A Finite Element Computational Framework for Active Contours on Graphs

TL;DR

This paper introduces a finite element-based computational framework for active contours on graphs, enabling efficient and flexible image segmentation and curve evolution modeling.

Contribution

It generalizes active contour models on graphs using the Finite Element Method and introduces a fast algorithm for constrained curve evolution.

Findings

Effective segmentation demonstrated on images

Framework reduces PDE to sparse nonlinear system

Supervised extension improves segmentation accuracy

Abstract

In this paper we present a new framework for the solution of active contour models on graphs. With the use of the Finite Element Method we generalize active contour models on graphs and reduce the problem from a partial differential equation to the solution of a sparse non-linear system. Additionally, we extend the proposed framework to solve models where the curve evolution is locally constrained around its current location. Based on the previous extension, we propose a fast algorithm for the solution of a wide range active contour models. Last, we present a supervised extension of Geodesic Active Contours for image segmentation and provide experimental evidence for the effectiveness of our framework.