Piecewise smooth Mumford-Shah on an arbitrary graph

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.