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.

本研究主要研究随机表面的时间演化过程。将特别强调实施数学模型模拟所需的计算机算法。了解界面和界面的运动对于许多工业过程(图像分析、晶体生长、薄膜、裂纹形核等)具有重要意义。这项研究的动机最初来自于对静止图像和视频的去噪和增强。因此，努力将集中在二维和三维情况下。到目前为止，很少有人注意到这类问题的随机版本，尽管它们被认为提供了一种比确定性方法更现实的选择。科学和工程中的许多问题都涉及移动边界和曲面。例如，从熔化和固化到视频中的自动边缘检测。到目前为止，为这些目的开发的数学方法通常不考虑随机性。这项研究将开始纳入这些效果，重点放在与图像和视频的去噪和增强相关的应用上。