Abstract: A method for determining an optimal labeling of pixels in computer vision includes modeling an image by a graph having interior nodes and edges where each image point p is associated with a graph node, each pair of nearest neighbor points p, q is connected by a graph edge, each graph node p is associated with a singleton potential c(p), and each graph edge is associated with a pairwise potential function d(p,q). A label is randomly assigned to each point to initialize unary variables including an indicator function that indicates which label is assigned to which point and dual variables including height variables associated with each node p and label a, and balance variables associated with each edge (p,q) and label a. For each label, a new label c is selected, a capacitated graph is constructed and solved. The label selection divides the image into disjoint regions.

Abstract: A method for registering digitized images using Markov Random Fields (MRFs) includes providing a source image f and a target image g, defining a deformation grid of control points, defining a coordinate transformation as T ? ( x ) = x + ? p ? G ? ? ? ( ? x - p ? ) ? d u p , where x is a point on the source image, p is a position vector of control point p, dp is a displacement vector for each control point, up is a label for point p associated with displacement dp, and ?( ) is a weighting function for the displacement vector, defining an MRF energy functional to be minimized by T as E t = 1 ? G ? ? ? p ? G ? V p t ? ( u p ) + 1 ? E ? ? ? p , q ? E ? V pq ? ( u p , u q ) , wherein |G| is a number of control points, |E| is a number of pairs of neighboring control points on a neighborhood system, t is an iteration counter, and associating the MRF with a primary linear program and solving the primary linear program usi

Abstract: A method for determining an optimal labeling of pixels in computer vision includes modeling an image by a graph having interior nodes and edges where each image point p is associated with a graph node, each pair of nearest neighbor points p, q is connected by a graph edge, each graph node p is associated with a singleton potential c(p), and each graph edge is associated with a pairwise potential function d(p,q). A label is randomly assigned to each point to initialize unary variables including an indicator function that indicates which label is assigned to which point and dual variables including height variables associated with each node p and label a, and balance variables associated with each edge (p,q) and label a. For each label, a new label c is selected, a capacitated graph is constructed and solved. The label selection divides the image into disjoint regions.

Abstract: A method for registering digitized images using Markov Random Fields (MRFs) includes providing a source image f and a target image g, defining a deformation grid of T ? ( x ) = x + ? p ? G ? ? ? ( ? x - p ? ) ? d u p , control points, defining a coordinate transformation as where x is a point on the source image, p is a position vector of control point p, dp is a displacement vector for each control point, up is a label for point p associated with displacement dp, and ?( ) is a weighting function for the displacement vector, defining an MRF energy functional to be minimized by T as E t = 1 ? G ? ? ? p ? G ? V p t ? ( u p ) + 1 ? E ? ? ? p , q ? E ? V pq ? ( u p , u q ) , wherein |G| is a number of control points, |E| is a number of pairs of neighboring control points on a neighborhood system, t is an iteration counter, and associating the MRF with a primary linear program and solving the primary linear program usin