Active polyhedron for 3D image segmentation

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 directed along a surface normal 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.

2. The method of claim 1 , further comprising determining iteratively the image-based speed of each vertex and the regularization term, and updated mesh vertices until the vertices of the polyhedron have converged.

3. The method of claim 1 , further comprising performing a mesh operation after updating the plurality of mesh vertices of the polyhedron to grow or shrink a surface of the polyhedron.

4. The method of claim 3 , wherein the mesh operation is one of an edge split, an edge collapse and a face split.

5. The method of claim 1 , wherein the regularization term prevents a surface of the polyhedron from self-intersecting.

6. The method of claim 5 , wherein the regularization term increases in influence as a vertex approaches a surface of the polyhedron.

7. The method of claim 6 , wherein the regularization term is based on electrostatic principles and does not penalize high curvature.

8. A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for three dimensional image segmentation of a volume of interest, the method steps 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 directed along a surface normal 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.

9. The method of claim 8 , further comprising determining iteratively the image-based speed of each vertex and the regularization term, and updated mesh vertices until the vertices of the polyhedron have converged.

10. The method of claim 8 , further comprising performing a mesh operation after updating the plurality of mesh vertices of the polyhedron to grow or shrink a surface of the polyhedron.

11. The method of claim 10 , wherein the mesh operation is one of an edge split, an edge collapse and a face split.

12. The method of claim 8 , wherein the regularization term prevents a surface of the polyhedron from self-intersecting.

13. The method of claim 12 , wherein the regularization term increases in influence as a vertex approaches a surface of the polyhedron.

14. The method of claim 13 , wherein the regularization term is based on electrostatic principles and does not penalize high curvature.