Texture Classification Using Wavelets with aCluster-Based Feature Extraction

Gang yua, Sagar V. Kamarthib

aDepartment ofMechanical Engineering and AutomationHarbin Institute ofTechnology (HIT) Shenzhen Graduate School

HIT Campus Xili Shenzhen University TownShenzhen, Guangdong 518055

P.R.China

bMechanical and Industrial EngineeringNortheastern University

360 Huntington Ave. 334SNBoston, MA 02115

U.S.A

Abstract-After several decades of research, the developmentof an effective feature extraction method for textureclassification is still an ongoing effort. In this paper, we proposea novel approach for texture classification using a newcluster-based feature extraction method that divides thematrices of computed two-dimensional wavelet coefficients intoclusters. The features that contain the information effective forclassifying texture images are computed from the energycontent of the clusters, and these feature vectors serve as inputpatterns to a neural network for texture classification. Theresults show that the discrimination performance obtained withthe proposed cluster-based feature extraction method issuperior to the performance obtained using conventionalfeature extraction methods, and robust to the rotation and scaleinvariant texture classification.

I. INTRODUCTION

Texture classification is a fundamental problem incomputer vision and pattern recognition with a wide varietyof applications such as remote sensing, medical imageanalysis and quality inspection. A critical issue in textureclassification is how to characterize textural structure anddefine a perceptually meaningful distance/similarity measurebetween textures, which remains a difficult problem, despiteextensive research work has been done for last four decades.

The feature extraction methods for texture classificationcan be roughly grouped into five categories: statistical,structural, model-based, spectral, and multi-scaleapproaches. Statistical methods are based on the localcorrelation of image pixels; some ofthe most useful statisticalmethods are co-occurrence matrices [1], autocorrelationfeatures [2-3], and gray level difference matrices [4].Structural methods use the texture primitives and syntacticrules for their placement to describe the texture [1].Model-based methods are based on the construction of amodel for texture descriptions; the most popular ones areMarkov random field models [5] and fractal models [6].

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Spectral methods are based on the distribution of the textureenergy over the frequencies [7]. Multi-scale methods arebased on multi-scale and multi-orientation processing oftexture information. Based on recent developments inspatial/frequency analysis, Gabor filters have beenintensively studied for texture analysis [8]-[12], but thedecompositions using Gabor filters are computationallyintensive, and the outputs of Gabor filters are not mutuallyorthogonal, which limits their applicability for textureanalysis. As a new spatial/scale analysis, wavelets can be usedto avoid most problems of Gabor filters, which provide aprecise and unifying framework for the analysis andcharacterization of a signal at different scales [13]. Previousresearch works using wavelets for texture classification arereviewed in section III.

In previous work [14], we developed a new cluster-basedfeature extraction method based on two-dimensional (2-D)discrete wavelet transform (DWT), and verified theeffectiveness of the method on a wood knot defect detectionproblem. In this paper, we investigate the effectiveness ofthecluster-based feature extraction method for textureclassification. Twenty four textures are used in theclassification experiments. The results show that thediscrimination performance obtained with the proposedcluster-based method is superior to the performance obtainedusing conventional feature extraction methods, and is robustto the rotation and scale invariant texture classification.

In the next section, we briefly review the 2-D discretewavelet transform (DWT) for image analysis. Previousresearch efforts on wavelet-based texture classification arereviewed in section III. Then, we introduce the proposedcluster-based feature extraction method in section IV. SectionV describes the experimental date sets, texture features, andclassification algorithm. Section VI demonstrates theeffectiveness of the proposed method by evaluating theresults using texture classification experiments.

II. 2-D DISCRETE WAVELET TRANSFORM Let an image be viewed as a finite energy function ( )yxf , .

Let Z and R denote the set of integers and real numbers, respectively. And let ( )

ZV

jj ∈2 be a separable multi-resolution

approximation of ( )RL 22 , and let ( ) ( ) ( )yxyx φφφ =, be the associated two-dimensional scaling function. If ( )xψ is the one-dimensional wavelet associated with the scaling function

( )xφ , then the 2-D separable wavelets can be defined as ( ) ( ) ( )yxyx ψφψ =,1 , ( ) ( ) ( )yxyx φψψ =,2 , and ( ) ( ) ( )yxyx ψψψ =,3 . For any wavelet decomposition

scale 0>J , an image ( )yxf , can be completely represented by the hierarchy of 13 +J discrete images { }JjfDfDfDfA jjjJ ≤≤1,,,, 3

222

122

, where

( ) ( ) ( )( ) ( )nmyxyxfnmfA jjjj

−−−−= 2,2,*,:, 22 φ (1)

and

( ) ( )( ) ( )nmyxyxffD jjppjj

−−−−∗= 2,2,,22

ψ

( )3,,2,1=p (2)

In (1) and (2), ( ) Znm 2, ∈ . This set of images is called an orthogonal wavelet representation in two dimensions [15]. The wavelet decomposition of an image can then be interpreted as a set of an independent, spatially oriented frequency channels. The schematic of 2-D wavelet decomposition for an original image is shown in Fig. 1, where the maximum decomposition scale J is taken to be 3 for simplicity of illustration. It can be seen that the original image is decomposed into a pyramid structure composed of A smooth image fA 32

, and the images fD j12

, fD j22

, and

fD j32

that represent high frequency details in the vertical, horizontal, and diagonal directions at resolution

( )3,2,12 =jj . Due to the orthogonality of this representation, the total number of pixels under this new representation is equal to the number of pixels in the original image.

Fig. 1. 2-D Discrete wavelet transform of an image.

III. PREVIOUS WORKS ON WAVELET-BASED TEXTURE CLASSIFICATION

In this section, some of important research contributions related to texture classification using wavelets are reviewed. The application of wavelets for texture classification has received considerable attention in the literature since Mallat [15] first used the standard 2-D DWT for texture analysis. Carter [16] reported the application of Morlet and Mexican hat wavelets for texture classification. He achieved 98% classification accuracy on 6 natural textures. However, Morlet and Mexican hat wavelet are not orthogonal, and Mexican hat wavelet doesn’t have direction selectivity. Laine and Fan [17] overcame the drawbacks of Carter’s work by using orthogonal and compactly supported wavelets based on wavelet packet analysis. They showed that wavelet packet representations of twenty five natural textures were classified without error by a simple two-layer network classifier. Chang and Kuo [18] introduced a tree-structured wavelet transform (TSWT) in which only significant frequency channels were decomposed further. The development of the new TCWT was motivated by the observation that a large class of natural textures can be modeled as quasi-periodic signals whose dominant frequencies are located in the middle frequency channels. They achieved more than 93.5% accuracy in classifying thirty natural textures for all four different distance measures. Unser [13] used over-complete wavelet representations by discrete wavelet frame (DWF) approach. Classification experiments with 12 Brodatz textures indicated that the DWF approach is superior to the standard critically sampled DWT approach. Kim and Udpa [19] proposed a novel approach to the texture classification problem using a new set of rotated 2-D wavelet filters. Twenty eight textures were used in the classification experiment using a Bayes classifier. The results showed that the discrimination performance obtained with the combined filter banks is superior to the performance obtained using the DWF filter bank alone. However, the research approaches [13], [15]-[19] reviewed above are based on the texture images with the same orientation; the performance of these methods are unknown when the texture images are rotated.

Porter and Canagarajah [20] initially tried to use standard DWT for rotation-invariant texture classification. Rotation invariance was achieved by combining pairs of diagonally opposite wavelet channels to form the single features; the wavelet decompositions from the diagonal direction were not used as they degraded the classification performance due to noise. Classification experiments with sixteen Brodatz textures showed more than 95% accuracy for both original and rotated textures. Pun and Lee [21] proposed a novel two-stage method for rotation-invariant texture classification of twenty Brodatz textures. In the first stage, a set of sorted and dominant wavelet packet features was extracted from a texture image and a Mahalanobis distance classifier was employed to output N best classes. In the second stage, another set of wavelet packet features was extracted from the polarized form of the sample textures and the most dominant wavelet packet features were selected and passed to the radial

basis function (RBF) classifier with the N best classes to output the final matched class. Experimental results showed that the proposed method outperforms the similar wavelet methods and the other rotation invariant texture classification schemes with an overall accuracy of 91.4%.

However, the method presented by Pun and Lee [21] may not be good for the textures with different scales. In this paper, we proposed a novel cluster-based method to divide the matrices of computed 2-D wavelet coefficients into clusters at each scale. The features that contain the information useful for classifying texture images are computed from the energy content of the clusters, and these feature vectors serve as input patterns to a neural network for texture classification. The classification accuracy of the proposed approach is evaluated using 24 Brodatz textures with original, rotated, scaled, and rotated and scaled versions of each texture.

IV. A NEW CLUSTER-BASED FEATURE EXTRACTION

METHOD In this section, a novel cluster-based method developed by

Gang et al. [14] for extracting features from 2-D wavelet coefficient matrix of each frequency channel is briefly reviewed. The 2-D wavelet coefficients in a matrix are grouped into clusters by a clustering procedure that is presented in the Appendix. The cluster formation is accomplished in unsupervised mode by using a set of representative images that pertain to a given application. In practical situations, this set of representative images can be the same as the one kept aside for training the classifier (e.g., a neural network).

A. Cluster Formation The procedure for cluster formation is illustrated in Fig. 2:

(a) compute 2-D DWT for every image in the set of representative images that are kept aside for training the classifier; in this step, 2-D wavelet coefficient matrices { }JjfDfDfDfA jjjJ ≤≤1,,,, 3

222

122

are constructed; (b)

first construct cumulative matrices ∑=

=K

k

fDfSD jj

1

12

12

,

∑=

=K

k

fDfSD jj

1

22

22

, and ∑=

=K

k

fDfSD jj

1

32

32

( )Jj ,...,2,1= , where

K is the number of images in the set of representative images; then construct matrices

( ) ( )( )fSDfSDfSD

G ppp

pjj

j

j 222

2

1 μσ

−=

( )Jjp ,...,2,1;3,2,1 == , where ( )Aμ and ( )Aσ denote the sample mean and standard deviation of the elements of the matrix A respectively; (c) apply a threshold of the form

( )γlnln2:22

−= jj LT , with 2e≥γ ( e is the Euler’s number),

to the elements of the matrices pjG

2, jL2

being the number of computed detail coefficients at each scale; this gives the

corresponding binary matrices; (d) pass the binary matrices obtained in the previous step through the clustering procedure to form the boundaries of the clusters. The clusters cVVV ,...,, 21 are determined once all the computed wavelet coefficients from each and every scale are labeled using the corresponding cluster labels. Therefore the cluster formation procedure divides the scheme of all computed wavelet coefficients into disjoint clusters cVVV ,...,, 21 from each of which a single robust feature ( )civi ,...,2,1= can be computed. The so obtained feature vectors cvvv ,...,, 21 serve as the input patterns to an image classifier such as a neural network.

Fig. 2. Cluster Formation Using the Clustering Procedure

B. Feature Extraction Method

From the procedure described in the previous subsection, clusters cVVV ,...,, 21 are determined from a set of representative images. The feature vectors that are input to an image classifier can be computed with a two-step procedure. In the first step, the 2-D DWT is applied to an image to obtain the matrix of wavelet coefficients, which is then divided into clusters cVVV ,...,, 21 according to the cluster formation procedure described above.

The second step consists of simply determining every component of the feature vector cvvv ,...,, 21 through the Euclidean norm

∑∈

=iVu

i uv 2: (3)

In other words, each feature iv is determined as the square roots of the energy of the wavelet coefficients in the corresponding cluster iV . Consequently, the number of features, c , of an image is equal to the number of clusters determined with the method described in the previous subsection.

V. EXPERIMENTAL IMPLEMENTATION

A. Experimental Data Sets The 24 textures from the Brodatz’s album [22] as shown in

Fig. 3 were equalized to 256 x 256 pixels and 256 gray levels.

Each image was divided into 16 disjoint 64 x 64 blocks, and each block was independently histogram-equalized to abolish luminance differences among textures.

Two experiments were used to evaluate the classification accuracy of the proposed method. Experiment I consists texture blocks at original orientation; the 24 texture categories include 384 blocks altogether. For experiment II, each original texture block was transformed into three additional blocks: a block rotated by 90 degrees, a 64 x 64 scaled block obtained from 45 x 45 pixels in the middle, and a block which was both rotated and scaled. The 24 texture categories include 1536 blocks altogether. Fifty percent of texture blocks are used for training and the rest are used for testing the classification accuracy. The classification accuracy is evaluated using ten different randomly selected training and testing data sets. B. Texture Features

Since one of the main objectives of this study is to demonstrate how the cluster-based feature extraction method improves the texture classification performance relative to those obtained using only the DWT, two sets of features based on both cluster-based and DWT methods are extracted at each decomposition scale. Haar wavelet is used in this paper for the wavelet decomposition because of its computational simplicity, and its fairly good classification performance compared to other wavelets [13]. The texture images from the training set are used to determine the cluster boundaries to form the feature vector cvvv ,...,, 21 using the feature extraction procedures presented in the previous section. All the features obtained by cluster-based method at each decomposition scale form the feature set C-DWT. In the meantime, all the features obtained from the energy content of frequency channels using the standard DWT form the feature set DWT.

C. Classification Algorithm

Probabilistic Neural Network (PNN) is a supervised neural network that is widely used in the area of pattern recognition. The original PNN, which was proposed by Specht [23], is a direct neural network implementation of the Parzen nonparametric probability density function estimation [24] and Bayes classification rule. A PNN is used in this paper for texture classification experiments because of the advantages it offers: rapid training speed and guaranteed convergence [25]. In addition, PNN is found superior to Multilayer Perceptrons [26], and Kohonen Self Organizing Maps in the application on cloud classification [27].

Fig. 3. 24 Brodatz Textures for Classification Experiments

VI. RESULTS AND DISCUSSIONS

The evaluation of the performance of cluster-based and standard DWT feature extraction methods based on Experiment I and II are presented and discussed in this section. The classification results from two experiments are listed in Table 1 and 2, which show the correct classification as a function of the number of decomposition scale and two feature sets for C-DWT and DWT respectively. Each classification accuracy number in Table 1 and 2 represents the result of an average of ten tests conducted with ten randomly selected training and testing data sets. The number of features used for each method in each experiment is shown within the parenthesis next to the classification rate.

In experiment I, the classification accuracy based on feature set C-DWT is better than that based on feature set DWT for each scale, especially scale 1 and 5. The highest classification accuracy (97.5%) is obtained using feature set C-DWT at scale 3, which is slightly better than the accuracy using feature set DWT at scale 3.

TABLE I CLASSIFICATION ACCURACY FOR THE EXPERIMENT I

In experiment II, the feature set C-DWT outperforms the feature set DWT at each scale, especially scale 1, 2 and 5. The highest classification accuracy (90.4%) is obtained using feature set C-DWT at scale 5, which is better than the highest classification accuracy (86.3%) obtained using feature set DWT at scale 4.

TABLE II CLASSIFICATION ACCURACY FOR THE EXPERIMENT II

Results from experiments I and II also show that increasing the number of scale does not guarantee improved classification accuracy for both feature sets C-DWT and

DWT. The cluster-based method provides additional discriminatory information to texture classification, especially for experiment II where texture images are rotated and scaled.

VII. CONCLUSIONS

In this paper, a new cluster-based feature extraction method using 2-D DWT is proposed for the texture classification problem. The proposed method divides the matrices of wavelet coefficients into clusters that are centered around the dominant coefficient positions. The experimental results on a large sample data set of twenty four natural textures with different scales and orientations show that the proposed cluster-based method provides additional discriminatory information to texture classification, and is superior to the conventional feature extraction methods. The proposed method has a great potential for other pattern recognition applications such as medical image analysis and quality inspection.

APPENDIX The clustering procedure for cluster boundary formation is

illustrated in Fig. 4: (a) label each occurrence of 1 in the binary matrix with a unique label (for example, if there are three 1s scattered in the matrix, label them as A, B, and C); (b) use A, B, and C as the seeds and centers to grow the clusters; in the first step, each labeled seed is expanded by one cell to the left, one to the right, one to the top and one to the bottom; (c) repeat the same expansion pattern for every labeled cell that is surrounded by one or more 0s; in this process, previous labeled cells should be left unchanged; (d) once all the 0s in the matrix are labeled, the cluster boundaries are drawn respecting the homogeneity of the labels in each cluster.

Fig. 4. Cluster Boundary Formation Using the Proposed Clustering Procedure

ACKNOWLEDGMENT This research is supported by the Scientific Research

Foundation for the Returned Overseas Chinese Scholars of State Education Ministry as well as by the research fund sponsored by the department of Mechanical and Automation at Harbin Institute of Technology Shenzhen Graduate School.

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