Geometric and statistical methods for image analysis and control

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This proposal has three parts: (i) image registration and analysis; (ii) spatiotemporal modeling; and (iii) control of rotating bodies (e.g. satellites). The first two topics are closely related, and my focus is on methods applicable to medical imaging. The third topic may seem unrelated, but in fact draws on a common mathematical base of geometry and mechanics.******The first subject of this proposal is geometric and statistical methods for image registration and analysis. We will develop new methods for registering, i.e. aligning, images, and describing shape deformations. These tasks are central to medical image analysis and many computer vision applications such as tracking and change detection. In the medical image domain, registration allows us to compare images from different people, or from the same person at different times, and do statistics on groups of images. Current registration methods work well for most images from healthy adults, but struggle with unusual images, including those of diseased or very young or old subjects, which are often precisely the ones of most interest. We will develop general methods that are more robust, more accurate or faster, and methods to simultaneously register images and detect abnormalities.***The second subject is spatiotemporal models of longitudinal data from multiple subjects (or objects), for example medical imaging or clinical disease progression data. Spatiotemporal models take into account both the patterns of change and the rates of changes. For example, to find statistical patterns in the progression of a certain disease, it is useful to take into account the fact that the disease may progress more or less quickly in different individuals, even if they are following the same path of progression. We will develop improved models and statistical techniques, for example incorporating rates of change that vary in different spatial regions.******A third subject of this proposal is the attitude control of rotating bodies via changes in the mass distribution. Just as a spinning skater can speed up by pulling her arms in, angular velocity in a general rotating “rigid” body (i.e. rigid in the absence of control forces) can be changed by changing its shape, i.e. its mass distribution. The general case is much more interesting than the skater example suggests: the angular velocity can change direction, not just amplitude. This kind of shape change can never be used to slow a rotating body down to rest, or initiate motion from rest, so it is not suitable for most control tasks. However, it may provide efficient solutions in some applications, for example in an imaging satellite, where it may suffice for a camera to point in the desired directions instantaneously, while always moving with nonzero velocity. I will study motion planning and optimal control for this problem, and also investigate a related problem in which a rigid object moves through a fluid by moving internal masses.********