Finsler Geodesics Evolution Model for Region based Active Contours

In this paper, we introduce a new deformable model for image segmentation, by reformulating a region-based active contours energy into a geodesic contour energy involving an asymmetric Finsler metric. As a consequence, we solve the region-based active contours energy minimization problem without resorting to level set functions, but using a robust Eikonal equation framework. By sampling a set of control points from the closed active contour in clockwise order, the active contours evolution problem is turned into finding a collection of minimal curves joining all the ordered control points. Therefore, the proposed model can blend the benefits of the curve evolution scheme and the Eikonal equation-based minimal path technique. Globally optimal minimal curves are obtained by solving an Eikonal equation, involving a Finsler metric, which is achieved at a modest numerical cost using a variant of the fast marching algorithm.