The investigator, together with his students and collaborators, will tackle important analytical and computational problems from image processing and computer vision that arise also in a variety of other fields, such as computer graphics, population dynamics, and materials science. A significant analytical component of the research program will focus on better understanding the coarsening phenomena observed in ill-posed diffusion equations that are encountered in such disparate fields as image processing (where they appear in models of image segmentation), granular flow (where they describe the formation of shear bands in granular materials), and population dynamics (where they model aggregation of certain types of bacteria). A second component of the research program will develop novel numerical algorithms for efficient computation of the motion of multiple phases under geometric motions arising as steepest descent for energies that contain bulk and surface tension terms. These interfacial motions are frequently encountered not only in fundamental image processing and vision procedures such as image segmentation, but also in materials science where they can describe grain boundary motion in polycrystalline materials. A number of numerical ideas will be utilized in this direction, including the level set method and some novel alternatives to it. The algorithms will be tested on large scale computations of high scientific interest, such as three dimensional simulations of grain growth in materials, using many grains. In addition, the investigator will continue his research program in extending successful image processing models to the context of surface processing in computer graphics.

The image processing and computer vision tasks that will be impacted by results from this research program include image denoising and segmentation, which are fundamental preliminary operations that are needed whenever useful information is to be extracted from images or video automatically. The goal of image denoising is to remove artifacts and noise from images so that subsequent operations can be performed more reliably. The goal of segmentation is to identify parts of an image occupied by distinct objects. Examples of practical applications where these procedures play a primary role include medical imaging, face recognition, and target identification and tracking. Insights gained from the analytical component of this research program will elucidate the nature of some of the most popular but incompletely understood techniques developed for these vision tasks, and consequently allow more effective use of these techniques. The new computational methods that will be developed as a major part of the project will allow efficient and accurate solution of the numerical problems encountered in these computer vision applications, and thus reduce the computer time needed for knowledge extraction from images and video. The numerical issues from computer vision that will be targeted by this research program have a lot in common with numerical issues seen in some central problems in materials science. This connection will in particular make it possible to apply the new computational methods to large scale simulations of the motion of grain boundaries in materials; this computational capability is highly desirable and would be invaluable in predicting the performance and reliability of materials.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
0748333
Program Officer
Leland M. Jameson
Project Start
Project End
Budget Start
2008-02-01
Budget End
2014-01-31
Support Year
Fiscal Year
2007
Total Cost
$400,000
Indirect Cost
Name
University of Michigan Ann Arbor
Department
Type
DUNS #
City
Ann Arbor
State
MI
Country
United States
Zip Code
48109