Billy Timlen Mentor: Imran Saleemi

 Goal: Have an optimal matching  Given: List of key-points in each image/frame, Matrix of weights between nodes ◦ Weights based on distance  Constraints: ◦ 1-1 Correspondance ◦ No intersections between correspondences  Need: ◦ Flow Optimization ◦ Disjunctive Constraint Algorithm

 Ford-Fulkerson Algorithm ◦ Finds the maximum flow of a graph ◦ Manipulate to return the path with the Max Flow  Optimal matching ◦ Consequences: Old  Hungarian Algorithm ◦ Finds Optimal Matching ◦ Easy to use with matrices and bipartite graphs

 Preferable ◦ Works with complete bipartite graphs ◦ Works well with matrices ◦ FAST ◦ Returns Matrix of Optimal Matching (1-1) and cost of the matching  Can now manipulate ◦ Create a conflict matrix or forcing matrix of what edges can be selected after each edge is selected ◦ Update after each run of the algorithm ◦ Need a way to represent edges that are impossible  Modify edge weights

 Bentley-Ottmann Algorithm ◦ Finds and reports all intersections in a set of line segments ◦ Adds to Shamos-Hoey Algorithm  Negative Disjunctive Constraint ◦ Can create a conflict matrix (impossible edges)  Pass conflict matrix to Flow Optimization  Positive Disjunctive Constraint ◦ Creates a Forcing matrix (possible edges)  Pass to Flow Optimization

 What we have: Flow Optimization Algorithm, Disjunctive Constraint Algorithm  Bentley-Ottmann ◦ Requires the use of Binary Search Trees and a priority queue  In the process of implementing  Apply result to the Optimization algorithms that we have ◦ Read papers of how to apply disjunctive constraints  Compare for correctness

 Implement Bentley-Ottmann  Manipulate Algorithms  Search for faster and more efficient algorithms