Résumé (EN)

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Currently, existing geodesic-based segmentation approaches usually exploit the image features in conjunction with regularization terms, such as curve length, for computing geodesic paths. In this paper, we consider a more complicated problem: finding simple 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 priors serve as a constraint for the construction of local metrics in the lifted space. The geodesic curves then can be efficiently computed through the single-pass Fast Marching method (FMM). 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.