Texture classification using Wavelet Packets with Genetic Algorithm as a tool for Threshold Selection

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1 1 Texture classification using Wavelet Pacets with Genetic lgorithm as a tool for Threshold Selection.SHEEL RNI Research Scholar, epartment of Instrumentation Engineering, Madras Institute of Technology, hromepet ampus, nna University, hennai , INI. R.S. RENGNTHN ean of Engineering, Madras Institute of Technology, hromepet ampus, nna University, hennai , INI. bstract - This paper describes a Genetic lgorithm based approach to classify textures at multiple scales using Wavelet Transform. If textures have no significant dominant frequency channel such as random texture or where multiple textures have similar dominant frequency channel, more number of features are to be extracted for classification. It is difficult to determine the number of features required a priori. The proposed algorithm start with one feature, eliminates unliely texture, progress with the next feature for further classification. The procedure is repeated until there is only one texture in the candidate list. controllable parameter serve as a threshold in eliminating the irrelevant texture. False classification and computational cost is reduced by the use of Genetic lgorithm as a front end to select the best threshold. lassification experiments on 7 rodatz textures are carried out and results are reported. Keywords : Wavelet transform, Image texture, Feature extraction, Genetic algorithm, Multi-resolution analysis, Texture classification 1. Introduction Texture is an important cue for the analysis of many types of images. It is used to point out intrinsic properties of surfaces, especially those that do not have smoothly varying intensity. It includes intuitive properties lie roughness, granulation and regularity. The ability to effectively classify and segment images based on textural features is of ey importance in medical image analysis, remote sensing and industrial monitoring of product quality. Early research wor [1] [2] [3] was based on the second order statistics of textures where the gray levels between neighboring pixels are characterized by a certain stochastic relationship. The above methods share one common weaness. They focus on analysis based on single scale. Wavelet Transform provide a good multi resolution analytical tool to characterize different scales of textures effectively. Wavelet and Wavelet pacet transform can be implemented efficiently with Pyramid & Tree structured transform respectively [4] [5]. In this paper, we apply tree structured wavelet transform for texture feature extraction and a genetic based progressive classification algorithm for further classification. The paper is organized as follows. In Section 1 a brief review of theory of wavelets and wavelet pacets are presented. Section 3 describes Feature extraction algorithm. In Section 4 threshold selection using genetic

2 2 algorithm and progressive classification is described. Experimental results are presented in Section5. oncluding remars are given in Section Review of Wavelet Transform and Wavelet Pacets. 2.1 Wavelet Transform y Wavelet transform, we mean the decomposition of a signal with a family of real orthonormal bases Ψ m,n (x) obtained through translation and dilation of a ernel function.ψ (x) nown as the mother wavelet, i.e., Ψ m,n (x) = 2 m/2 Ψ(2 m x - n) (1) where m and n are integers. ue to the orthonormal property, the wavelet coefficients of a signal f(x) can be easily computed via + c m,n = f(x) Ψ m,n (x) dx (2) - and the synthesis formula f(x) = c m,n Ψ m,n (x) (3) m,n can be used to recover f(x) from its wavelet coefficients. To construct the mother wavelet Ψ (x), we may first determine a scaling function φ(x), which satisfies the two-scale difference equation [6] φ(x) = 2 h() φ (2x-) (4) Then, the wavelet ernel Ψ(x) is related to the scaling function via Ψ(x) = 2 g() φ (2x-) (5) where g() = (-1 ) h (1-) (6) The coefficients h() and g() play a very crucial role in a given discrete Wavelet Transform. To perform the wavelet transform does not require the explicit forms of φ(x) and Ψ(x) but only depends on h() and g(). onsider a J-level wavelet decomposition which can be written as f 0 (x) = c 0, φ 0, (x) J = (c J+1, φ J+1, (x) + (d j+1, Ψ j+1, (x)) (7) j=0 where coefficients c 0, are given and coefficients c j+1,n and d j+1,n at scale j+1 are related to the coefficients c j, at scale j via c j+1, n = j, h (-2n) (8) d j+1, n = j, g (-2n) where 0 j J. Thus, (8) provides a recursive algorithm for wavelet decomposition through h() and g(), and the final outputs include a set of J level wavelet coefficients d j,n 1 j J, and the coefficient c J,n for a low resolution component φ J, (x). y using a similar approach, we can derive a recursive algorithm for function synthesis based on its wavelet coefficients d j,n, 1 j J, and c J,n. c j, = c j+1, n h (-2n) + d j +1,n g (-2n) (9) n n The signal c j, pass through a pair of filters H and G with impulse responses h(n) and g(n) and downsampling the filtered signals by two (dropping every other sample), where h(n) and g(n) are defined as h(n) = h(-n), g(n) = g(-n) The pair of filters H and G correspond to the halfband low pass and high pass filters, respectively, and are called the quadrature mirror filters. The signal decomposition scheme is performed recursively to the output of the lowpass filter h. It leads to the conventional wavelet transform or the so-called pyramid- structured wavelet decomposition.the coefficients h b () of the attle-lemarie Wavelet are symmetric, i.e., h b ()=h b (-)[5]. 2.2 Wavelet Pacets The pyramid structured wavelet transform decomposes a signal into a set of frequency channels that have narrower bandwidths in the lower frequency region. The transform is suitable for signals consisting primarily of smooth components so that their information is concentrated in the low frequency

3 3 regions. However, for quasi-periodic signals the dominant frequency channels are located in the middle frequency region. To analyze quasi periodic signals wavelet pacet {Wn} n =0 can be generated from a given function W 0 as follows : W 2n (x)= 2 h() W n (2x-) (10) W 2n+1 (x) = 2 g() W n (2x-) where the function Wo (x) can be identified with scaling function φ and W 1 with the mother wavelet Ψ. Then, the library of wavelet pacet bases can be defined to be the collection of orthonormal bases composed of functions of the form W n (2 l x - ), where l, ε Z, n ε N. Each element of the library is determined by a subset of the indices : a scaling parameter l, a localization parameter, and an oscillation parameter n. The treestructured wavelet transform algorithm described in Section 3 represent a function in terms of wavelet pacet basis. energy value in the same scale. That is, if e < e max, stop decomposing this region where is a constant less than If the energy of a subimage is significantly larger, apply the above decomposition procedure to the subimage. The size of the smallest sub image is used as stopping criterion for further decomposition. If decomposed channel has a very narrow size, the features extracted may not be robust. 4 level tree structured wavelet transform domain and Quad tree representation are shown in Fig.1. 1 (LL) 2 2 hannel (HL) The 2- wavelet (or wavelet pacet) basis functions can be expressed by the tensor product of two 1- wavelet (or wavelet pacet) basis functions along the horizontal and vertical directions. The corresponding 2- filter coefficients can be expressed as 1 (LH) 1 (HH) h LL (,l) = h()h(l), h LH (,l) = h()g(l), h HL (,l) = g()h(l), h HH (,l) = g()g(l) where the first and second subscripts denote the lowpass and high pass filtering characteristics in the x-and y- directions, respectively. 3. Texture Feature Extraction 1. ecompose a given textured image with 2- twoscale wavelet transform into 4 sub images, which can be viewed as the parent and children nodes in a tree. 2. alculate energy of each decomposed image. If the decomposed image is x (m,n), with 1 m M and 1 n N, the energy is M N 1 ( x (m,n). ( 11) e = MN i=1 j=1 3. If the energy of a subimage is significantly smaller than others, stop the decomposition in this region since it contains less information. This step can be achieved by comparing the energy with the largest (a) 29 Fig.1.(a) Tree Structured Wavelet Transform omain (b) Quad Tree Representation (b)

4 4 4. Texture lassification 4.1 Learning phase 1. Given m samples obtained from the same texture, decompose each sample with the tree structured wavelet transform and calculate the normalized energy at its leaves which defines an energy function nown as energy map. 2. Generate a representative energy map for each texture by averaging the energy maps over all m samples. 3. Repeat the process for all textures. 4.2 lassification Phase 1. ecompose an unnown texture using treestructured wavelet transform and construct its energy map. 2. The channel with large energy value x j, j=1,2., are used as features and arrange them in order, i.e., x 1 > x 2 > x j-1 > x j > x j +1 >. 3. Order textures in the database into a candidate list, and perform the following iteration from the first feature (i.e., x, =1). i. Remove textures from the candidate list if they do not have the same leaf node as the th dominant channel of the unnown texture. ii. For the remaining textures, denote the energy value in this channel by m i,j for texture i and feature j and calculate the Euclidean istance. J i = j =1 (x j m i,j ) 2 iii. Let min = Min i.if i > T min remove texture i from the list. If there is only one texture left, assign the unnown texture to this texture. The constant T in 3(iii) is a controllable parameter which serve as threshold for eliminating irrelevant textures. 4.3 Threshold Selection using Genetic algorithm for the basis of more robust threshold selection strategy for improving the performance of our texture classification system. hoosing an appropriate evaluation function is an essential step for successful application of genetic algorithm to any problem domain. The process of evaluation involve the steps presented in Fig 2. In order to use genetic algorithms as the search procedure, it is necessary to define a fitness function which will be evaluated by adding the weighted sum of the match score of all of the correct recognitions and subtracting the weighted sum of the match score of all the incorrect recognitions [7] i.e., F = S i * W i - S j * W j (12) The range of the value of F is dependent on the number of testing events and their weights. In order to normalize and scale the fitness function F to a value acceptable for genetic algorithm, the following operations were performed: Fitness (f i ) = 100 [ (F/TW) *100] (13) where m TW=total weighted testing examples = Wi s indicated in the above equations, after the value of F was normalized to the range [-100,100], the subtraction ensures that the final evaluation is always positive (the most convenient form of fitness for genetic algorithm), with lower values representing better classification performance. Input Texture n i=1 Progressive lassification j= n+1 Fig.2. Genetic lgorithm based progressive lassifier. m Tree Structured Wavelet ecomposition Threshold Selection i=1 Feature Vector Extraction Genetic lgorithm Genetic algorithms are best nown for their ability to efficiently search large spaces about which little is nown a priori. Since genetic algorithms are relatively insensitive to noise, they seem to be an excellent choice

5 5 5. Experimental Results 5.1 Texture selection & Sampling 7 rodatz texture with size 512 X 512 were used to construct pattern boo as shown in Fig 3.Each texture class was then broen down into 128 X 128 sub samples. To obtain a large amount of data for classifier, we adapted a method of overlapped sampling. We extracted 32 samples of size 128 X 128 from each original 512 X 512 sample texture. The amount of overlap was fixed as 48 pixels column wise for extracting all sub samples. 5.2 Partition of Wavelet pacet space Wavelet decomposition was performed on each 128*128 sub image.the discrete filters were obtained from attle Lemarie cubic spline wavelet basis function. ue to down sampling at each decomposition, the size of each sub sample was reduced by a factor of 4. Thus an input image of size 128 X 128 results in 4 X 4 with 4 level tree structured wavelet transform. Table.1 shows the energy map with first 5 dominant channels for 32 samples of texture 29 with threshold = Fig.3. rodatz Textures:9- Grass Lawn, 12- ar, 19- Woolen loth, 24 - Pressed alf Leather, 29- each Sand, 38 - Water, Pebbles Table 1. The First 5 ominant hannels for Texture 29 Occur ominant Frequency hannels Ence In order to obtain an unbiased estimate of the performance of texture classification procedure, testing and training sets should be independent. leave-one-out algorithm (each sub image is classified one by one so that other sub image serve as training data) is used for reliable classification. 5.3 iscrimination using a simple Minimum istance lassifier: To decide the efficacy, the performance of a simple minimum distance classifier was evaluated. Textures that cannot be discriminated easily requires more number of features, since they are similar to other textures whose dominant frequencies are in the low frequency region. Increased number of features and iterating the controllable parameter T that serve as threshold for eliminating irrelevant texture increases the computational cost. daptive threshold selection using genetic algorithm improve the percentage of correct classification with reduced computational complexity Parameter Settings: Population Size : 10 hromosome Length : 04 Maximum number of generations : 05 Probability of ross over (P c ) : 1.0 Probability of Mutation (P m ) : 0.025

6 6 Gene ratio ns Table.2. lassification Results of 7 Texture lasses Thres hold (T) verage Number of Features Fitness Func tion (f i) Percentage of orrect lassificati on (P) Evaluation Function (fi) ssigned lass Text ure 9 I Generations Evaluation Function Features Fig.4. Performance of Genetic lgorithm Table 3 onfusion Matrix (T= ) Number of Errors: 13 (out of 224) Total Score: 94.20% Table 2. shows the overall correct classification as a function of threshold (T) and average number of features with attle Lemarie cubic spline wavelet basis. fter 5 Generations, the best solution found by genetic algorithm was features on the average of all samples of 7 textures and correct classification rate was 94.20% for a threshold of Table.3 shows the misclassification results when assigned to a different class of texture. Fig.4 shows the performance of Genetic lgorithm. 6. Summary and onclusion genetic algorithm based progressive classification algorithm in selecting a threshold for texture analysis is presented. The results indicate that the adaptive threshold selection strategy using genetic algorithm yield a significant reduction in computational cost in setting the value of threshold for different textures. This is an important step towards the application of machine learning techniques for automating the construction of classification system for difficult image processing problems. References: [1]. R.W.onners and.. Harlow, theoretical comparison of texture algorithm, IEEE Trans. Pattern nal. nd Machine Intell., vol. 2,1992, pp , [2]. R.M.Haralic, K.Shamugam, and I. irstein, Textural features for image classification, IEEE Trans. on SM, vol. 8, 1973, pp , [3]. P..hen and T. Pavlidis, Segmentation by texture using correlation, IEEE Trans. on Pattern nal. and Machine Intell., vol.5, 1983, pp [4]. Mallat.S, theory for multiresolution signal decomposition: The Wavelet representation, IEEE Trans. on Pattern nalysis and Machine Intelligence, vol.11., 1989, pp [5]. Tianhorng hang &..Jay Kuo, Texture nalysis and classification with Tree Structured Wavelet Transform, IEEE Trans. on Image Processing, vol. 2, 1993, pp [6]. I. aubechies, Orthonormal bases of compactly supported wavelets, ommunications on Pure and pplied Mathematics, vol.41,1998, pp [7]. Vafaie, H., and e Jong, K.., Improving the performance of Rule Induction System Using Genetic lgorithms, Proceedings of the First International Worshop on Multi-strategy Learning, Harpers Ferry, W. Virgina, US, 1991.