and following through some computational calculations, it can be shown that the QMF bank requires always less (or at most, equal) computations to the purely Haralick feature system. • Further research in minimizing the computational load has been done with polyphase networks and pseudo-QMF banks and have been shown to be reduced by up to 50%.

23. Conclusions

24. Conclusions • QMF features work better than Harralick features. • Advantages of QMF: • Efficient information extraction: • Low-Low provides information on the spatial dependence • Other bands interactions provide structural information. • Implementation advantage: • Independent manipulation of the subbands, easy for parallel implementation. • CON and IMC have the best overall performances.