Fuzzy clustering driven anisotropic diffusion: enhancement and segmentation of cardiac MR images

Previously, we proposed a second rank tensor conductance function with an explicit dependence on the space coordinates and the data function. This scheme gives the equations an intrinsic anisotropic character not present in previous approaches, and allows the use of a priori knowledge of the system in multi-feature and multi-dimensional images. In this article we extend this scheme by introducing a fuzzy clustering algorithm that, using information about the intensity distribution, divides the image domain into regions and assigns every pixel in the image a degree of membership to the clusters, i.e. a probability of belonging to each of the regions. For this purpose we employ a fuzzy c-means algorithm in which we introduce a priori knowledge about the system by using a planispheric coordinate system that exploits the approximate elliptic-paraboloidal shape and symmetry of the left ventricle. The fuzzy classification of the image domain provides a measure of the probability that neighbouring pixels belong to the same tissue type, and is therefore incorporated into the diffusion process by means of the conductance function. The clustering is updated at regular intervals during the diffusion process, and the initially coarse segmentation of the image is gradually improved until it converges to a meaningful segmentation of the image regions as the smoothing action of the diffusion process clears the image from noise