Optimal Control for the Analysis of Image Sequences

0925875-Niethammer通过将图像演化视为一个动态系统，该研究将专注于分析动态变化的图像序列的最优控制方法。我们将发展纵向、横截面和随机设计方法。具体地说，我们将探索(1)时变图像数据的动态建模，(2)它们的最优内插，(3)它们的最佳逼近和平滑，(4)它们的最优滤波，(5)以及图像回归，(6)图像外推，以及(7)基于最优控制理论的有效的求解方法。在这项拟议的研究中，将探索和开发几种分析时变图像的新方法。它们具有普遍的适用性。这项研究将对当前的成像研究产生直接影响，并将为未来的应用奠定基础。例子的应用范围从分析显微镜图像以监测单个细胞的时空现象，到通过磁共振成像研究大脑结构变化。在生物医学成像的背景下，开发的技术最终将通过活体监测对疾病进展产生新的见解，使疾病能够及早发现，也将成为促进个性化医学的基石，个性化医学需要考虑个体发育差异和年龄影响。所有开发的方法都将以开源的形式提供给社区。S的教学目标是通过以下方式减少研究领域之间的交流障碍：(1)提供图像分析课程，其中包括与生物和医学研究小组的学生小组合作；(2)为本科生和暑期学生提供实践图像分析项目的机会；(3)向非计算机专业的学生教授图像分析的基础知识和实践方面的知识。

0925875-NiethammerThe research will focus on an optimal control approach for the analysis of dynamically changing image sequences, by treating image evolution as a dynamical system. We will develop methods for longitudinal, cross-sectional, and random designs. Specifically, we will explore (1) the dynamic modeling of time-varying image data, (2) their optimal interpolation, (3) their optimal approximation and smoothing, (4) their optimal filtering, (5) as well as image regression, (6) image extrapolation, and (7) efficient solution approaches based on optimal control theory.Intellectual Merit While the type of methods we will develop are already very advanced for example for scalar-valued data, the theory and methodology is much less developed, but of equal importance, for the case of time-varying images, which we will focus on. Several novel methods for the analysis of time-varying images will be explored and developed within the proposed research. They have general applicability. The research will have immediate impact on current imaging studies and will form the basis for future applications.Broader Impact The developed methods will have broad applicability, from natural image tracking, to video processing and medical image analysis. Example uses will range from the analysis of microscopy images to monitor spatio-temporal phenomena in individual cells, to the study of structural brain changes by magnetic resonance imaging. In the context of biomedical imaging, the techniques developed will ultimately lead to new insight into disease progression through in vivo monitoring, will enable early disease detection, and will also be a cornerstone to facilitate personalized medicine, which needs to account for individual developmental differences and age effects. All developed methods will be made available to the community in open-source form. This will allow for easy adaptations and the creation of customized image analysis solutions.The PI?s pedagogical goal is to reduce the communication barriers between research fields in the following ways: (1) by offering image analysis courses which include student group collaborations with research groups within biology and medicine, (2) by providing opportunities for undergraduates and summer students for hands-on image analysis projects, (3) and by teaching non computer-science majors about the fundamentals and practical aspects of image analysis.