International Journal of Advancements in Research & Technology, Volume, Issue4, April-3 49 ISSN 78-7763 Texture Classification Using Curvelet Transform S. Prabha, Dr. M. Sasikala Department of Electronics and Instrumentation Engg, Anand Institute of Higher Technology, Chennai Department of Electronics and Communication Engg, C.E.G Campus, Anna University, Chennai. Abstrat-Brain tumors are due to abnormal growths of tissue in the brain. The most common group is gliomas, followed by meningiomas. Magnetic resonance imaging (MRI) is currently an indispensable diagnostic imaging technique for the early detection of any abnormal changes in tissues and organs. It possesses fairly good contrast resolution for different tissues. It is therefore widely used to provide images which distinguish brain tumours from normal tissues. Although MRI can clearly supply the location and size of tumours, it is unable to classify tumour types, determination of which usually requires a biopsy. However a biopsy is a painful process for patients, and in some cases such as brain stem gliomas, may be too hazardous. These limitations necessative development of new analysis techniques that will improve diagnostic ability. One promising technique is texture analysis, which characterizes tissues to determine changes in functional characteristics of organs at the onset of disease. In this work texture classification based on curvelet transform has been performed. A curvelet based texture feature set is extracted from the region of interest. Texture features set consists of entropy and energy. Fuzzy-c-means algorithm is used as a classifier to classify two sets of brain images, benign tumour and malignant tumour. Index Terms: Active contours; Curvelets; Texture classification; Magnetic resonance image.. INTRODUCTION The analysis of texture in images provides an important cue to the recognition of objects. It has been recently observed that different image objects are best characterized by different texture methods (Kaplan 999). Successful applications of texture analysis methods have been widely found in industrial, biomedical, remote sensing areas and target recognition Texture methods used can be categorized as statistical, geometrical, model based and signal processing which is proposed by Tuceryan and Jain (998). Some statistical methods used are co-occurrence matrix features and auto correlation function. Tuceryan and Jain (99) proposed geometrical methods in which textures are considered to be composed of texture primitives and are extracted and analyzed. Several stochastic models have been proposed for texture modeling and classification such as Gaussian Markov random fields and spatial auto correlation function model proposed by Patrizio, Alessandro and Gaetano (). The signal processing techniques are mainly based on texture filtering for analyzing the frequency contents either in spatial domain or in frequency domain. Filter bank instead of a single filter has been proposed, giving raise to several Copyright 3 SciResPub. multi channel texture analysis systems such as gabor filters and wavelet transforms proposed by Unser (989). The major disadvantage of gabor transform is that its output are not mutually orthogonal which may result in a significant correlation between texture features. In the last decade, Arivazhagan and Ganesan(3) performed texture classification method based on wavelet transform. The success of wavelets is mainly due to the good performance for piecewise smooth functions in one dimension. Unfortunately, such is not the case in two dimensions.wavelets in two dimensions are obtained by a tensor product of one dimensional wavelet and they are thus good at isolating the discontinuity across an edge, but will not see the smoothness along the edge (Minh and Martin 3). To overcome the weakness of wavelets in higher dimensions, Candes and Donoho(998) pioneered a new system of representations named ridgelets which deal effectively with line singularities in two dimensions. The idea is to map a line singularity into point singularity using the radon transform. So ridgelet transform allows representing edges and other singularities in a more efficient way than wavelet transform which is proposed by Patrizio Campisi,Alessandro and Gaetano(). In image processing, edges are typically curved rather than straight and ridgelets alone cannot yield efficient representations. However at sufficiently fine scales, curved edges are almost straight and so to capture curved edges, one ought to be able to deploy ridgelets in a localized manner, at sufficiently fine scales. Candes and Donoho() proposed another multiscale transform called curvelet transform which is designed to handle curve discontinuities well. Here the idea is to partition the curves into collection of the ridge fragments and then handle each fragment using the ridglet transform. Lucia Dettori and Lindsay Semler(7) proposed automated imaging system for classification of tissues in medical images obtained from CT scan It is found that curvelet transform outperforms all other multi-resolution techniques yielding high accuracy rates. The texture classification algorithm proposed in this article consists of four main steps: segmentation of region of interest from MRI scans, application of the discrete curvelet transform on the region of interest, extraction of the most discriminative texture features from the curvelet coefficients and creation of a classifier(fuzzy-c-means) that identifies the various tissues. The general algorithm is summarized in the methodology diagram below (Fig. )
International Journal of Advancements in Research & Technology, Volume, Issue4, April-3 5 ISSN 78-7763 Brain Image Benign /Malignant tumor Segmentation of region of interest Classifier Curvelet Transform Texture Descriptors Where C is any other variable curve, and the constants c and c depending on C, are the averages of u inside C and respectively outside C. In this simple case, it is obvious that C, the boundary of the object, is the minimizer of the fitting term inf { F ( C ) F ( )} ( ) ( ) C F C F C C Fig. Block Diagram of Texture Classification The paper is structured as follows: Section describes segmentation of region of interest using active contour model. Section 3 discusses the discrete curvelet transform and feature extraction. Section 4 presents texture classification methods.. SEGMENTATION In this work, segmentation of region of interest is performed using active contour model without edges (Tony ). The model can detect objects whose boundaries are not necessarily defined by gradient. Energy is minimized which can be seen as a particular case of the minimal partition problem. In this work, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. The initial curve can be anywhere in the image, and interior contours are automatically detected. The model is trying to separate the image into regions based on intensities.. DESCRIPTION OF THE MODEL The evolving curve C is defined in Ω, as the boundary of an open subset ω of Ω (i.e. ω Ω, and C= ω). In this work, inside(c) denotes the region ω, and outside(c) denotes the region Ω\ ω. Our method is the minimization of an energy based-segmentation. Assume that the image u is formed by two regions of approximatively piecewise-constant intensities, i o of distinct values u and u. Assume further that the object i to be detected is represented by the region with the value u. i Let denote its boundary by C. Then u u inside the object o [or inside (C )], and u u outside the object [or outside (C )]. Consider the following fitting term: This can be seen easily. For instance, if the curve C is outside the object, then F(C)> and F(C). If the curve C is inside the object, then F(C) but F(C)> If the curve C is both inside and outside the object, then F(C)> and F(C)>. Finally, the fitting energy is minimized if C=C, i.e., if the curve C is on the boundary of the object. In our active contour model minimize the above fitting term and add some regularizing terms, like the length of the curve C, and (or) the area of the region inside C. Therefore, we introduce the energy functional F(c,c, C), defined by F( c, c, C). Length( C) v. Area( inside( C)) + + c dxdy inside( C ) c dxdy outside( C ) Where μ, v,, > are fixed parameters. In almost all our numerical calculations fix the value of = = and v =. Therefore consider the minimization problem as inf F( c, c, C) c, c, C Benign and malignant tumor images are given as input to the active contour model which gives segmented image as shown in fig.. F(C)+F(C)= inside( C) c dxdy Copyright 3 SciResPub. + outside ( C ) c dxdy
International Journal of Advancements in Research & Technology, Volume, Issue4, April-3 5 ISSN 78-7763 Fig. Input image and segmented image using active contour model 3. Discrete Curvelet transform Curvelets are effective at detecting image activity along curves. The discrete version implemented in this work uses a USFFT (Unequally spaced Fast Fourier transform) algorithm. The fast discrete curvelet transform is simpler, faster and less redundant. This approach uses a decimated rectangular grid tilted along the main direction of each curvelet. The discrete curvlet transform is implemented via USFFT in four steps.. Apply the D FFT(fast fourier transform) and obtain Fourier samples f[n, n ], n/ <= n, n < n/.. For each scale/angle pair (j, l), resample (or interpolate) f[n, n ] to obtain sampled values f[n, n n tanө l ] for (n, n ) Є Pj. 3. Multiply the interpolated (or sheared) object f with the parabolic window U j, effectively localizing f near the parallelogram with orientation ө l, and obtain f n, n ] f [ n, n n tan ] U [ n, ] [ l j n 4. Apply the inverse D FFT to each f j,l, hence collecting the discrete coefficients c D (j,l,k). The approximate scales and orientations can be seen in fig 3. Fig. 3 Finite tiling by the polar wedges Fig. 3 illustrates the basic digital tiling. The windows U j,l, smoothly localize the fourier transform near the sheared wedges obeying the parabolic scaling. The shaded region represents one such typical wedge. The inputs to the curvelet transform are x and nscales. x is N by N pixel array of an image. nscales defines number of scales including the coarsest wavelet level. The output of curvelet transform represents cell array of curvelet coefficients in which integer scale varies from coarsest to finest scale. Two parameters involved in the digital implementation of the curvelet transform are number of resolution and number of angles at the coarsest level. The parameters are bound by the two constraints: the maximum number of resolutions depends on the original image size and the number of angles at the second coarsest level must be at least eight and multiple of four. Several features were calculated on the curvelet coefficient. The following four feature vectors were investigated: entropy and energy. Since the region of interest is 6x6 pixels, the maximum possible resolution extraction is two levels of resolutions. 4. Texture classification method The original image is decomposed using discrete curvelet transform. Texture features are calculated from each Curvelet sub-band. In order to improve the classification gain, cooccurrence matrix is formed for each sub-band of discrete curvelet transform, which gives the information about the spatial distribution of gray scale values. From the cooccurrence matrix, the features such as energy and entropy are calculated. 4. Feature Extraction Texture classification is based on the texture features extracted from the curvelet co-efficient. A gray tone spatial dependence matrix approach introduced by Haralick (979), which is well known statistical method for extracting second order texture information from images is used. Twodimensional co-occurrence (gray-level dependence) matrices are generally used in texture analysis because they are able to capture the spatial dependence of gray-level values within an image. The gray-level co-occurrence matrix can reveal certain properties about the spatial distribution of the gray levels in the texture image. A D co-occurrence matrix, P is an n x n matrix, where n is the number of gray-levels within an image. A pixel with the gray level intensity value i occurs in a specific spatial relationship to a pixel with the value j in graylevel co-occurrence matrix (GLCM). The matrix acts as an accumulator so that P[i, j] counts the number of pixel pairs having the intensities i and j. Pixel pairs are defined by a distance and direction which can be represented by a displacement vector d =(dx,dy), where dx represents the number of pixels moved along the x-axis, and dy represents the number of pixels moved along the y-axis of an image. In order to quantify this spatial dependence of gray level values, Copyright 3 SciResPub.
International Journal of Advancements in Research & Technology, Volume, Issue4, April-3 5 ISSN 78-7763 various textural features including Entropy, Energy (Angular Second Moment), are calculated. This method is based on the estimation of the second order joint conditional probability density function P(i,j/ d,ө) where ө=,45,9 and 35 degrees. Each P(i,j / d,ө) is the probability going from gray level i to gray level j, given that the inter sample spacing is d and the direction is given by angle ө (offset degree). This is also referred to as cooccurrence matrix. The co-occurrence matrix is calculated for the source images for ө = degrees and distance d = (offset distance). Four texture features are calculated from the cooccurrence matrix. Let P(i,j) denote the co-occurrence matrix and N the number of distinct gray level in the quantized image. The following four texture features are calculated from cooccurrence matrix. 4. Entropy 5. RESULTS AND DISCUSSION Twenty benign tumor images and sixteen malignant tumor images are used for the study. The tumor regions in the MRI brain images are segmented using active contour model. Benign tumor images used in this work are shown in fig.4. Malignant tumor images are shown in fig.5. Curvelet transform is applied to the region of interest. For region of interest of 6x6 pixels, finest scale curvelet subband matrix is obtained. Texture features such as entropy and energy are extracted from each curvelet sub band. Then feature values are given as input to fuzzy-c-means algorithm, all benign tumor images are correctly classified, only one malignant tumor image is not correctly classified. Curvelet based feature extraction yielded higher accuracy rates than wavelet and ridgelet transform.table shows tumor classification of benign and malignant images. The classification accuracy obtained for curvelet transform is 97.%. Entropy measures the randomness of a gray-level distribution. The entropy is expected to be high if the gray levels are distributed randomly throughout the image Entropy M N i j P[ i, j ] log P[ i, j ] Where P[i,j] are the pixel values at the (i,j) coordinates of the image. The size of the image is M*N. 4.3 Energy (Angular second moment) Energy measures the number of repeated pairs. The energy is expected to be high if the occurrence of repeated pixel pairs is high Energy M N i j P [ i, j ] Where P[i,j] are the pixel values at the (i,j) coordinates of the image. The size of the image is M*N. 4.4 Fuzzy c-means Algorithm Unsupervised clustering method is used as a classifier for detecting brain tumor images. In the unsupervised clustering method, fuzzy-c-means algorithm is used for classification. Fuzzy c-means (FCM) is a data clustering technique in which a dataset is grouped into number of clusters with every data point in the dataset belonging to every cluster to a certain degree. For example, a certain data point that lies close to the center of a cluster will have a high degree of belonging or membership to that cluster and another data point that lies far away from the center of a cluster will have a low degree of belonging or membership to that cluster. In this paper the extracted feature value of energy and entropy from the curvelet transform are given as input to FCM. FCM automatically classifies the benign and malignant tumors with high classification accuracy.. Fig.4 benign tumor images Fig.5 Malignant tumor images Table Tumor Classification Tumor Correct Classification Mis- Classification Benign() Malignant(6) 5 Total(36) 35 Copyright 3 SciResPub.
International Journal of Advancements in Research & Technology, Volume, Issue4, April-3 53 ISSN 78-7763 REFERENCES ) Kaplan, L.M (999), Extended fractal analysis for texture classification and segmentation, IEEE Transactions on Image Processing, Vol. 8, No., pp.57-585. ) Haralick R. M., Shanmugam K., and Dinstein I (973), Texture features for image classification, IEEE Transactions on System Man Cybernat, Vol. 8, No. 6, pp. 6-6. 3) Tuceryan M. and Jain A. K (99), Texture Segmentation Using Voronoi Polygons, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol., pp. -6. 4) Patrizio Campisi, Alessandro Neri, and Gaetano Scarano (), Model based rotation invariant texture classification, IEEE Transactions on International Conference on Information Processing, pp.7-. 5) Unser M., and Eden M (989), Multi-resolution feature extraction and selection for texture segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol., No.7, pp. 77-78. 6) Arivazhagan. S and Ganesan. L (3), Texture classification using wavelet transform, Pattern Recognition Letters, pp. 53 5. 7) Candes J (998), Ridgelets: theory and applications, Ph.D. thesis, Department of Statistics, Stanford University. 8) Haralick R.M (979), Statistical and structural approaches to texture, Proceedings of the IEEE, Vol. 67, pp. 786-84. 9) J.L. Starck, E. Candes, and D.L. Donoho (), The Curvelet Transform for Image Denoising, IEEE Transactions on Image Processing, Vol., No.6, pp. 67-684. ) Lucia Dettori and Lindsay Semler (7), A comparison of wavelet, ridgelet and curvelet-based texture classification algorithm in computed tomography, Computers in biology and medicine, Vol.37,pp.486-498. ) Arivazhagan, and L.Ganesan (6), Texture classification using curvelet statistical and cooccurrence features, IEEE Transactions on pattern recognition. ) Tony F Chan and Luminita A. Vese(), Active Contours Without Edges, IEEE Transactions on Image Proceesing, Vol., No.. Copyright 3 SciResPub.