Geodesic Models with Convexity Shape Prior

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.

A multiscale circular geodesic model for image segmentation

“…In [14], a path combination model is proposed, in which the simplicity term is introduced to solve the problem of shortcuts, self-overlaps and intersections that exist in the minimal path model. In [15], a method to incorporate region-based homogeneity features into the proposed geodesic model is presented, thus solving the region-based segmentation problem under shape a priori constraints. In [16,17], the Randers metric was construct, which is able to take into account edge anisotropy information and region-based homogeneity penalization.…”