The research in this proposal will develop probabilistic models that learn abstract images properties and invariant features from the statistical regularities of natural images. The long-term goal of this research is to understand the essential computational principles underlying the transformation of visual sensory codes into increasingly abstract representations that reveal the intrinsic properties of natural visual images and scenes. The specific aims are to develop probabilistic models for learning efficient, hierarchical representations of natural images; to extend these models to allow overcomplete representations and additive noise; and finally to model the natural image density variation in local spatial and temporal regions. This research will provide a deeper understanding of the theoretical issues and computational challenges involved in deriving abstract and invariant representations from statistical regularities in natural images. Progress toward these goals will have a broad impact in applications that require discovery and encoding of intrinsic structures in complex visual images and scenes, such as image compression, visual scene analysis, image processing, and machine vision. The statistical models proposed in this research are broadly applicable and could also have impact in many areas of signal processing, knowledge discovery, and data mining.
