The 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.
