Shape from texture for smooth curved surfaces in perspective projection

Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; this paper presents a systematic analysis of first- and second-order texture distortion cues for the case of a smooth, curved surface. In particular, several kinds of texture gradients are analyzed and are related to surface orientation and surface curvature. The local estimates obtained from these cues can be integrated to obtain a global surface shape, and it is shown that the two surfaces resulting from the well-known tilt ambiguity in the local foreshortening cue typically have qualitatively different shapes. As an example of a practical application of the analysis, a shape-from-texture algorithm based on local orientation-selective filtering is described, and some experimental results are shown.