Constrained Point Correspondence

1. Constrained Point Correspondence Billy Timlen Mentor: ImranSaleemi

2. Point Correspondence Problem • Relating parts of one image to parts of another image • Constraints: • 1-1 Correspondence • No intersections between correspondences • Uses: • Comparing two images side by side • Tracking and Detection

3. Graph Theory Approach • Take key-points from each image to create bipartite graph • Bipartite graph: graph where between two sets of nodes there are adjacencies between sets but none within the sets • Find the maximum flow of the network and apply linear constraint • No intersections • Do these two processes simultaneously

4. Maximum Flow Network

5. Maximum Matching

6. Linear Programming • Method of optimizing a linear function applying linear equality/inequality constraints • Want to maximize the number of correspondences while minimizing the number of intersections • Represent the linear constraint using a conflict graph which depicts all possible intersections

7. Goals • Have a more correct method of comparing and contrasting images by comparing to other images • Possible use in tracking • Apply algorithm to other graph theory related problems • Use as a tool in other vision related fields

8. Accomplished So Far • Created small data set of images of varying sizes and viewpoints • Function that creates a Bipartite Graph between key-points • Returns a matrix of all possible line segments and weights • Function that creates a conflict matrix based on intersections

9. Results So Far

10. Results So Far

12. Still To Do • Apply well-known algorithm to find the Maximum Flow of the network while minimizing cost • Looked at Hungarian Algorithm – Too specific, can’t manipulate • Looked at Ford-Fulkerson Algorithm • Looking at Maximum Matching Algorithms • Apply Conflict Graph Simultaneously • Have preliminary results using a naïve approach