CAREER: Unifying Segmentation and Other Image Processing Problems via Variational PDE's

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0133736Yezzi, AnthonyGA Tech Res CorpThis research is centered around problems of segmentation in image processing. Segmentation, which may be described as the problem of locating meaningful regions within an image, is a crucial problem in medical imaging, military imaging, and a variety of other image based applications. The two goals of this research are to (1) advance the state of the art in image segmentation and (2) develop frameworks to solve segmentation jointly with other image processing problems. A key an example of (2) will focus around the problem of image registration (aligning common objects seen within two or more images). Tradiditionally, the problems of segmentation (locating the objects in each image) and registration (lining them up) are solved separately.This research explores methods for solving such problems simultaneously, with the important benefit that one of the problems need not be fully solved before starting the solution of the other problem. The Principal Investigator's approach to problems (1) and (2) will draw strongly from the mathematical theories of differential geometry, curve and surface evolution, the calculus of variations, and partial differential equations (PDE's). PDE's comprise very natural and powerful mathematical tools due to their flexibility, ease of implementation, and mathematical rigor. Their current and previous applications to problems in image processing (including segmentation) have demonstrated their strong potential in this field.Under the recommended level of support, the PI will make every attempt to meet the original scope and level of effort of this project.