Maximum Likelihood Segmentation of Ultrasound Images with Rayleigh Distribution

This study presents a geometric model and a computational algorithm for segmentation of ultrasound images. A partial differential equation (PDE)- based flow is designed in order to achieve a maximum likelihood segmentation of the target in the scene. The flow is derived as the steepest descend of an energy functional taking into account the density probability function of the gray levels of the image as well as smoothness constraints. To model the gray level behavior of ultrasound images, the classic Rayleigh probability distribution is considered. The steady state of the flow presents a maximum likelihood segmentation of the target. A finite difference approximation of the flow is derived, and numerical experiments are provided. Results are presented on ultrasound medical images as fetal echography and echocardiography.