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

We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with widely used Wilson-Cowan equations [48], 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 [20] and largely used over the last years for several image processing problems [24,38,28]. The resulting model is capable to describe assimilation and contrast visual bias at the same time, the main novelty being its explicit dependence on local image orientation. We report several numerical tests showing the ability of the model to explain, 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, describing long-range connectivity between different hypercolumns in the primary visual cortex.