Stochastic modeling and image indexation

拟议的研究是由几个正在进行的项目，在以下两个统一的主题。测度值过程与随机建模。下面这三种复杂的现象，尽管有着明显的不同，但它们有什么共同之处呢：流体的湍流、细菌种群的遗传进化、金融市场上商品价值的波动？所有这三个可以建模的非线性随机偏微分方程（或一些相关的离散近似方案）的伪装适定的鞅问题;和所有这三个可以建立，模拟和分析通过相互作用的粒子系统。我未来几年的目标是追求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。我在此的目标是继续为目前正在开发的用于图像和地形数据库的基于内容的图像搜索系统作出贡献，以期在遥感和电信方面得到许多应用。我计划在专门针对多分辨率影像数据库的估算方法中加入层次结构，以确定这些数学特征（拟摘录和编制索引）最适合多重比较测试框架，以便从这些数据库中自动编制索引和检索;在成像界开发利用许多尚未开发（或很少使用）的统计资源，以创建、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.