1. A method for three dimensional image segmentation of a volume of interest comprising: providing a three dimensional image of the volume of interest; providing an initial polyhedron having a plurality of mesh vertices within the three dimension image; determining an image-based speed at each vertex of the polyhedron using an ordinary differential equation (ODE) that describes the vertex motion of the polyhedron; determining a regularization term at each vertex of the polyhedron; updating the plurality of mesh vertices of the polyhedron, integrating the image-based speed of each vertex over a face of the polyhedron; and determining an output polyhedron approximating a shape of the volume of interest.