Surface Segmentation Using Implicit Divergence Constraint Between Adjacent Minimal Paths

We introduce a novel approach for object segmentation from 3D images using modified minimal path Eikonal equation. The proposed method utilizes an implicit constraint - a second order correction to the inhomogeneous minimal path Eikonal - preventing the adjacent minimal path trajectories to diverge uncontrollably. The proposed modification greatly reduces the surface area uncovered by minimal paths allowing the use of the calculated minimal path set as parameter lines of an approximate surface. It also has a loose connection with the true minimal surface Eikonal equations that are also deduced.