A common point of partial differential equation and graph theory based image segmentation methods lies in creating and optimizing their energy functions. From the viewpoint of creating energy models

statistical image features from nonparametric estimation are measured with Bhattacharyya metrics

which is further embedded into energy function construction in Geodesic Active Contour (GAC)and Graph Cuts (GC)models in this paper. The improved GAC and GC models benefit from the energy function based on the aforementioned metric

which introduces a pull-back strength into the GAC to prevent boundary leaking and to help the GC model in accurately estimating the distribution from small samples and unstable distribution function as well as extracting objects in more detail. Then

the proposed methods are applied to the medical image segmentation scenario and a bone and meniscus segmentation framework on knee MRI sequence is presented. In the experimental section

quantitative and qualitative comparisons are conducted respectively. Experimental results show the increased precision of our method in segmenting medical images such as knee MRI sequences

which are affected by the noise and the partial volume effect.