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J. Imaging
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Mathematical Modeling of Human Vision and Its Application to Image...
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Mathematical Modeling of Human Vision and Its Application to Image Processing

A special issue of Journal of Imaging (ISSN 2313-433X). This special issue belongs to the section "Image and Video Processing".

Deadline for manuscript submissions: closed (21 November 2021) | Viewed by 9829

Special Issue Editors

Dr. Alexey Mashtakov

E-Mail Website
Guest Editor
Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Moscow, Russia
Interests: sub-Riemannian geometry; invariant control systems on lie groups; optimal control; nonlinear geometric control theory; motion planning; applications to robotics; mechanics; image processing and modelling of human visual system
Special Issues, Collections and Topics in MDPI journals
Dr. Emre Baspinar

E-Mail Website
Guest Editor
INRIA Sophia Antipolis Méditerranée, Valbonne, France
Interests: mean-field equations and neuronal population models; multiple timescale dynamical systems; complex dynamical systems; geometric modeling of visual perception via Lie groups; non-linear PDEs for image processing/analysis; differential geometry; sub-Riemannian geometry

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to the mathematical modeling of human vision and its application to image processing (image segmentation, enhancement, inpainting). The scope of the Special Issue is to expose the modern mathematical models of the mechanisms involved in the perception of visual information by the human brain and discuss the brain-inspired methods in image processing which are based on these models.

Dr. Alexey Mashtakov
Dr. Emre Baspinar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Journal of Imaging is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modelling
  • human vision
  • brain-inspired methods
  • image processing
  • computer vision
  • nonholonomic systems
  • geometric control
  • scale space

Published Papers (4 papers)

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Research

26 pages, 2722 KiB  
Article
Microsaccades, Drifts, Hopf Bundle and Neurogeometry
by Dmitri Alekseevsky
J. Imaging 2022, 8(3), 76; https://doi.org/10.3390/jimaging8030076 - 17 Mar 2022
Cited by 1 | Viewed by 2235
Abstract
The first part of the paper contains a short review of the image processing in early vision is static, when the eyes and the stimulus are stable, and in dynamics, when the eyes participate in fixation eye movements. In the second part, we [...] Read more.
The first part of the paper contains a short review of the image processing in early vision is static, when the eyes and the stimulus are stable, and in dynamics, when the eyes participate in fixation eye movements. In the second part, we give an interpretation of Donders’ and Listing’s law in terms of the Hopf fibration of the 3-sphere over the 2-sphere. In particular, it is shown that the configuration space of the eye ball (when the head is fixed) is the 2-dimensional hemisphere SL+, called Listing hemisphere, and saccades are described as geodesic segments of SL+ with respect to the standard round metric. We study fixation eye movements (drift and microsaccades) in terms of this model and discuss the role of fixation eye movements in vision. A model of fixation eye movements is proposed that gives an explanation of presaccadic shift of receptive fields. Full article
(This article belongs to the Special Issue Mathematical Modeling of Human Vision and Its Application to Image Processing)
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37 pages, 1060 KiB  
Article
Retinal Processing: Insights from Mathematical Modelling
by Bruno Cessac
J. Imaging 2022, 8(1), 14; https://doi.org/10.3390/jimaging8010014 - 17 Jan 2022
Cited by 2 | Viewed by 2973
Abstract
The retina is the entrance of the visual system. Although based on common biophysical principles, the dynamics of retinal neurons are quite different from their cortical counterparts, raising interesting problems for modellers. In this paper, I address some mathematically stated questions in this [...] Read more.
The retina is the entrance of the visual system. Although based on common biophysical principles, the dynamics of retinal neurons are quite different from their cortical counterparts, raising interesting problems for modellers. In this paper, I address some mathematically stated questions in this spirit, discussing, in particular: (1) How could lateral amacrine cell connectivity shape the spatio-temporal spike response of retinal ganglion cells? (2) How could spatio-temporal stimuli correlations and retinal network dynamics shape the spike train correlations at the output of the retina? These questions are addressed, first, introducing a mathematically tractable model of the layered retina, integrating amacrine cells’ lateral connectivity and piecewise linear rectification, allowing for computing the retinal ganglion cells receptive field together with the voltage and spike correlations of retinal ganglion cells resulting from the amacrine cells networks. Then, I review some recent results showing how the concept of spatio-temporal Gibbs distributions and linear response theory can be used to characterize the collective spike response to a spatio-temporal stimulus of a set of retinal ganglion cells, coupled via effective interactions corresponding to the amacrine cells network. On these bases, I briefly discuss several potential consequences of these results at the cortical level. Full article
(This article belongs to the Special Issue Mathematical Modeling of Human Vision and Its Application to Image Processing)
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10 pages, 3143 KiB  
Article
Liouville Integrability in a Four-Dimensional Model of the Visual Cortex
by Ivan Galyaev and Alexey Mashtakov
J. Imaging 2021, 7(12), 277; https://doi.org/10.3390/jimaging7120277 - 17 Dec 2021
Viewed by 1740
Abstract
We consider a natural extension of the Petitot–Citti–Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account. The occluded contours are completed via sub-Riemannian geodesics in the four-dimensional space M of positions, orientations, and [...] Read more.
We consider a natural extension of the Petitot–Citti–Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account. The occluded contours are completed via sub-Riemannian geodesics in the four-dimensional space M of positions, orientations, and curvatures. Here, M=R2×SO(2)×R models the configuration space of neurons of the visual cortex. We study the problem of sub-Riemannian geodesics on M via methods of geometric control theory. We prove complete controllability of the system and the existence of optimal controls. By application of the Pontryagin maximum principle, we derive a Hamiltonian system that describes the geodesics. We obtain the explicit parametrization of abnormal extremals. In the normal case, we provide three functionally independent first integrals. Numerical simulations indicate the existence of one more first integral that results in Liouville integrability of the system. Full article
(This article belongs to the Special Issue Mathematical Modeling of Human Vision and Its Application to Image Processing)
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21 pages, 2435 KiB  
Article
Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase
by Emre Baspinar
J. Imaging 2021, 7(12), 271; https://doi.org/10.3390/jimaging7120271 - 9 Dec 2021
Cited by 1 | Viewed by 1920
Abstract
We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two-dimensional [...] Read more.
We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two-dimensional corrupted input image via a Gabor transform and represents those values in terms of cortical cell output responses in the model geometry. Then, it performs completion via a diffusion concentrated in a neighborhood along the neural connections within the model geometry. The diffusion models the activity propagation integrating orientation, frequency and phase features along the neural connections. Finally, the algorithm transforms the diffused and completed output responses back to the two-dimensional image plane. Full article
(This article belongs to the Special Issue Mathematical Modeling of Human Vision and Its Application to Image Processing)
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