Texture Classification Using QMF Bank-Based Sub-band

Decomposition

A. Kundu J.L. ChenCarole Bakhos Evan Kastner

Dave Abrams Tommy Keane

Rochester Institute of Technology

Pattern Recognition

May 6th, 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 = ΣiΣj(i-j)2 pθ(i,j) Angular second momentum = ΣiΣj pθ2 (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 8 + 6 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 8 + 6 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 validand 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

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.