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

Abstract

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A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

“…In [ 44 , 45 , 46 ], a variant of the Wilson-Cowan (WC) model based on a variational principle and adapted to the geometry of V1 was employed to model the neuronal activity and generate illusory patterns for different illusion types. The modelling considered in these works is strongly inspired by the integro-differential model firstly studied in [ 47 ] for perception-inspired Local Histogram Equalisation (LHE) techniques and later applied in a series of work, see, for example, [ 48 , 49 ] for the study of contrast and assimilation phenomena.…”

“…The modelling considered in these works is strongly inspired by the integro-differential model firstly studied in [ 47 ] for perception-inspired Local Histogram Equalisation (LHE) techniques and later applied in a series of work, see, for example, [ 48 , 49 ] for the study of contrast and assimilation phenomena. By further incorporating a cortical-inspired modelling, the authors showed in [ 44 , 45 , 46 ] that cortical Local Histogram Equalisation (LHE) models are able to replicate visual misperceptions induced not only by local contrast changes, but also by orientation-induced biases similar to the ones in Figure 2 . Interestingly, the cortical LHE model [ 44 , 45 , 46 ] was further shown to outperform both standard and cortical-inspired WC models and was rigorously shown to correspond to the minimisation of a variational energy, which suggests more efficient representation properties [ 50 , 51 ].…”

“…By further incorporating a cortical-inspired modelling, the authors showed in [ 44 , 45 , 46 ] that cortical Local Histogram Equalisation (LHE) models are able to replicate visual misperceptions induced not only by local contrast changes, but also by orientation-induced biases similar to the ones in Figure 2 . Interestingly, the cortical LHE model [ 44 , 45 , 46 ] was further shown to outperform both standard and cortical-inspired WC models and was rigorously shown to correspond to the minimisation of a variational energy, which suggests more efficient representation properties [ 50 , 51 ]. One major limitation in the modelling considered in these works is the use of neuronal interaction kernels (essentially, isotropic 3D Gaussian), which are not compatible with the natural sub-Riemannian structure of V1 proposed in the CPS model.…”

A bio-inspired geometric model for sound reconstruction

“…Recently, these equations have been coupled with the neurogeometric model of V1 to great benefit. For instance, in [4][5][6] they allowed replicating orientation-dependent brightness illusory phenomena, which had proved to be difficult to implement for non-cortical-inspired models. See also [39] for applications to the detection of perceptual units.…”

“…As in the case of V1 [8], we model neuronal connections via these dynamics. In practice, this amounts to assuming that the excitation starting at a neuron X 0 = (ω , ν ) evolves as the stochastic process {A t } t≥0 naturally associated with (6). This is given by the following stochastic differential equation:…”