We examined the perception of 3D shape for surfaces folded, carved, or stretched out of textured materials. The textures were composed of sums of sinusoidal gratings or of circular dots, and were designed to differentiate between orientation and frequency information present in perspective images of the surfaces. Correct perception of concavities, convexities, saddles, and slants required the visibility of signature patterns of orientation modulations. These patterns were identical to those identified previously for developable surfaces (A. Li & Q. Zaidi, 2000; Q. Zaidi & L. Li, 2002), despite the fact that textures were statistically homogeneous on developable surfaces but not on carved or stretched surfaces. Frequency modulations in the image were interpreted as cues to distance from the observer, which led to weak but qualitatively correct percepts for some carved and stretched surfaces but to misperceptions for others, similar to the misperceptions for developable surfaces (A. Li & Q. Zaidi, 2003). Irrespective of whether texture on the surface is homogeneous or non-homogeneous, similar neural modules can be used to locate signature orientation modulations and thus extract shape from texture cues.