MAnET Metric Analysis for Emergent Technologies

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

Ph.D. Thesis

“Minimal Surfaces in Sub-Riemannian Structures and Functional Geometry of the Visual Cortex” on May 14, 2017

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:

• [Course] Mathematical database and digital Libraries - a.a. 2014-2015 Bologna, Italy
• [Course] Language courses - a.a. 2014-2015 Bologna, Italy

Local training activities:

• [Course] Harmonic maps between manifolds (lecturer F. Bonsante) - a.a. 2014-2015 Bologna, Italy
• [Course] Numerical analysis (lecturer B. Ayuso) - a.a. 2014-2015 Bologna, Italy
• [Course] Pde e semigroup theory (lecturer A. Favini) - a.a. 2014-2015 Bologna, Italy
• [Course] Robotics in Lie groups (lecturer J.Selig) - a.a. 2014-2015 Bologna, Italy
• [Seminars] Local training activity for MAnET Project - a.a. 2014-2015 Bologna, Italy
• [Seminars] Topics in Mathematics, periodic seminar organized by N. Arcozzi, S. Francaviglia, M. Galli - a.a. 2014-2015 Bologna, Italy

Network-wide training activities:

• [Workshop] Geometrical Models in Vision - October 22-24, 2014 Paris, France
• [Workshop] Sub-Riemannian Analysis, PDE and Applications - January 26-30, 2015 Berna, Swiss
• [Workshop] Geometric Analysis in the Heisenberg group - March 4-6, 2015 Bologna, Italy
• [Conference] The First International Conference on Mathematical NeuroScience - June 8-10, 2015 Antibes - Juan les Pins, France
• [Workshop] A mathematical tribute to Ennio De Giorgi - September 19-23, 2016 Pisa, Italy
• [Summer School] Neurogeometry - July 2-14, 2017 Cortona, Italy
• [Conference] Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy

Organization activities:

• [Conference] Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy

Outreach:

• [Course] Mathematical Analysis I - a.a. 2016-2017 Bologna, Italy
• [Thesis co-supervisor] Analysis of transient states in EMG signals with applications to robotic prostheses - 2018 Bologna
• [Thesis co-supervisor] A mathematical model of the motor cortex - 2017 Bologna

Talks and Poster Presentations:

• [Talk] Surface reconstruction via mean curvature flow at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
• [Talk] Surface reconstruction through mean curvature flow in the sub-Riemannian geometry of primary visual cortex model at The total variation flow and related nonlinear evolution problems - July 11-15, 2016 Salzbrug, Austria
• [Talk] Surface reconstruction through mean curvature flow in the sub-Riemannian geometry of primary visual cortex model at MAnET Metric Analysis Meeting - January 18-19, 2017 Paris, France
• [Talk] Geometrical models of the primary visual cortex at Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 25, 2018 Bologna, Italy

Secondment:

• CAMS/EHESS - December 2016 to March 2017 Paris, France
• INAIL - April 1 to June 30, 2017 Bologna, Italy

Publications and Preprints

• E. Baspinar, G. Citti, A. Sarti, A geometric model of multi-scale orientation preference maps via Gabor functions on Journal of Mathematical Imaging and Vision Vol 60 Springer Verlag 2018 pp. 1–13 open access version
• E. Baspinar, G. Citti, A diffusion driven curvature flow preprint
• E. Baspinar, G. Citti, Uniqueness of viscosity mean curvature flow solution in two sub-Riemannian structures preprint
• E. Baspinar, Surface reconstruction via mean curvature flow report
• E. Baspinar, Surface reconstruction through mean curvature flow in the sub-Riemannian geometry of primary visual cortex model report
• E. Baspinar, Geometrical models of the primary visual cortex report