Texture Classification Using QMF Bank-Based Sub-band Decomposition A. Kundu J.L. Chen Carole BakhosEvan Kastner Dave AbramsTommy Keane Rochester Institute of Technology Pattern Recognition May 6 th, 2008

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

Introduction

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

Quadrature Mirror Filter Bank

QMF Filter Bank 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.

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

Tree Structure of Separable 2D QMF 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.

Feature Measures and System Description

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

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 = Σ i Σ j (i-j) 2 pθ(i,j) Angular second momentum = Σ i Σ j pθ 2 (i,j)

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)

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

Experimental Results

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

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 for testing)

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 for testing)

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

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)

Experiment Descriptions Cont’ Tables 1 – 2 Compare The Haralick Features To The QMF Features for the Varied Testing Sets As Described Above. 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

Results and Analysis Comparison 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.

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%.

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.