A Fully Automatic k-means-based Algorithm for Image Segmentation

The aim of this paper is to create a fully automatic adaptive k-means segmentation algorithm. In particular we model the gray scale values of the volume image with a White Gaussian Process and we superimpose a prior model on the region process in the form of Markov Random Field. These assumptions require the use of estimators for the parameters of the two functions. The estimation of the mean and the standard deviation of the White Gaussian Process is adaptive, and this has been achieved using rectangular windows of decreasing size which delimits the region where the mean has to be computed. The initial estimation is computed over the whole image and then it is refined decreasing the size of the window. The Hammersley-Clifford theorem allows us to model the region process in term of a Gibbs Distribution. The Gibbs parameter β is estimated using a correlation-based technique. The segmentation is obtained maximizing the a poster density function (MAP estimation) using an Iterated Conditional Modes (ICM) technique. Unlike other techniques our algorithm is fully automatic, in the sense that all the parameters of the model are estimated during the segmentation process, and there is no need to fix a priori values that, as we will prove, can effect the outcome of the segmentation