Global Minimum for Curvature Penalized Minimal Path Method

Minimal path or geodesic methods have been widely applied to image analysis and medical imaging [18]. However, traditional minimal path methods do not consider the effect of the curvature. In this paper, we propose a novel curvature penalized minimal path approach implemented via the anisotropic fast marching method and asymmetric Finsler metrics. We study the weighted Euler’s elastica based geodesic energy and give an approximation to this energy by an orientation-lifted Finsler metric so that the proposed model can achieve a global minimum of this geodesic energy between the endpoint and initial source point. We also introduce a method to simplify the initialization of the proposed model. Experiments show that the proposed curvature penalized minimal path model owns several advantages comparing to the existed state-of-the-art minimal path models without curvature penalty both on synthetic and real images.