Unique Geometry and Texture from Corresponding Image Patches

We present a sufficient condition for the recovery of a unique texture process and a unique set of viewpoints from a set of image patches that are generated by observing a flat texture process from unknown directions and orientations. We show that four image patches are sufficient in general, and we characterize the ambiguities that arise when this condition is not satisfied. The results are applicable to the perception of shape from texture and to texture-based structure from motion.