Cortical-Inspired Wilson–Cowan-Type Equations for Orientation-Dependent Contrast Perception Modelling

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Serval ID
serval:BIB_875572BDDAD5
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Cortical-Inspired Wilson–Cowan-Type Equations for Orientation-Dependent Contrast Perception Modelling
Journal
Journal of Mathematical Imaging and Vision
Author(s)
Bertalmío Marcelo, Calatroni Luca, Franceschi Valentina, Franceschiello Benedetta, Prandi Dario
ISSN
0924-9907
ISSN-L
1573-7683
Publication state
Published
Issued date
11/06/2020
Language
english
Abstract
We consider the evolution model proposed in Bertalmio (Front Comput Neurosci 8:71, 2014), Bertalmio et al. (IEEE Trans Image Process 16(4):1058-1072, 2007) to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson-Cowan equations (Wilson and Cowan in BioPhys J 12(1):1-24, 1972), mainly in terms of efficient representation properties. Then, in order to explicitly encode local directional information, we exploit the model of the primary visual cortex (V1) proposed in Citti and Sarti (J Math Imaging Vis 24(3):307-326, 2006) and largely used over the last years for several image processing problems (Duits and Franken in Q Appl Math 68(2):255-292, 2010; Prandi and Gauthier in A semidiscrete version of the Petitot model as a plausible model for anthropomorphic image reconstruction and pattern recognition. SpringerBriefs in Mathematics, Springer, Cham, 2017; Franceschiello et al. in J Math Imaging Vis 60(1):94-108, 2018). The resulting model is thus defined in the space of positions and orientation, and it is capable of describing assimilation and contrast visual bias at the same time. We report several numerical tests showing the ability of the model to reproduce, in particular, orientation-dependent phenomena such as grating induction and a modified version of the Poggendorff illusion. For this latter example, we empirically show the existence of a set of threshold parameters differentiating from inpainting to perception-type reconstructions and describing long-range connectivity between different hypercolumns in V1.
Keywords
Modelling and Simulation, Statistics and Probability, Geometry and Topology, Applied Mathematics, Condensed Matter Physics, Computer Vision and Pattern Recognition
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Create date
09/07/2020 20:43
Last modification date
12/01/2021 6:26
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