Manifold-Based Image Understanding

摘要

This project aimed toward a unified theory and practical toolset for the analysis and processing of signal and image manifolds for signal and image understanding purposes. The unifying theme was the multiscale geometric structure of signal and image families and manifolds. Specifically, we developed theory and tools for model-based signal and image recognition and registration, sensing and compressing data on manifolds, and data-driven manifold modeling and learning. The results of our work include (1) the smashed filter, a new tool for compressive classification; (2) our theoretical proof of the sufficiency of random projections to compressively capture signals on a manifold, with application to the theory of compressive sensing; and (3) the development of new theory and algorithms for learning manifold models for signal and image families.