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Problem Accurate Point Correspondence Find maximum matching while applying disjunctive constraints

Optimal algorithms for topologically constrained point correspondence William Timlen 2 , Imran Saleemi 1 ,Mubarak Shah 1 1 University of Central Florida 2 Providence College. Key points Extract SIFT points Apply user defined threshold and non maximal suppression

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Problem Accurate Point Correspondence Find maximum matching while applying disjunctive constraints

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  1. Optimal algorithms for topologically constrained point correspondenceWilliam Timlen2, Imran Saleemi1,Mubarak Shah11University of Central Florida 2Providence College • Key points • Extract SIFT points • Apply user defined threshold and non maximal suppression • Eliminates close points and overlapping points • Problem • Accurate Point Correspondence • Find maximum matching while applying disjunctive constraints • Our disjunctive constraint is linear intersections • Minimize the matching cost and the intersections between correspondences • Applications: • Image Correspondence, Detection and Tracking, etc. • Results • Test Set: Pairs of images found on Bing Mapswhich are close both in scale and orientation • Intersections between correspondences should be minimal • Process • Take all the possible correspondences and create a complete bipartite graph. • # of edges = (keypoints1)(keypoints2) • Proposed Method • Extract key points between two images/frames • Create a bipartite graph of all possible correspondences. • Find the maximum flow (matching) using an optimization algorithm and then solve using linear programming with linear constraints • I took a greedy approach by performing Hungarian Algorithm and applied linear constraint iteratively • Disjunctive Constraint: Intersection between different correspondences • Create a conflict matrix to represent all intersections between each correspondence • m1 = slope of line 1 • m2 = slope of line 2 • c1 = y1 – m1x1 • c2 = y2 – m2x2 • Create a weighted graph based on the dot product between SIFT descriptors of corresponding key-points • Run an optimization algorithm with the weighted graph • Used the Hungarian Algorithm • # of possible permutations = (nCk)(k!) • Pass correspondences through the disjunctive constraint • Re-adjust weights of intersecting correspondences • N = Maximum Number of Keypoints • K = Minimum Number of Keypoints • Future Work • Apply flow optimization algorithm and disjunctive constraints in a max-cut / min-flow optimization,

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