Romain Yildizoglu's home page

I am a PDH student in mathematical image processing. I work at Institut de Mathématiques de Bordeaux (IMB), France.

Contact

At IMB : office 155
email: ryildi@gmail.com

Research interests

In my thesis I study different relaxations of non-convex functionals that can be found in image processing. Some problems, such as image segmentation, can indeed be written as the minimization of a functional. The minimizer of the functional represents the segmentation. Different methods have been proposed in order to find local or global minima of the non-convex functional of the two-phase piecewise constant Mumford-Shah model. With a convex relaxation of this model we can find a global minimum of the non-convex functional. I present and compare some of these methods and I propose a new model with a narrow band. This model finds local minima while using robust convex optimization algorithms. Then a convex relaxation of a two-phase segmentation model is built that compares two given histograms with those of the two segmented regions. I also study some relaxations of high-dimension multi-label problems such as optical flow computation. A convex relaxation with a new algorithm is proposed. The algorithm is iterative with exact projections. A new algorithm is given for a relaxation that is convex in each variable but that is not convex globally. I study the problem of constructing a solution of the original non-convex problem with a solution of the relaxed problem and I compare existing methods with new ones.

Publications

Romain Yildizoglu, Jean-François Aujol, Nicolas Papadakis, Active Contours without Level Sets, IEEE International Conference on Image Processing 2012. [hal]
Romain Yildizoglu, Jean-François Aujol, Nicolas Papadakis, A convex formulation for global histogram based binary segmentation, in Energy Minimization Methods in Computer Vision and Pattern Recognition, pages 335-349. Springer, 2013.[hal]
Nicolas Papadakis, Romain Yildizoglu, Jean-François Aujol, High dimension multilabel problems : Convex or nonconvex relaxation ?, SIAM Journal on Imaging Sciences, 6(4) :2603-2639. 2013 [hal]
Antoine, M., Sargos, P., Saut, O., Pouypoudat, C., Desjardins, M., Loizeau, H., Ternisien, P., Yildizoglu, R., Stoeckle, E., Henrique de Figueireido, B., Caron, J., and Kantor, G. (2014). Geometrical analysis of organs motion for preoperative high dose (54gy) helical tomotherapy of retroperitoneal liposarcoma. In American Society for Radiation Oncology’s 56th annual meeting (ASTRO).