Surface Motions in Random Media

随机介质中的表面运动

• 批准号: 9870217
• 负责人: Rene Carmona
• 金额: $ 7.92万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870217&HistoricalAwards=false
• 关键词: Surface; Motions; Random; Media

This research is concerned with the analysis of the time evolution of random surfaces. Special emphasis will be placed on the computer algorithms needed to implement simulations of the mathematical models. The understanding of the motion of interfaces and boundary surfaces is of great importance for many industrial processes (image analysis, crystal growth, thin films, crack nucleation, etc.) The motivation for this research came originally from the denoising and enhancement of still images and videos. For this reason, the efforts will concentrate on the two and three dimensional cases. Very little attention has been given so far to stochastic versions of such problems, even though they are believed to offer a more realistic alternative that deterministic approaches. Many problems in science and engineering involve moving boundaries and surfaces. Examples range from melting and solidification to the automatic detection of edges in videos. The mathematical methods that have been developed for these purposes so far usually do not take randomness into account. This research will begin to incorporate such effects, focussing on applications that are related to the denoising and enhancement of images and videos.

这项研究涉及对随机表面的时间演变的分析。 将特别重点放在实施数学模型模拟所需的计算机算法上。对于许多工业过程（图像分析，晶体生长，薄膜，裂纹成核等），对接口和边界表面运动的理解非常重要视频。 因此，努力将集中在两个维度和三维案例上。 到目前为止，人们对此类问题的随机版本的关注很少，尽管人们认为它们提供了一种更现实的选择，即确定性方法。 科学和工程中的许多问题都涉及移动边界和表面。 示例范围从熔化和凝固到视频中边缘的自动检测。 到目前为止，出于这些目的而开发的数学方法通常不考虑随机性。 这项研究将开始纳入此类效果，重点关注与图像和视频增强和增强相关的应用。