Contact Information:
Office: CH 440H
Telephone #: (614) 292-0463
E-mail: kurtek.1@stat.osu.edu
Webpage: http://www.stat.osu.edu/~kurtek.1/
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Research
My main research interests lie in the area of statistical image analysis, and more specifically, statistical shape analysis. I am interested in developing novel tools for registration, comparison and statistical modeling of shapes of objects present in 2D and 3D images. There is a strong need for such automated tools in medical diagnostics, face recognition, graphics, bioinformatics, video surveillance, undersea imaging, terrain mapping, and satellite image analysis.Recently, I have worked on developing novel methods for shape analysis of parameterized surfaces. Such a framework requires a Riemannian metric that allows: (1) re-parameterizations of surfaces by isometries, and (2) efficient computations of geodesic paths between surfaces. These tools allow for computing Karcher means and covariances (using tangent PCA) for shape classes, and a probabilistic classification of surfaces. To solve these problems, we developed two different representations of surfaces: (1) q-maps and (2) square root normal fields (SRNFs). We used the natural L2 metric on the space of these representations to induce a Riemannian metric on the space of parameterized surfaces. We also developed computational tools for computing geodesic paths in the shape space of surfaces. This process requires optimal re-parameterizations (deformations of grids) of surfaces and achieves a superior alignment of geometric features across shapes. The resulting statistical summaries are better representatives of the original data and lead to parsimonious shape models. We used the shape mean and covariance to specify a normal probability model on shape classes, which can then be used for random sampling or different classification tasks. We have demonstrated the strengths of this methodology through improved random sampling and more natural geodesic paths between surfaces. We have applied this methodology in many settings including shapes of subcortical structures in the brain or endometrial tissue in medical imaging, and highly articulated shapes in graphics.
For a more detailed description of my and related research visit Statistical Shape and Modeling Group's page at the Florida State University: Statistical Shape and Modeling Group.
Deformation of a horse into a cow.