Research Article
Texture Classification by Shearlet Band Signatures
PRIST University, Tanjore, Tamil Nadu, India
S. Audithan
Department of Computer Science, PRIST University, Tamil Nadu, India
Image texture is a key spatial attribute used in image processing and pattern recognition. It has received a considerable attention over the last few decades and the approaches to texture classification span a wide range of methods. Curvelet transform is applied by Arivazhagan et al. (2006) for classifying the texture images. From the sub-bands of curvelet transform, curvelet statistical features and curvelet co-occurrence features are extracted. The experimental result shows that the success rate is improved in comparison with traditional methods.
Classification of texture images based on Gaussian Markov Random Field model (GMRF) on linear wavelets is proposed by Reddy et al. (2010). Seven features are calculated from the wavelet transformed image by using least square error estimation method. For classifying texture, a novel scheme is introduced by Shen and Yin (2009) using curvelet transform. Mean and variance of the curvelet transform sub-bands are used as features. By the group features, discrimination can be found to classify texture images.
In order to improve the performance of texture classification system, three texture feature extraction method is described by Pharsook et al. (2011). Feature extraction method consists of gray level co-occurrence matrix and GMRF features. The classification is done by using Support Vector Machine (SVM). A detailed literature review is presented by Tou et al. (2009) for the classification of texture images based on various feature extraction techniques.
Three different methods, to classify texture images are presented by Arvis et al. (2004). The methods are multi spectral extension, joint colour texture features and grey scale texture features. Among the three methods multispectral gives the better results. An approach for colour texture classification by the use of Discrete Wavelet Transform (DWT), a multi-resolution analysis and neural network ensemble is investigated by Sengur (2009). The extracted features are Entropy and energy features.
DWT based texture classification is proposed by Hiremath and Shivashankar (2006). From, the sub band images the features are constructed. Euclidean distance and minimum distance classifier is used to classify an unknown texture image. This method gives the better classification rate at reduced computational cost. A wavelet based supervised classification model is proposed for classifying the texture by Aujol et al. (2003). In order to analyze the textures, energy distribution in each sub-band is used.
In this study, an efficient approach based on DST for gray texture classification is proposed. Texture information is captured by extracting entropy feature form the shearlet decomposed image. This study also gives a comparative analysis between the proposed systems with wavelet, Gabor and statistical based methods.
DISCRETE SHEARLET TRANSFORM
The most important step of any classification system is feature extraction. A new shearlet band signature, entropy is proposed based on discrete shearlet transform introduced by Easley et al. (2008). An N*N image consists of a finite sequence of values:
where, Identifying the domain with the finite group Z2N , the inner product of image x, y: is defined as:
(1) |
Thus the discrete analog of is l2Z2N. Given an image fεl2 (Z2N), let f^[k1, k2] denote its 2D Discrete Fourier Transform (DFT):
(2) |
The brackets in the equations [·,·] denote arrays of indices, and parentheses (·,·) denote function evaluations. Then the interpretation of the numbers f[k1, k2] as samples f[k1, k2] = f(k1, k2) is given by the following equation from the trigonometric polynomial:
(3) |
First, to compute:
(4) |
In the discrete domain, at the resolution level j, the Laplacian pyramid algorithm is implemented in the time domain. This will accomplish the multi scale partition by decomposing faj-1[n1, n2]0≤n1, n2<Nj-1 into a low pass filtered image fja[n1, n2], a quarter of the size of faj-1[n1, n2] and a high pass filtered image fdj-1[n1, n2]. Observe that the matrix faj-1[n1, n2] has size Nj*Nj, where, Nj =2-2jN and fa0[n1, n2] is equal to [n1, n2] has size N*N. In particular:
(5) |
Thus, fjd[n1, n2] are the discrete samples of a function fjd[x1, x2] whose Fourier transform is fjd(ξ1, ξ2). In order to obtain the directional localization the DFT on the pseudo-polar grid is computed and then one-dimensional band-pass filter is applied to the components of the signal with respect to this grid. More precisely, the definition of the pseudo-polar co ordinates (u, v)εR2 as follows:
(6) |
(7) |
After performing this change of co ordinates, gj (u, v) = fjd(ξ1, ξ2) is obtained and for l = 1-2j,..., 2j-1:
(8) |
This expression shows that the different directional components are obtained by simply translating the window function W. The discrete samples gj [n1, n2] = gj(n1, n2) are the values of the DFT of fjd[n1, n2] on a pseudo-polar grid. That is, the samples in the frequency domain are taken not on a Cartesian grid, but along lines across the origin at various slopes. This has been recently referred to as the pseudo-polar grid. One may obtain the discrete Frequency values of fjd on the pseudo-polar grid by direct extraction using the Fast Fourier Trans-form (FFT) with complexity ON2log N or by using the Pseudo-polar DFT (PDFT).
PROPOSED METHOD
The proposed method for texture classification based on shearlet band signature is shown in Fig. 1.
In general, a typical classification system mainly consists of two phases; feature extraction phase and classification phase. In the feature extraction phase, the features which characterize the given texture image is extracted. In the classification stage, the type of the unknown texture image is assigned to a known type by using the features extracted.
Fig. 1: | Proposed texture classification system |
The shearlet band signature, entropy is used to characterize the given texture image in the proposed system. To extract the signature, initially the decomposition of texture image is done by using DST. The decomposition produces a number of sub-bands which depends on the levels and directions used. From the sub-bands, the proposed shearlet entropy is extracted. Entropy is a geometric quantify of randomness of the texture of the input image. To calculate the entropy, the histogram of the sub-band image is generated. The zero entries in the histogram are removed and normalized. Then the entropy is calculated by the formula:
(9) |
where, pi is the non zero histogram value. This process is carried out for all the sub-bands of the shearlet decomposed image. All the shearlet entropy signatures are combined together to make the feature set of the particular texture image. In the same way, feature set for all the texture images are extracted and stored for future reference.
The classifier used to assign a target class to an unknown texture image is KNN classifier. The proposed shearlet entropy features are extracted for the unknown texture image. Then the Euclidean distance metric is used to calculate the distance between the entropy features of the unknown texture image to the feature reference list. The reference texture image class which gives the minimum distance is assigned to the class of unknown texture image. The time consumption of the proposed classification is very low. The performance of the classification system is measured in terms of classification accuracy. This is measured as the percentage of test set images that are correctly classified into the same texture class.
EXPERIMENTAL RESULTS
The performance evaluation of the proposed texture classification system based on DST is carried on using Brodatz Album. The original size of the texture images in this album is 640x640 and all are 8 bit gray scale images. The proposed system is compared with other multi-resolution methods such as wavelet transform (Wang and Yong, 2008), Tree Structured Wavelet Transform (TSWT) (Chang and Kuo, 1993), Gabor transform (Manjunath and Ma, 1996), F16b (Randen and Husoy, 1999) and Pyramid Structured Wavelet Transform(PSWT) (Mallat, 2003).
Table 1: | Classification rate of the proposed texture classification system using 2-level DST |
Also, the proposed method is compared with the combination of multi resolution methods with statistical based methods such as Gabor and GLCM (Clausi and Deng, 2005) and wavelet with GLCM (Van de Wouwer et al.,1999). The same technique in the aforesaid methods is used to extract the images and select the training and testing texture images.
Table 2: | Classification rate of the proposed texture classification system using 3-level DST |
From each original image, 128x128 pixel sized images are extracted with an overlap of 32 pixels between vertical and horizontal direction. From a single 640x640 texture image, 256 128x128 images are obtained. For the experiments, 81 images are randomly selected from the 256 images. Among the 81 images, 40 images are randomly chosen to train the classifier and the remaining images are used to test the classifier. In this experiment, 2 and 3-level shearlet transform with all possible direction is used to decompose the texture images.
Table 3: | Comparative analysis of the proposed system with other techniques in the literature |
The performance of the proposed system is evaluated by varying the number of directions from 2 to 64. Table 1 and 2 shows the classification accuracy of the proposed texture classification system using shearlet entropy based on 2 and 3-level decomposition, respectively. As the number of levels and directions used in DST increases, the classification accuracy also increases. Since, DST is able to capture more information at higher directions. For 2-level decomposition, the classification accuracy increases from 90.87% (2 directions) to 99.62% (32 directions). The maximum classification accuracy achieved by 3-level decomposition with 32 directions is 99.68%. Table 3 shows the comparative analysis of the proposed system with other techniques in the literature in terms of classification accuracy. It is observed that the wavelet transform produces better performance than Gabor transform. Also the fusion of GLCM increases the classification accuracy. However, the proposed system based on DST outperforms all methods in terms of average classification accuracy.
In this study, shearlet band signatures based texture classification of 40 Brodatz texture images is presented. The decomposition of texture image is done by using 2 and 3-level DST with varying the direction from 2 to 64 at each level. Then the proposed shearlet band signatures, entropy of each sub-band are calculated. These shearlet based band signatures are used to characterize the training images and then used to classify the testing images. The proposed system consistently achieves over 99% classification accuracy for 2 and 3-level decomposition with 6 directions and above. Experimental results show that the proposed shearlet based texture classification system outperforms Wavelet and Gabor transform based classification systems.