Geodesic Models with Convexity Shape Prior

TL;DR

This paper introduces new geodesic models with a convexity shape prior for image segmentation, utilizing orientation-lifting and Hamiltonian fast marching to compute curvature-penalized paths efficiently.

Contribution

It develops a novel orientation-lifting based geodesic model incorporating convexity constraints for improved image segmentation.

Findings

Effective curvature-penalized geodesic paths computed via fast marching.

Enhanced segmentation results with convexity shape prior.

Applicable to interactive image segmentation tasks.

Abstract

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.