Piecewise smooth Mumford-Shah on an arbitrary graph

1. A non-transitory computer readable medium embodying instructions executable by a processor to perform a method for recovering a contour using combinatorial optimization, the method steps comprising:

receiving an input image;

initializing functions for gradient f, smooth background g, and contour r;

determining an optimum of the gradient f of a region R in the input image;

extending the optimum of the gradient f of region R to a complement of R;

determining an optimum of the smooth background function g for a region Q corresponding to the complement of R;

extending the optimum of the smooth background function g of region Q to a complement of Q; and

determining an optimum contour r according to the optimum of the gradient f and the optimum of the smooth background function g using combinatorial optimization.

2. The computer readable medium of claim 1 , wherein the optimum contour r is a mesh smoothing segmentation of the input image.

3. The computer readable medium of claim 1 , wherein the optimum contour r is a filtering of the input image.

4. The computer readable medium of claim 1 , wherein the optimum contour r is a point clustering of the input image.

5. The computer readable medium of claim 1 , wherein the input image is a non-uniformly sampled image.

6. A non-transitory computer readable medium embodying instructions executable by a processor to perform a method for recovering a contour using combinatorial optimization, the method steps comprising:

receiving an input image comprising a plurality of pixels;

initializing a segmentation model of the input image as a graph comprising a plurality of nodes, wherein each pixel of the image is associated with a respected node of the graph, and the segmentation model including functions for gradient smooth background g, and contour r;

determining a foreground by the gradient f of a region R in the input image;

extending the foreground of the gradient f of region R to a complement of R to determine an extended foreground;

determining a background by the smooth background function g for a region Q corresponding to the complement of R;

extending the background of the smooth background function g of region Q to a complement of Q to determine an extended background; and

determining a contour r according to the extended foreground and the extended background, wherein the contour r is a segmentation of the input image.

7. The computer readable medium of claim 6 , wherein the input image is two-dimensional.

8. The computer readable medium of claim 6 , wherein the input image is three-dimensional.

9. The computer readable medium of claim 6 , wherein extending the output of the gradient f includes a first set of the pixels of the input image outside of a foreground.

10. The computer readable medium of claim 6 , wherein extending the output of the smooth background function g includes a second set of the pixels of the input image outside of a background.

11. The computer readable medium of claim 6 , wherein the segmentation of the input image is a mesh smoothing segmentation.

12. The computer readable medium of claim 6 , wherein the segmentation of the input image is a filter of the input image.

13. The computer readable medium of claim 6 , wherein the segmentation of the input image is a point clustering.

14. The computer readable medium of claim 6 , wherein the input image is a non-uniformly sampled image.