ROTATION INVARIANT TRANSFORMS IN TEXTURE FEATURE EXTRACTION

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1 ROTATION INVARIANT TRANSFORMS IN TEXTURE FEATURE EXTRACTION GAVLASOVÁ ANDREA, MUDROVÁ MARTINA, PROCHÁZKA ALEŠ Prague Institute of Chemical Technology Department of Computing and Control Engineering Technická 1905, Prague 6, Czech Republic Phone: Fax: Abstract: Image analysis forms a general interdisciplinary area connecting general methods of signal processing and applications in measurement, biomedicine and environmental engineering. The paper is devoted to selected mathematical methods of image features extraction enabling their reliable classification invariant to image components rotation. The first methods under study assumes initial image segmentation using watershed transform as a basic method allowing definition of image segments with different features. The following step includes definition of image features necessary for image components classification. This problem is studied with the support of Radon transform that is able to change texture rotation to its translation followed by an appropriate method of image component feature extraction. The second method presents basic principle of feature based image segmentation using feature vector assigned to all image pixels estimated from their neighbourhood having a selected shape and size. Various statistical methods estimating features of these root pixels are studied in the paper as well. Proposed methods are verified for simulated images formed by the mixture of different textures and then applied to selected biomedical images. All algorithms are presented in the Matlab environment. Keywords: Image segmentation, watershed transform, feature extraction, Radon transform, classification, biomedical image processing 1 INTRODUCTION Problems associated with image segmentation, feature extraction and classification occur in many area of signal processing including applications in biomedicine, environmental image processing, crystallography etc. The initial problem is in image segmentation followed by image segments feature extraction. Various methods are used in this area to find image features invariant to texture rotation, translation, scaling and illumination including Radon and wavelet transforms [Procházka and Gavlasová, 2005; Gavlasová and Procházka, 2005; Torres-Méndez et al., 2000; Arivazhagan and Ganesan, 2004; K. Jafari-Khouzani and H. Soltanian-Zadeh, 2005; Toft, 1996]. Neural networks [Gavlasová et al., 2005; Haykin, 1994] are then often used for image features classification. Another approach to image analysis is based upon selection of appropriate features of all image pixels. Values of such a feature vector are evaluated from each root pixel neighbourhood of the selected shape and size [Rushing et al., 2002; Lowe, 1999]. Image pixels can be classified directly into the given number of levels in this way. The paper is devoted to description of fundamental methods of image segmentation and the following feature extraction using Radon transform at first. This approach to image classification is then compared with that using feature based image segmentation based upon selection of feature vector values associated with each image pixel. Proposed methods are verified using simulated images and then used for processing of real magnetic resonance images. 2 IMAGE COMPONENTS SEGMENTATION Image segmentation methods studied in the paper consist of distance and watershed transform application followed by image ridge lines estimation. Image components features are then evaluated from their boundary signals as well as texture structures. R128 1

Segmentation [Arivazhagan and Ganesan, 2003; Gonzales et al., 2004] represents an important initial step of image processing.

segment, its boundary signal and its texture The process of classification assumes further the definition of a pattern matrix containing features of separate image segments.

segment structure transform of boundary signal or segment structure allowing its translation and rotation independence using appropriate transforms Proposed methods of image segmentation have been

2 Segmentation [Arivazhagan and Ganesan, 2003; Gonzales et al., 2004] represents an important initial step of image processing. The proposed algorithm consists of these steps image thresholding to convert it to the black and white form distance and watershed transform use to find image ridge lines presented extraction of a segment, its boundary signal and its texture The process of classification assumes further the definition of a pattern matrix containing features of separate image segments. Many possibilities of their extraction [Nixon and Aguado, 2004] include analysis of image boundary signal or the texture inside its area analysis of statistical properties of the boundary signal or segment structure transform of boundary signal or segment structure allowing its translation and rotation independence using appropriate transforms Proposed methods of image segmentation have been applied both to simulated and to selected MR images. Results obtained for a selected image are presented in Fig. 1. (a) SIMULATED IMAGE (b) RIDGE LINES (c) SEGMENT Figure 1 Image components segmentation presenting (a) original simulated image, (b) ridge lines evaluated by the watershed transform, and (c) a selected image component 3 RADON TRANSFORM IN IMAGE FEATURES EXTRACTION To find image features independent to image segments rotation and translation it is useful to apply Radon and wavelet transforms as the fundamental tools used in the proposed approach. The classification of image features obtained in this way [Procházka and Gavlasová, 2005] allows an efficient classification of image segments independent to texture rotation. Radon transform forming a very important mathematical tool used in tomography is based upon works of Johann Radon born in 1887 in Litoměřice. His doctoral dissertation has been defended in Vienna in 1910 and his most appreciated works were devoted to integral geometry. The Radon transform [Bracewell, 2003] belonging to this category introduced in 1917 is defined as a collection of 1D projections around an object at angle intervals Θ. The Radon transform of a two-dimensional (2-D) function f(x, y) is defined as R(Θ,r)[f(x, y)]= + + f(x, y)δ(r x cos Θ y sin Θ)dxdy (1) where r is the perpendicular distance of a line from the origin and Θ is the angle formed by the distance vector. It is possible to analyse this relation taking into account that the value of δ function is nonzero for its argument equal to zero only which means that R128 2

3 r x cos Θ y sin Θ = 0 (2) y = x cot Θ + r/ sin Θ (3) which for a constant value of Θ represents the set of parallel lines used for the integration of the given image for parameter r. The plane (x, y) is transformed in this way to the plane (Θ,r). A discrete Radon transform called Hough transform has been introduced in 1972 by R. O. Duda and P. E. Hart [1972] as a basic tool for image features extraction. Its inverse version forms moreover the fundamental mathematical tool in computer tomography allowing the reconstruction of the two dimensional image from its projections having rotating sources of beams and the set of rotating sensors. Figure 2 Block diagram of the proposed technique The use of Radon and wavelet transforms for extraction of rotation and translation invariant image components features is presented in Fig. 2. At first all image components are identified using distance and watershed transforms. Then the Radon transform of individual image segments is evaluated followed by the translation-invariant wavelet transform to evaluate its scale components forming basis for the corresponding image segment features. Rotation of the given image corresponds to the translation after the application of the Radon transform along its parameter Θ. 4 FEATURE BASED IMAGE SEGMENTATION There are many possibilities that can be used for feature based image segmentation (FBIS) and content based image retrieval (CBIR) systems [C.W.Shaffrey, 2003; Rushing et al., 2002] that can be used to find image segments. The principle of these methods is based in many cases on the construction of the feature vector associated with each image pixel evaluated from values in the boundary of each root pixel. The fundamental algorithm assumes processing of the intensity image defined by a given matrix R with its values in the range 0, 1. Fig. 3 presents the main command for its processing using the neighborhood of each root pixel of the square shape and given size defined as a matrix B in this case. Feature values evaluated by the user defined function feature can estimate the root pixel feature in % Feature Based Image Segmentation % R - Initial image % F - Feature matrix % L - Number of final image levels global L Region = [7,7]; % Selection of the neighbourhood size Feature = feature ; % The name of function evaluating the root pixel feature F = nlfilter(r,region,feature); Figure 3 The basic method used for feature based image segmentation R128 3

the range I 1, 2,,L for the given number of levels L using many methods including feature estimation derived from pixel values in each matrix B based upon histogram values used as an estimate of the

transforms Selected results of a simulated image processing is presented in Fig. 4 for image classification into four levels.

(a) ORIGINAL IMAGE (b) FEATURE BASED IMAGE SEGMENTATION (c) FEATURE BASED IMAGE SEGMENTATION Figure 4 Feature based image segmentation presenting (a) original simulated image, (b) feature matrix

4 the range I 1, 2,,L for the given number of levels L using many methods including feature estimation derived from pixel values in each matrix B based upon histogram values used as an estimate of the most probable intensity level I standard deviation of pixel values in each matrix B describing changes of its intensity values image energy values using appropriate methods including selected wavelet transforms Selected results of a simulated image processing is presented in Fig. 4 for image classification into four levels. Figs 4(b) and (c) provide comparison of feature matrices obtained from the neighborhood of each root pixel using the standard deviation of their intensities and their histogram values. (a) ORIGINAL IMAGE (b) FEATURE BASED IMAGE SEGMENTATION (c) FEATURE BASED IMAGE SEGMENTATION Figure 4 Feature based image segmentation presenting (a) original simulated image, (b) feature matrix evaluated through standard deviations of image pixel intensities in the neighbourhood of each root pixel, and (c) feature matrix estimated through histogram values 5 RESULTS Proposed methods were verified for simulated images formed by the mixture of different textures and then applied to selected biomedical images. An example of this application is presented in Fig. 5 for its segmentation into 4 levels and a selected square neighbourhood of each root pixel in this case. All algorithms have been verified in the Matlab environment. (a) ORIGINAL IMAGE (b) FEATURE BASED IMAGE SEGMENTATION Figure 5 Application of the image feature based segmentation to the MR image presenting (a) original biomedical image and (b) its segmentation into four levels R128 4

5 6 CONCLUSION The paper presents a study to image classification using two different methods. The first one is based upon the watershed transform allowing to process the image without any previous knowledge of the number of image segments being very sensitive to image oversegmentation. Appropriate selection of features of separate segments allows the following classification into the given number of classes using standard methods of neural network classification. The second method is based upon the direct estimation of pixel features using their neighbourhood. This method is restricted to the initial knowledge of image levels. This method can be very efficient in the case of properly chosen properties of feature vectors associated with all image pixels. ACKNOWLEDGMENTS The work has been supported by the research grant of the Faculty of Chemical Engineering of the Institute of Chemical Technology, Prague No. MSM References ARIVAZHAGAN, S.; GANESAN, L Texture Segmentation Using Wavelet Transform. Pattern Recogn. Lett., 24, 16, ARIVAZHAGAN, S.; GANESAN, L Automatic Target Detection Using Wavelet Transform. Eurasip Journal on Applied Sig. Proc., 17, BRACEWELL, R. N Fourier Analysis and Imaging. Kluwer Academic Press. C.W.SHAFFREY Multiscale Techniques for Image Segmentation, Classification and Retrieval. Ph.D. thesis, University of Cambridge, Department of Engineering, Signal Processing and Communication Laboratory. GAVLASOVÁ, A.; PROCHÁZKA, A Simulink modelling of radon and wavelet transforms for image feature extraction. In International Conference Technical Computing Prague. GAVLASOVÁ, A.; PROCHÁZKA, A.; MUDROVÁ, M Wavelet use for image classification. In Process Control PC GONZALES, R. C.; WOODS, R. E.; EDDINS, S. L Digital Image Processing Using MATLAB. Prentice Hall. HAYKIN, S Neural Networks, A Comprehensive Foundation. New York: Macmillan College Publishing Company. K. JAFARI-KHOUZANI AND H. SOLTANIAN-ZADEH Rotation-Invariant Multiresolution Texture Analysis Using Radon and Wavelet Transforms. IEEE Trans. on Image processing, 14, 6, LOWE, D. G Object recognition from local scale-invariant features. In International Conference on Computer Vision. Corfu. NIXON, M.; AGUADO, A Feature Extraction & Image Processing. NewNes Elsevier. PROCHÁZKA, A.; GAVLASOVÁ, A Wavelet transform in classification of biomedical images. In IFMBE European Conference on Biomedical Engineering. R. O. DUDA AND P. E. HART Use of the Hough Transformation to Detect Lines and Curves in Pictures. Comm. ACM, 15, 1, RUSHING, J.; RANGANATH, H.; HINKE, T.; GRAVES, S Image segmentation using association rule features. IEEE Transactions on Image Processing, 11, 5, ISSN /01. TOFT, P The Radon Transform - Theory and Implementation. Ph.D. thesis, Technical University of Denmark. TORRES-MÉNDEZ, L.; RUIZ-SUÁREZ, J.; SUCAR, L.; GÓMEZ, G Translation, rotation and scale-invariant object recognition. IEEE Transactions on Systems, Man, and Cybernetics, 30, 1, ISSN /00. R128 5

Texture Segmentation and Classification in Biomedical Image Processing

Texture Segmentation and Classification in Biomedical Image Processing Aleš Procházka and Andrea Gavlasová Department of Computing and Control Engineering Institute of Chemical Technology in Prague Technická