This work deals with the computer vision problem of recognizing and locating rigid shapes in the plane which have been subjected to unknown rotation, scaling, and noise. The recognition task includes both locating the overall pattern and identifying each of its features. Location is achieved by finding a geometric registration function that does a good job of superimposing the instance and the model. Identifying the features requires matching each model feature with the corresponding instance feature. A pruned tree-search algorithm is developed which makes effective use of the Soviet ellipsoid algorithm for feasibility of linear constraints. An interesting blend of theoretical analysis and practical implementation shows that the resulting algorithm has an expected runtime that is theoretically asymptotically quadratic in the number of feature points, but practically linear in n for patterns with fewer than 100 points.
Introduction • Task Abstraction • Prior Approaches • A Linear Programming Approach • Geometry of Registrations and Ellipsoids • Worst-Case Number of Feasible Matchings • Random Patterns • Expected Cost of Feasibility Testing • Expected Size of Search Tree • Monte Carlo Trials • Conclusions
Model-Based Image Matching Using Location is a 1984 ACM Distinguished Dissertation.