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Cortical-inspired Wilson–Cowan-type equations for orientation-dependent contrast perception modelling

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dc.contributor.author Bertalmío, Marcelo
dc.contributor.author Calatroni, Luca
dc.contributor.author Franceschi, Valentina
dc.contributor.author Franceschiello, Benedetta
dc.contributor.author Prandi, Dario
dc.date.accessioned 2020-07-08T08:34:51Z
dc.date.available 2020-07-08T08:34:51Z
dc.date.issued 2020
dc.identifier.citation Bertalmío M, Calatroni L, Franceschi V, Franceschiello B, Prandi D. Cortical-inspired Wilson–Cowan-type equations for orientation-dependent contrast perception modelling. J Math Imaging Vis. 2021;63:263-81. DOI: 10.1007/s10851-020-00960-x
dc.identifier.issn 0924-9907
dc.identifier.uri http://hdl.handle.net/10230/45083
dc.description.abstract We consider the evolution model proposed in Bertalmío (Front Comput Neurosci 8:71, 2014), Bertalmío 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.
dc.description.sponsorship The authors acknowledge the anonymous referees for their suggestions which improved significantly the quality of their manuscript. M. B. acknowledges the support of the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 761544 (Project HDR4EU) and under Grant Agreement No. 780470 (Project SAUCE), and of the Spanish government and FEDER Fund, Grant Ref. PGC2018-099651-B-I00 (MCIU/AEI/FEDER, UE). L. C., V. F. and D. P. acknowledge the support of a public grant overseen by the French National Research Agency (ANR) as part of the Investissement d’avenir program, through the iCODE project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02 and of the research project LiftME funded by INS2I, CNRS. V. F. acknowledges the support received from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant No. 794592 and from the INdAM project Problemi isoperimetrici in spazi Euclidei e non. V. F. and D. P. also acknowledge the support of ANR-15-CE40-0018 project SRGI - Sub-Riemannian Geometry and Interactions. B. F. acknowledges the support of the Fondation Asile des Aveugles.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.relation.ispartof Journal of Mathematical Imaging and Vision. 2020 Jun 11
dc.relation.ispartof Journal of Mathematical Imaging and Vision. 2021;63:263-81.
dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1007/s10851-020-00960-x
dc.title Cortical-inspired Wilson–Cowan-type equations for orientation-dependent contrast perception modelling
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1007/s10851-020-00960-x
dc.subject.keyword Wilson–Cowan equations
dc.subject.keyword Primary visual cortex
dc.subject.keyword Orientation-dependent modelling
dc.subject.keyword Contrast perception
dc.subject.keyword Variational modelling
dc.subject.keyword Geometrical optical illusions
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/761544
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/780470
dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PGC2018-099651-B-I00
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion

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