ITR/AP: Variational-PDE Models Using Level Sets for Computer Vision

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This project will attack several important problems in image processing and computer vision. The applications for this work include object detection and recognition (e.g. for tracking objects in video surveillance), segmentation of medical images (e.g. for recognizing white and gray matter in MRI brain data), occlusion and analysis of missing information (e.g. for finding depth from 2-D images), and direction diffusion (e.g. for analyzing fingerprints). The project will work at the boundary between computational and applied mathematics, computer science and engineering, and medical imagery.The research is based on using level set techniques applied to variational models and partial differential equations derived from the images. The work uses an active contour model without edges for object detection, based on the Osher-Sethian level set method and Mumford-Shah segmentation techniques. This model has many advantages over classical ones, including automatic detection of interior contours and robustness with respect to noise. The project will generalize and extend this basic model and provide computationally efficient implementations.