Efficient and Robust Segmentations Based on Eikonal and Diffusion PDEs

In this paper, we present efficient and simple image segmentations based on the solution of two separate Eikonal equations, each originating from a different region. Distance functions from the interior and exterior regions are computed, and final segmentation labels are determined by a competition criterion between the distance functions. We also consider applying a diffusion partial differential equation (PDE) based method to propagate information in a manner inspired by the information propagation feature of the Eikonal equation. Experimental results are presented in a particular medical image segmentation application, and demonstrate the proposed methods.