Fast Asymmetric Fronts Propagation for Image Segmentation

TL;DR

This paper presents a novel asymmetric fronts propagation model based on Finsler metrics and Eikonal PDEs, improving image segmentation by preventing front leaking and enabling efficient interactive segmentation tasks.

Contribution

Introduces a Finsler metric-based asymmetric fronts propagation model for image segmentation, enhancing control over front leakage and computational efficiency.

Findings

Effective in foreground and background segmentation

Improves tubularity segmentation accuracy

Offers efficient interactive segmentation methods

Abstract

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow. The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to image segmentation applications. Specifically, the foreground and background segmentation is implemented by the Voronoi index map. In addition, for the application of tubularity segmentation, we exploit the level set lines of the geodesic distance map associated to the proposed Finsler metric providing that a thresholding value is given.