Scaling properties of Mach bands and perceptual models

Abstract

Mach bands are the pronounced light and dark bands visible where a luminance plateau meets a ramp as in a penumbra. A great deal of effort has been devoted to study these in order to understand the underlying neural circuitry. A number of theoretical models, linear and non-linear, have consequently been proposed starting from the seminal studies of Ernst Mach himself. In this work we demonstrate why no linear model of visual perception can explain the Mach band illusion although many such attempts have been made starting from that of Mach to some recent ones. From the same approach, we also systematically demonstrate why the Mach bands are weak or inexistent at step changes of intensity. A new aspect, viz. the scaling properties of the widths of Mach band has been studied to provide a unified approach to solve both these problems in vision. © 2012 Springer-Verlag.