Surface Segmentation Using Implicit Divergence Constraint Between Adjacent Minimal Paths
This work addresses segmentation challenges in 3D imaging, presenting an incremental improvement to existing minimal path methods.
The paper tackles the problem of object segmentation from 3D images by introducing a modified minimal path Eikonal equation with an implicit divergence constraint, which reduces the uncovered surface area and enables the use of minimal paths as parameter lines for an approximate surface.
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.