Constrained Point Correspondence

Constrained Point Correspondence

Billy TimlenMentor: Imran Saleemi

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

Point Correspondence Problem

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

Graph Theory Approach

Maximum Flow Network

Maximum Matching

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

Linear Programming

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

Goals

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

Accomplished So Far

Results So Far

Results So Far

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

Still To Do