We describe an ideal observer model for estimating "shape from texture" which is derived from the principles of statistical information. For a given family of surface shapes, measures of statistical information can be computed for two different texture cues--density and orientation of texels. These measures can be used to predict lower bounds on the variance of shape judgements of "ideal" and human observers. They can also predict optimal weights for cue integration for the inference of shape from texture. These weights are directly proportional to the information carried by each cue. The ideal observer model therefore predicts that the variance of subjects' responses in a psychophysical shape judgement task should reflect the statistical importance of individual texture cues. Our results show that human performance in shape judgements for a one-parameter family of parabolic cylinders is often better than what an ideal observer achieves using a density cue alone. Therefore other information, for example the compression cue, must be used by human observers. For the first time, such results have been obtained without recourse to the unnatural cue conflict paradigms used in previous experiments. The model makes further predictions for the perception of planar slanted surfaces in the case of wide field of view.