Optimal algorithms for topologically constrained point correspondenceWilliam Timlen2, Imran Saleemi1,Mubarak Shah1
1University of Central Florida 2Providence College
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.
Create a weighted graph based on the dot product between SIFT descriptors of corresponding key-points
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
Results Test Set: Pairs of images found on Bing Maps which are close
both in scale and orientation Intersections between correspondences should be minimal
Key points Extract SIFT points Apply user defined threshold and non maximal suppression
Eliminates close points and overlapping points
N = Maximum Number of Keypoints
K = Minimum Number of Keypoints
m1 = slope of line 1m2 = slope of line 2c1 = y1 – m1x1
c2 = y2 – m2x2
Future Work Apply flow optimization algorithm and disjunctive constraints
in a max-cut / min-flow optimization,
Process Take all the possible correspondences and create a complete bipartite
graph. # of edges = (keypoints1)(keypoints2)
Disjunctive Constraint: Intersection between different correspondences Create a conflict matrix to represent all intersections between each
correspondence
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
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