Surface orientation from texture: ideal observers, generic observers and the information content of texture cues

Perspective views of textured, planar surfaces provide a number of cues about the orientations of the surfaces. These include the information created by perspective scaling of texture elements (scaling), the information created by perspective foreshortening of texels (foreshortening) and, for textures composed of discrete elements, the information created by the effects of both scaling and foreshortening on the relative positions of texels (position). We drive a general form for ideal observers for each of these cues as they appear in images of spatially extended textures, (e.g. those composed of solid 2-D figures). As an application of the formulation, we derive a set of 'generic' observers which we show perform near optimally for images of a broad range of surface textures, without special prior knowledge about the statistics of the textures. Using simulations of ideal observers, we analyze the informational structure of texture cues, including a quantification of lower bounds on reliability for the three different cues, how cue reliability varies with slant angle and how it varies with field of view. We also quantify how strongly the reliability of the foreshortening cue depends on a prior assumption of isotropy. Finally, we extend the analysis to a naturalistic class of textures, showing that the information content of textures particularly suited to psychophysical investigation can be quantified, at least to a first-order approximation. The results provide an important computational foundation for psychophysical work on perceiving surface orientation from texture.