An Image Segmentation Method Based on a Discrete Version of the Topological Derivative

I. LARRABIDE; R. A. FEIJÓO; A. A. NOVOTNY; E. TAROCO; M. MASMOUDI

Rio de Janeiro

Congreso; 6th World Congress on Structural and Multidisciplinary Optimization (WCSMO6).; 2005

Universidade Federal de Rio de Janeiro

Computed tomography (CT) and magnetic resonance imaging (MRI) have introduced 3D data sets into clinical radiology. 3D data sets provide information for analysis not available in 2D imaging and challenge the traditional 2D viewing and interpretation used in most clinical environments. Despite the 3D format of CT and MRI, they are largely interpreted and analyzed as individual 2D image slices. One of the most important stages in medical image analysis is segmentation of objects or definition of their contours. Although improving imaging techniques (e.g., contrast agents, biological markers) should facilitate the segmentation process, medical images are relatively di±cult to segment for several undesired properties like low signal-to-noise and contrast-to-noise ratios and multiple and discontinuous edges. Our aim in this paper is to present an image segmentation method based on a discrete version of the well established concept of topological derivative. More speci¯cally, we compute the topological derivative for an appropriate functional associated to the image indicating the cost endowed to an specific image segmentation. Further, we propose an image segmentation algorithm based on this approach. Finally, some results are presented in order to show the computational performance of this methodology.