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