The darker-is-deeper heuristic for the perception of 3D shape from shading: Is it perceptually or ecologically valid?

The darker-is-deeper heuristic was originally proposed by Langer and Zucker (1994) for approximating 3D shape from shading under conditions of diffuse illumination that typically occur for outdoor scenes on a cloudy day, and it is based on the assumption that vignetting is the primary source of luminance variation under those conditions. It was later rejected as a model of human perception by Langer and Bülthoff (2000), because points in concavities that appear to be the deepest are most often located on local luminance maxima. Despite that result, this heuristic has continued to be described in the literature as a viable model of human perception (e.g., Chen & Tyler, 2015; Tyler, 1998), based entirely on the appearance of image intensity gratings, which have little or no connection to real 3D surfaces or patterns of illumination. In this article we will present a large number of examples to show what actually happens when surfaces are viewed under directional and diffuse illuminations. The results will highlight a number of well-known phenomena in addition to vignetting that can influence the pattern of shading on a surface under diffuse illumination, and they will also demonstrate that the darker-is-deeper heuristic is generally invalid for all types of illumination, except in unusual circumstances.