Geometric Potential Force for the Deformable Model

Deformable models often vary in object boundary representation and the external force field used. Conventional methods, i.e. geodesic active contour model [1], have difficulties in dealing with boundary concavities, weak edges and image noise. Some approaches such as the generalized gradient vector flow (GGVF) [3] showed some improvements but have convergence issues caused by saddle or stationary points in its force field. Very recently, Xie and Mirmehdi [2] proposed a novel edge based model which showed significant improvements in handling weak edges and complex geometries. However, its analogy based on magnetostatics can not be directly applied to 3D or higher dimensional space. In this work, we provide the generalization of the MAC model [2] and define the external force field based on hypothesized geometrically induced interactions between the relative geometries of the deformable model and the object boundaries (characterized by image gradients). In other words, the magnitude and direction of the interaction forces are based on the relative position and orientation between the geometries of the deformable model and image object boundaries, and hence, it is called the geometric potential force (GPF) field. The bidirectionality of the new external force field can facilitate arbitrary cross-boundary initialization, which is a very useful feature to have, especially in the segmentation of complex geometries, and in handling weak edges. Similar to MAC, the proposed external force field is dynamic in nature as it changes according to the relative position and orientation between the evolving deformable model and object boundary.