DDMA/University of Michigan Collaborations

• Shape metrics: DDMA works with Selim Esedoglu to develop models and techniques for comparing shapes in images and image-like data. These methods are variational: they require the minimization of suitable energies. This is often accomplished by solving the associated partial differential equations. Part of the work concerned developing algorithms for numerically solving the relevant partial differential equations.
• Object extraction from radiography data: Selim Esedoglu worked with DDMA to develop models and numerical methods for extracting possibly partially occluded symmetric objects from x-ray radiography images of scenes that contain several such objects.
• We have collaborated on theoretical investigations about the performance and reliability of state of the art image processing models, and development of efficient numerical algorithms for their solution.
• Part of the research funds provided by LANL were used to pay summer salary to Matt Elsey, a graduate research assistant at the applied and interdisciplinary mathematics program of the University of Michigan. During the past summer, the student worked on a project for surface denoising. This is an important problem that arises in many contexts, such as computer graphics (fairing of surfaces), computer vision (face recognition), and medical imaging (fitting surfaces to point clouds). U Mich made important progress in developing a promising new regularization term to be used in such appplications that allows for discontinuities in the normals of the surfaces (especially important for reconstructing man-made objects).