Report #2 – Week 3Billy 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

Point Correspondence

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

Flow Optimization

Hungarian Algorithm

Hungarian Examples

Hungarian Algorithm

Hungarian Algorithm

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

Hungarian Algorithm

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

Constraint

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

What we need

Implement Bentley-Ottmann

Manipulate Algorithms

Search for faster and more efficient algorithms

To Do