Diffeomorphic Reconstruction Of A 2D Simple Non Parametric Manifold From Level Set Data Via Shape Gradients

TL;DR

This paper introduces a variational method for reconstructing 2D simple manifolds as triangulated surfaces from level set data, ensuring smooth boundaries through shape gradients and energy minimization.

Contribution

It presents a novel shape gradient-based variational framework for reconstructing 2D manifolds from level set data, emphasizing smooth boundary recovery.

Findings

Successful reconstruction of 2D manifolds with smooth boundaries

Effective energy minimization via gradient descent

Triangulated surface meshes accurately match object boundaries

Abstract

A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics of the surface. Minimization of the energy through an iterative procedure using the gradient descent method yields a triangulated surface mesh which matches the boundary of the object of interest and this model ensures the smoothness of the boundary.