A Region-based Randers Geodesic Approach for Image Segmentation

The minimal path model based on the Eikonal partial differential equation has served as a fundamental tool for the applications of image segmentation and boundary detection in the passed two decades. However, the existing approaches commonly only exploit the image edge-based features for computing minimal paths, potentially limiting their performance in complicated segmentation situations. In this paper, we introduce a new variational image segmentation model based on the minimal path framework and the eikonal PDE, where the region-based appearance term that defines then regional homogeneity features can be taken into account for estimating the associated minimal paths. This is done by constructing a Randers geodesic metric interpretation to the region-based active contour energy. As a result, the minimization of the active contour energy is transformed to finding the solution to the Randers eikonal PDE. We also suggest a practical interactive image segmentation strategy, where the target boundary can be delineated by the concatenation of the piecewise geodesic paths. We invoke the Finsler variant of the fast marching method to estimate the geodesic distance map, yielding an efficient implementation of the proposed Eikonal region-based active contour model. Experimental results on both synthetic and real images exhibit that our model indeed achieves encouraging segmentation performance.