Manifold-Based Image Understanding

The rapid growth of sensing and imaging technology, combined with the need for near-real-time action based on the sensed data, has rendered automatic processing, understanding, and decision-making vital to our national security. A unified theory and practical toolset was developed for the analysis and processing of signal and image manifolds for signal and image understanding purposes. The unifying theme is the multiscale geometric structure of signal and image families and manifolds. Specifically, theory and tools were developed for (1) model-based signal and image recognition and registration, (2) sensing and compressing data on manifolds, and (3) data-driven manifold modeling and learning.