Hyperbolic Planforms in Relation to Visual Edges and Textures Perception

摘要: We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of brain. This allows us make predictions kinds patterns that should be observed in activity real brains through, e.g., optical imaging, opens door design experiments test these hypotheses. study specific problem visual edges textures perception suggest features may represented at population level cortex a second-order tensor, structure perhaps within hypercolumn. then extend classical ring model this case show its natural framework is non-Euclidean hyperbolic geometry. brings beautiful group isometries certain subgroups which have direct interpretation terms populations are assumed encode tensor. By studying bifurcations solutions tensor equations, analog Wilson Cowan under assumption invariance with respect action subgroups, we predict appearance characteristic patterns. These can described by what call or H-planforms reminiscent Euclidean planar waves planforms were used previous work account some hallucinations. If could through brain imaging techniques they would reveal built-in acquired corresponding subgroups.