An Elastica Geodesic Approach with Convexity Shape Prior

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 the image features in conjunction with geometric regularization terms (such as curve length or elastica length) for computing geodesic paths. In this paper, we consider a more complicated problem: finding simple and closed geodesic curves which are imposed a convexity shape prior. The proposed approach relies on an orientation-lifting strategy, by which a planar curve can be mapped to an high-dimensional orientation space. The convexity shape prior serves as a constraint for the construction of local metrics. The geodesic curves in the lifted space then can be efficiently computed through the fast marching method. In addition, we introduce a way to incorporate region-based homogeneity features into the proposed geodesic model so as to solve the region-based segmentation issues with shape prior constraints.