Emre Baspinar
Ph.D. student @ Alma Mater Studiorum Università di Bologna - Dipartimento di Matematica (UNIBO)
since 10/1/2014 for 3 years.
under the supervision of Prof. Giovanna Citti
Research
Physical motivation for our study is perceptual completion and formation of subjective surfaces performed on corrupted geometric structures in images. Main consideration for such image reconstruction procedure is compatibility of the reconstructed part with the existing contextual information in the corrupted image. In order to handle compatibility problem, we use the geometry of cortical based model of Citti-Sarti, which is the lifting in SE(2) and is motivated from visual cortex architecture. Reconstruction process via this model is realized as a diffusion driven motion by curvature. Therefore, we focus on mean curvature flow for reconstruction of corrupted parts of a surface. We can separate our study into two parts. In the first part, we study new methods, inspired by Bence-Merriman-Osher (BMO) numerical algorithm for tracking the evolution of a surface through time in both R and SE(2).
Complementary training activities:
- Mathematical database and digital Libraries - A.A 2014/15 Bologna, Italy
Local training activities:
- Harmonic maps between manifolds (lecturer F. Bonsante) - A.A 2014/15 Bologna, Italy
- Local training activity for MAnET Project - A.A 2014/15 Bologna, Italy
- Numerical analysis (lecturer B. Ayuso) - A.A 2014/15 Bologna, Italy
- Pde e semigroup theory (lecturer A. Favini) - A.A 2014/15 Bologna, Italy
- Topics in Mathematics, periodic seminar organized by N. Arcozzi, S. Francaviglia, M. Galli - A.A 2014/15 Bologna, Italy
- Robotics in Lie groups (lecturer J.Selig) - A.A.2014/15 Bologna, Italy
Network-wide training activities:
- Sub-Riemannian Analysis, PDE and Applications - January 26-30, 2015 Berna, Swiss
- The First International Conference on Mathematical NeuroScience - June 8-10, 2015 Antibes - Juan les Pins, France
- Geometric Analysis in the Heisenberg group - March 4-6, 2015 Bologna
- Geometrical Models in Vision - October 22-24, 2014 Paris, France
- A mathematical tribute to Ennio De Giorgi - September 19-23, 2016 Pisa, Italy
Secondment:
- The total variation flow and related nonlinear evolution problems - July 11-15, 2016 Salzbrug, Austria
Publications and Preprints
- G.Citti, E.Baspinar A diffusion driven curvature flow preprint
- G.Citti, E.Baspinar Uniqueness of viscosity mean curvature flow solution in two sub-Riemannian structures preprint
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