Surface Segmentation Using Implicit Divergence Constraint Between Adjacent Minimal Paths

TL;DR

This paper presents a new 3D object segmentation method using a modified minimal path Eikonal equation with an implicit divergence constraint, improving surface coverage and stability of minimal paths.

Contribution

It introduces a second order correction to the minimal path Eikonal equation to control divergence and enhance surface segmentation accuracy.

Findings

Reduces uncovered surface area in segmentation

Improves stability of minimal path trajectories

Provides a new approximation for minimal surface equations

Abstract

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.