3D MULTIFRACTAL ANALYSIS: APPLICATION FOR EPILIPSY DETECTION IN SPECT IMAGING Lopes R. 1,2 , Makni N. 1,2 , Viard R. 1 , Steinling M. 3 , Maouche S. 2 , Betrouni N. 1 1 Inserm, U703 Pavillon Vancostenobel, CHRU Lille Lille Cedex 59037, France 2 LAGIS, CNRS UMR 8146 USTL, Bâtiment P2, Villeneuve d’Ascq, 59655, France 3 Nuclear Medicine Department (SCMN) University Hospital of Lille, France ABSTRACT In medical imaging, many texture analysis methods were studied with different degrees of effectiveness. These last years, works showed the usefulness of the fractal geometry to characterize textures. The fractal dimension provides a global aspect of the texture, while the multifractal analysis provides a local and global aspect of the texture. In this study, we were interested in the detection of epileptic fit sources on brain SPECT images. The detection problem is formulated as a 3D multifractal analysis scheme. The first results obtained on a base of 5 patients show that this method can be effective for this application. Key Words—3D mutlifractal analysis, SPECT imaging, epilepsy, detection. 1. INTRODUCTION During the last years, many works based on texture analysis were applied in medical image analysis [1;2]. Among the most wide-spread tools, the co-occurrence matrix and Haralick parameters [3-5], Fourier spectrum-based methods [6] and the Gabor filter [7;8]. Recently, fractal geometry has emerged as a new texture analysis way. After applications mainly in the discrimination of two states (healthy versus pathological, for example), works enabled to experience of the usefulness of this geometry concerning the texture heterogeneities detection [9;10]. First works concerning this field used the fractal dimension, which enables to take into account the degree of regularity of the organizational structure related to the physical system’s behaviour. This method gives only a global view of the surface in general and of the texture in particular. As an improvment, the multifractal analysis was used in medical imaging in various fields, such as the classification [11], the segmentation [12] and the discrimination between healthy and pathological patient [13]. We are interested here in the multifractal analysis because it enables a local and global study of image irregularities. The multifractal approach was introduced in the 1980s with Mandelbrot multiplicative cascade models of energy dissipation in fully developed turbulence. For image analysis, its application is still restricted to 2D case. By this work, we introduce a 3D model with an application for the epileptic fit sources detection on SPECT images. 2. METHOD 2.1 Theoretical aspect We start with the following definitions due to Vehel et al.[14], to formulate this approach in 3D. Definition 1: Let E be a set. A paving on E is a set İ of subsets of E containing the empty set and stable under finite intersection. The pair (E, İ) is called a paved space. We note P(E) the power set of E. Definition 2: Let (E, İ) be a paved space. A Choquet İ capacity is a function c: P(E) ĺ  with the following properties: - c is non decreasing: if B A  , then ) B ( c ) A ( c d . - If (A n ) is an increasing sequence of subsets of E, i.e. 1 n n A A   , then   n n n n A c A c sup  ｸ ｸ ｹ ｷ ｨ ｨ ｩ ｧ  . - If (A n ) is a decreasing sequence of elements of İ, i.e. n 1 n A A   , then   n n n n A c inf A c  ｸ ｸ ｹ ｷ ｨ ｨ ｩ ｧ  . 1199 978-1-4244-2003-2/08/$25.00 ©2008 IEEE ISBI 2008