Surface Motions in Random Media

本研究主要是对时间演化的分析 随机的表面。 将特别强调计算机 实现模拟所需的算法 数学模型了解界面和边界面的运动对许多工业生产具有重要意义 过程（图像分析、晶体生长、薄膜、裂纹成核等）这项研究的动机最初来自于 静态图像和视频的去噪和增强。 基于这个原因， 工作将集中在二维和三维情况。 很少有人注意到迄今为止的随机版本 这些问题，即使他们被认为提供了一个更 确定性方法的现实替代方案。 科学和工程中的许多问题都涉及到移动边界和表面。 示例范围从熔化和固化到视频中边缘的自动检测。 到目前为止，为这些目的而开发的数学方法通常没有考虑随机性。 这项研究将开始纳入这些影响，重点放在应用上 与图像和视频的去噪和增强有关。

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.