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

本研究的重点是建立自然场景图像模式的统计模型，以研究信息缩放为指导，即图像数据在缩放过程中统计属性的变化。该研究将整合两种统计和数学理论在图像建模和表示中的应用：(1)空间统计模型，如起源于统计物理学的马尔可夫随机场和吉布斯分布；(2)表示和编码理论，包括小波和稀疏编码，起源于谐波分析。目前这两个领域的研究几乎是相互孤立的，随机场模型在随机（高熵）状态下工作得更好，而编码理论在结构化（低熵）状态下工作得更好。pi识别了一个基本概念，即图像熵率，它的缩放行为连接了两个区域，即纹理图案的高熵区域和几何图案的低熵区域。更重要的是，这种联系揭示了两者之间一个最关键的机制，即对象模式的中熵机制。pi建议将这三种机制整合在一个统一的理论框架内，这种整合将导致强大的模型和算法用于自然图像模式的学习和识别。尺度和建模问题在许多科学领域都很重要。作为生物学应用，拟议的研究还包括基于PI和合作者所做的工作的1D ChIP-chip数据的建模和分析。ChIP-chip是一种分离和鉴定活细胞中特定DNA结合蛋白所占据的基因组位点的技术。该技术在研究基因调控方面发挥着重要作用。拟议的工作将加强分析这类数据的现有方法。日常环境的图像包含了令人眼花缭乱的各种图案和物体，如树木、树叶、草、河流、房屋、汽车、人物、面孔、狗等。图像是大数组的数字。为了教计算机自动学习这些模式并从这些图像数据中识别它们，理解自然图像的数学和统计特性并开发简单但通用的统计模型以及用于表示和识别这些模式的高效计算算法至关重要。本研究的目标是研究自然图像的信息内容，并在统一的框架内开发这些模型和算法。所提出的研究将对统计学和计算机视觉做出有益的贡献。后者的目标是教会计算机像人类一样准确、毫不费力地看东西。

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.