Aspects of Invariants for Object Recognition
Final rept. 1 Dec 2000-31 May 2004
TEXAS ENGINEERING EXPERIMENT STATION COLLEGE STATION
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This report is the Final Report for this contract. It details the work done since our last progress report and provides a summary of all the achievements and results that we have obtained. In particular, it details our success in applying newly developed techniques from geometric invariant theory and shape theory, including discrimination metrics, to problems in target recognition. One of the most significant successes was the creation of a global theory of objectimage equations for point features in the generalized weak perspective case. These equations offer a necessary and sufficient, pose independent, robust test for geometric consistency between an object and a purported image of that object. The work also included the development of optimal discrimination metrics and the proof of a metric duality result that shows one can work in either image space or object space to create a natural notion of distance between an object and an image. In addition, similar results were obtained in the radar case orthographic projection where the shape spaces, objectimage equations, and metrics were worked out explicitly for small numbers of feature points.
- Numerical Mathematics
- Active and Passive Radar Detection and Equipment
- Target Direction, Range and Position Finding