Alexey Mashtakov
Post Doc @ Technische Universiteit Eindhoven (TU/e)
since 4/14/2014 for 2 years.
under the supervision of Dr. R. Duits, Prof. B.M. ter Haar Romeny
Research
The project is devoted to usage of sub-Riemannian geodesics on Lie groups in image analysis. General idea is to bring metric analysis techniques to the image processing community. It turned out, that introducing sub-Riemannian (SR) geometry on an image (more precisely in its lift to a chosen Lie group) shows very promising results in the problem of extraction of salient curves from the image. The following topics were studied: 1) Data-driven SR-geodesics on SE(2) 2) SR-geodesics on SO(3) with cuspless spherical 3) SR-geodesics on SE(3) with cuspless spatial projectionprojections 4) Superintegrability of SR-structures on unimodular 3D Lie groups
Network-wide training activities:
- [Conference] Data-driven Sub-Riemannian Geodesics in SE(2), Bekkers, E.J., Duits, R, Mashtakov, A. and Sanguinetti, G.R. at SSVM 2015 - May 31, to June 4, 2015 Lège Cap Ferret, France
Talks and Poster Presentations:
- [Talk] Analysis of cusps and characterization of the existence set in an association field model on the retinal sphere at International Conference on Differential Equations and Dynamical Systems, - July 4-9, 2014 Suzdal, Russia
- [Poster] R. Duits, E. Bekkers, M. H. J. Janssen, S. P. L. Meesters, A. Mashtakov, M. J. Portegies & G. Sanguinetti Lie Group Analysis for Medical Image Processing at Geometrical Models in Vision - October 22-24, 2014 Paris, France
- [Talk] Sub-Riemannian Problems on 3D Lie Groups with Applications to Retinal Image Processing at Sub-Riemannian Analysis, PDE and Applications - January 26-30, 2015 Berna, Swiss
- [Poster] A. Mashtakov, R. Duits, Y. Sachkov, G. Sanguinetti, E. Bekkers, I. Beschastnyi, B.M. ter Haar Romeny, Sub-Riemannian Problems on 3D Lie Groups with Applications to Retinal Image Processing at International School and Workshop Geometry, Dynamics and Control - July 13, 2015 Lake Baikal, Buryatian Republic
- [Poster] A. Mashtakov, R. Duits, Y. Sachkov, G. Sanguinetti, E. Bekkers, I. Beschastnyi, B.M. ter Haar Romeny, Sub-Riemannian Problems on 3D Lie Groups with Applications to Retinal Image Processing at Nonholonomic days in Pereslavl - August 8, 2015 Pereslavl-Zalesskiy, Russia
- [Talk] Sub-Riemannian Problems on Lie Groups with Applications to Medical Image Processing at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
Secondment:
- UNIBO - January 12 to April 12, 2016 Bologna, Italy
Publications and Preprints
- A. Mashtakov, Y. L. Sachkov., Integrability of left-invariant sub-Riemannian structures on the special linear group SL2(R) on Differential Equations Vol 50 Maik Nauka-Interperiodica Publishing 2014 pp. 1541-1547
- E. J. Bekkers, R. Duits, A. Mashtakov, G. Sanguinetti, A PDE approach to data-driven sub-Riemannian geodesics in SE(2) on SIAM Journal on Imaging Sciences Vol 8 Society for Industrial and Applied Mathematics Publications 2015 pp. 2740-2770 open access version
- A. Mashtakov, Y. L. Sachkov, Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups on Differential Equations Vol 51 Springer Verlag 2015 pp. 1476-1483 open access version
- G. Sanguinetti, E. Bekkers, R. Duits, M. Janssen, A. Mashtakov, J. M. Mirebeau, Sub-Riemannian Fast Marching in SE(2) on Lecture Notes in Computer Science Vol 9423 Springer Verlag 2015 pp. 366-374 open access version
- R. Duits, A. Ghosh, T. Dela Haije, A. Mashtakov, On sub-Riemannian geodesics in SE(3) whose spatial projections do not have cusps on Journal of Dynamical and Control Systems Vol 22 Springer Verlag 2016 pp. 771-805 open access version
- A. Mashtakov, A. ArdentovYuri, L. Sachkov, Relation between Euler’s elasticae and sub-Riemannian geodesics on SE(2) on Regular and Chaotic Dynamics Vol 21 Springer Verlag 2016 pp. 832-839
- A. Mashtakov, R. Duits, Yu. Sachkov, E. J. Bekkers, I. Beschastnyi, Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in {\text {SO(3)}} on Journal of Mathematical Imaging and Vision Vol 58 Springer Verlag 2017 pp. 239-264
- A. Mashtakov, Sub-Riemannian Problems on Lie Groups with Applications to Medical Image Processing report
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