From Information Scaling to Regimes of Statistical Models of Natural Image Patterns

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

The focus of the proposed research is to develop statistical models for image patterns of natural scenes, guided by the study of information scaling, i.e., the change of statistical properties of the image data over the scaling process. The proposed research will integrate two streams of statistical and mathematical theories in image modeling andrepresentation: (1) spatial statistical models such as Markov random fields and Gibbs distributions originated from statistical physics; and (2) representation and coding theories including wavelets and sparse coding originated from harmonic analysis. At present the two areas are studied almost in mutual isolation, with random field models working (better) in stochastic (high-entropy) regime while the coding theories working (better) in structured (low-entropy) regime. The PIs identify a fundamental concept, the image entropy rate, whose scaling behavior connects the two regimes, namely the high-entropy regime of texture patterns and low-entropy regime of geometric patterns. More important, the connection reveals a most crucial regime in between, that is, the mid-entropy regime of object patterns. The PIs propose to integrate the three regimes within a unified theoretical framework, and this integration will lead to powerful models and algorithms for learning and recognition of natural image patterns. The issue of scale and modeling is important in many scientific areas. As a biological application, the proposed research also includes modeling and analysis of 1D ChIP-chip data, based on the work done by the PI and collaborators. ChIP-chip is a technology for isolation and identification of genomic sites occupied by specific DNA binding proteins in living cells. This technology is playing an important role in studying gene regulation. The proposed work will strengthen existing methods for analyzing such data. Images of daily environments contain a bewildering variety of patterns and objects, such as trees, foliage, grass, rivers, houses, cars, human figures, faces, dogs, etc. The images are large arrays of numbers. In order to teach computers to automatically learn these patterns and recognize them from such image data, it is crucial to understand the mathematical and statistical properties of natural images and to develop simple but general statistical models as well as efficient computational algorithms for representing and recognizing these patterns. The goal of the proposed research is to study the information contents of natural images and to develop such models and algorithms within a unified framework. The proposed research will make useful contributions to both statistics and computer vision. The goal of the latter is to teach computers to see as accurately and effortlessly as human beings do.