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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 561–568 (Mi nd683)  

Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System

A. P. Mashtakov

Ailamazyan Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia

Abstract: This paper summarizes results of a sequence of works related to usage of sub-Riemannian (SR) geometry in image processing and modeling of the human visual system. In recent research in psychology of vision (J. Petitot, G.Citti, A. Sarti) it was shown that SR geodesics appear as natural curves that model a mechanism of the primary visual cortex V1 of a human brain for completion of contours that are partially corrupted or hidden from observation. We extend the model to include data adaptivity via a suitable external cost in the SR metric. We show that data adaptive SR geodesics are useful in real image analysis applications and provide a refined model of V1 that takes into account the presence of a visual stimulus.

Keywords: sub-Riemannian, detection of salient lines, vision, visual cortex, brain-inspired methods

Funding Agency Grant Number
Russian Science Foundation 17-11-01387
This work was supported by the Russian Science Foundation under grant 17-11-01387 and performed at the Ailamazyan Program Systems Institute of the Russian Academy of Sciences.


DOI: https://doi.org/10.20537/nd190415

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MSC: 93C10, 93C15
Received: 31.05.2019
Accepted:03.09.2019

Citation: A. P. Mashtakov, “Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System”, Nelin. Dinam., 15:4 (2019), 561–568

Citation in format AMSBIB
\Bibitem{Mas19}
\by A. P. Mashtakov
\paper Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 561--568
\mathnet{http://mi.mathnet.ru/nd683}
\crossref{https://doi.org/10.20537/nd190415}


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