Stochastic modeling and image indexation

拟议的研究由以下两个统一主题下的几个正在进行的项目组成。度量价值过程和随机建模。以下这三个复杂现象有什么共同之处，尽管它们明显不同：流体的湍急流动，细菌种群的遗传进化，以及金融市场上一种商品的价值波动？这三个问题都可以用非线性随机偏微分方程组(或一些相关的离散近似方案)来模拟，可以伪装成适定的鞅问题；并且这三个问题都可以通过相互作用的粒子系统来建立、模拟和分析。我在未来几年的目标是继续我正在进行的关于这些粒子系统的基本性质的研究项目。基于内容的图像搜索系统中的统计建模。我在这里的目标是继续促进目前在图像和地形数据库上使用的基于内容的图像搜索系统的发展，以期在遥感和电信方面有许多应用。我计划将层级结构纳入专门用于多分辨率图像数据库的估计方法；确定最适合多重比较检验框架的那些数学特征(要提取和编入索引)，以便在这类数据库内自动编制索引和检索；在成像界内开发许多尚未开发(或稀有使用)的统计资源，用于建立、维护和利用基于内容的图像数据库和搜索系统。

The proposed research is composed of several ongoing projects, under the following two unifying themes.1. Measure valued processes and stochastic modeling. What do the three following complex phenomena have in common, in spite of their obvious dissimilarities : the turbulent flow of a fluid, the genetic evolution of a population of bacteria, the fluctuation of the value of a commodity on the financial market? All three can be modeled by nonlinear stochastic partial differential equations (or some associated discrete approximation scheme) in the guise of well-posed martingale problems ; and all three can be built, simulated and analyzed via interacting particle systems. My objective for the years to come is the pursuit of my ongoing research projects on the fundamental properties of these systems of particles.2. Statistical modeling in content-based image searching systems. My goal here is to continue to contribute to the ongoing development of content-based image searching systems used on both image and topographic databases, with a view towards many applications in remote sensing and telecommunications. I plan to incorporate hierarchical structures in the estimation methodology specifically destined for multi-resolution imagery databases ; to identify those mathematical characteristics (to be extracted and indexed) that best suit a framework of multiple comparison tests for the purposes of automatic indexation and retrieval from within such databases; to develop the use, within the imaging community, of many as yet untapped (or sparsely used) statistical resources, in the creation, maintenance and exploitation of content-based image databases and searching systems.