Apr 15 2015 Wednesday 16:00
Gözde Ünal, Faculty of Engineering and Natural Sciences, Sabancı University
Mathematical Modeling in Medical Imaging

Abstract: In this seminar, I will present an overview of some of my recent work on medical computer vision. The first problem I will talk about is using higher-order tensors in modelling of tree-like structures such as vascular trees in human brain and the heart. We embed the tensor in a 4D space rather than 3D in order to untangle the bifurcating (or even n-furcating) structures/branches in the data in a higher-dimensional space. This led to a highly performing and efficient vessel segmentation framework [1, 2], which is demonstrated on different applications. The second problem I’ll present is on modeling the changes of tumor in brain MRI, which is important for radio-therapy planning and follow-up assessment of the cancer disease. I will present a method for estimation of deformation in brain images, and how it is used to calculate tumor response measures [3,4]. Third, I will show a novel volumetric shape representation based on the screened Poisson partial differential equation and its low dimensional embeddings we call SPEMs [5], which is applied to a nonrigid shape retrieval problem.

[1] S. Cetin, G. Unal, “A Higher-order tensor Vessel tractography for segmentation of vascular structures”, to appear, IEEE Transactions on Medical Imaging, 2015.
[2] S. Cetin, A. Demir, A. Yezzi, M. Degertekin, G. Unal, “Vessel Tractography Using an Intensity Based Tensor Model With Branch Detection”, IEEE Transactions on Medical Imaging, 32(2):348-63; 2013.
[3] A. Hamamci and G. Unal, “Registration of Brain Tumor Images Using Hyper-Elastic Regularization”, Computational Biomechanics for Medicine: Models, Algorithms and Implementation, Eds. A. Wittek, K. Miller, P.M.F. Nielsen, 2013, pp. 101-114, Springer.
[4] A. Hamamcı, N. Kucuk, K. Karaman, K. Engin, G. Unal, “Tumor-Cut: Segmentation of Brain Tumors on Contrast-enhanced MR Images for Radiosurgery Applications”, IEEE Transactions on Medical Imaging, Vol.31, No: 3, 790-804, 2012.
[5] R.A. Guler, S. Tari, G. Unal, “Screened Poisson Hyper-Fields for Shape Coding”, SIAM Journal on Imaging Sciences, Vol. 7 (4), pp. 2558-2590, 2014.