Abstract

Illusory Mach bands have long been regarded as artifacts of edge-enhancing mechanisms, yet key properties have remained unexplained. We present a quantitative model that treats Mach bands as the useful end products of a hypothesized mechanism for distinguishing certain illumination and reflectance changes in a scene. The model mechanism selectively locates illumination changes associated with shadow penumbra boundaries and labels these with Mach bands while suppressing detection of other types of image boundaries (e.g., abrupt object edges) and high frequency image noise. The noise suppression mechanism requires a penumbra contrast sensitivity maximum from general principles alone that matches published data. Model calculations on both idealized intensity patterns and video images demonstrate that the key spatial and spatial-frequency characteristics of Mach bands are quantitatively accounted for. The long-puzzling absence of Mach bands at abrupt edges (where typical edge enhancers produce maximal responses) also follows directly from the model mechanism and is associated with the ability to distinguish cast shadow illumination changes (with penumbra edges) from reflectance changes at abrupt object boundaries in an image. The useful detection selectivity and noise suppression properties required by the Mach band model suggest the operation of a distinct component of the visual system that contributes to lightness perception.

© 1992 Optical Society of America