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

该研究的重点是在信息尺度研究的指导下，建立自然场景图像模式的统计模型，即图像数据在尺度过程中的统计特性的变化。该研究将在图像建模和表示中融合两种统计和数学理论：(1)源于统计物理的马尔可夫随机场和吉布斯分布等空间统计模型；(2)源于调和分析的表示和编码理论，包括小波和稀疏编码。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)机制下工作得更好，而编码理论在结构化(低熵)机制下工作得更好。PI定义了一个基本的概念，即图像的熵率，它的缩放行为将两个区域联系在一起，即纹理模式的高熵区域和几何模式的低熵区域。更重要的是，这种联系揭示了介于两者之间的一个最关键的制度，即对象模式的中熵制度。PI提出在一个统一的理论框架内集成这三种机制，这种集成将产生用于自然图像模式学习和识别的强大模型和算法。规模和建模问题在许多科学领域都很重要。作为生物学应用，建议的研究还包括基于PI和合作者所做的工作的1D芯片数据的建模和分析。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置的技术。这项技术在研究基因调控方面发挥着重要作用。这项拟议的工作将加强现有的分析此类数据的方法。日常环境的图像包含令人眼花缭乱的各种模式和对象，如树木、树叶、草、河流、房屋、汽车、人物、人脸、狗等。图像是大量数字。为了教会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表示和识别这些模式的高效计算算法是至关重要的。该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样的模型和算法。拟议的研究将对统计学和计算机视觉做出有益的贡献。后者的目标是教计算机像人类一样准确和毫不费力地看东西。

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.