Discriminable textures with identical buffon needle statistics

A method is presented for generating pairs of textures for which the statistics of intersection with any collinear set of points placed at random on either texture are the same. The constraint that such "Buffon needle statistics" be identical is stronger than identity of second-order statistics. Nonetheless, many such texture pairs are effortlessly distinguishable. An example is given of such a texture pair, whose components are composed of either congruent ellipses or circles of various radii. The discriminability of such texture pairs implies that adequate models for human texture preception must contain local nonlinearities which receive input from non-collinear points.