A commonly used representation of a visual pattern is the set of marginal probability distributions of the output of a bank of filters (Gaussian, Laplacian, Gabor etc...). This representation has been used effectively for a variety of vision tasks including texture classification, texture synthesis, object detection and image retrieval. This paper examines the ability of this representation to discriminate between an arbitrary pair of visual stimuli. Examples of patterns are derived that provably possess the same marginal statistical properties, yet are "visually distinct." These results suggest the need for either employing a large and diverse filter bank or incorporating joint statistics in order to represent a large class of visual patterns.