My research is in image processing, inverse problems and scientific computing. To solve problems in these areas, I develop numerical tools for partial differential equations (PDE), variational problems, and optimization (shape optimization and PDE-constrained optimization).
07.20.2021 - Organized the Minisymposium on Advances in Shape Optimization Algorithms at the SIAM Conference on Optimization (see conference web page)
Currently I am developing computational methods for shape analysis and shape reconstruction from direct and indirect measurements (e.g. by a camera, a microscope, a CT-scanner, etc). In the case of direct measurements (i.e. images), I solve the image segmentation problem, namely the problem of detecting objects, regions or boundaries in given images. In the case of indirect measurements, I deal with tomographic reconstruction or nondestructive testing. I have also been developing algorithms for statistical shape analysis based on the elastic shape dissimilarity metric.
Previously I developed and implemented numerical algorithms to enable simulations of nonlinear physics of material microstructures. This code is incorporated in the software package, Object-Oriented Finite Element Analysis of Microstructures (OOF), distributed by NIST (see OOF web page). I have also developed fast reconstruction algorithms for inverse problems governed by PDEs.
See research gallery for more information about my research.
PhD, Applied Mathematics and Scientific Computing , 2006
University of Maryland at College Park, MD, USA
MSc, Computer Science, 2003
University of Maryland at College Park, MD, USA
BSc, Computer Engineering & Physics , 1999
Bogaziçi (Bosphorus) University, Istanbul, Turkey
Shape calculus for shape energies in image processing, arXiv:1307.5797. (pdf file)
Texture segmentation from a manifold learning perspective , with M. Vazquez, T. Sauer, T. Berry, submitted.
VEMOS: A GUI for evaluation of similarity metrics on complex data sets , with E. Fleisig, NIST Technical Note 2160, June 2021. (pdf file)
On Computing elastic shape distances between curves in d-dimensional space , with J. Bernal, J. F. Lawrence, C. R. Hagwood, NIST Technical Note 2164, June 2021. (pdf file)
An efficient Lagrangian algorithm for an anisotropic geodesic active contour model, Proceedings of 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), June 2017.(pdf file)
Fast dynamic programming for elastic registration of curves, with J. Bernal, C. R. Hagwood, Proceedings of the 2nd Workshop on Differential Geometry in Computer Vision and Machine Learning (Diff-CVML), July 2016. (pdf file)
FFT-based alignment of 2d closed curves with application to elastic shape analysis, with J. Bernal, C. R. Hagwood, Proceedings of the 1st Workshop on Differential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (Diff-CV), September 2015. (pdf file)
Fast minimization of region-based active contours using the shape Hessian, Proceedings of 5th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), May 2015. (pdf file)
A fast algorithm for elastic shape distances between closed planar curves, with J. Bernal, C. R. Hagwood, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2015. (pdf file)
An efficient curve evolution algorithm for multiphase image segmentation, Proceedings of the International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), January 2015. (pdf file)
First variation of the general curvature-dependent energy , with R. H. Nochetto, Mathematical Modeling and Numerical Analysis, 46(1):59-79, 2012. (pdf file)
OOF3D: An image-based finite element solver for materials science , with V. R. Coffman, A. C. E. Reid, S. A. Langer, Mathematics and Computers in Simulation, 82(12):2951–2961, 2012.
A flexible and efficient numerical framework for image segmentation by energy minimization , with P. Morin, R. H. Nochetto, Proceedings of the International Workshop on Discrete Geometry and Mathematical Morphology, pp:42-46, August 2010.
A multilevel algorithm for inverse problems with elliptic pde constraints" with G. Biros, Inverse Problems, 24:034010, 2008 (selected for editorial board highlights). (pdf file)
A variational shape optimization approach for image segmentation with a Mumford-Shah functional, with P. Morin, R. H. Nochetto, SIAM J. on Sci. Comp., 30:3028–3049, 2008. (pdf file)
Discrete gradient flows for shape optimization and applications, with P. Morin, R. H. Nochetto, M. Verani, Comput. Method Appl. M., 196(37-40):3898–3914, 2007. (pdf file)
Recognizing sand ripple patterns from side-scan sonar images , with J. David, Y. Goncharov, C. Y. Kao, P. Suwannajan, NCSU Reports, July 2002.
A variational shape optimization framework for image segmentation , PhD Thesis.