Inability of Humans to Discriminate between Visual Textures That Agree in Second-Order Statistics—Revisited

TLDR

Human visual texture discrimination cannot distinguish pairs of random textures generated by a one‑dimensional Markov process that share identical first‑ and second‑order statistics, highlighting a limitation of earlier models. The study introduces three novel two‑dimensional, non‑Markovian texture generation methods that produce pairs with identical first‑ and second‑order but differing third‑order statistics. These methods are evaluated using a model in which early local feature extractors detect simple elements such as dots and edges, while a global processor compares only first‑ or second‑order statistics of the extracted features. All three methods yield texture pairs that are indistinguishable to observers, even though the elements appear markedly different, and a counterexample shows that identical second‑order statistics can still permit discrimination, thereby supporting the proposed two‑stage feature‑analysis model.

Abstract

In an earlier study by Julesz (1962) pairs of random textures were generated side-by-side using a Markov process with different third-order joint-probability distributions but identical first- and second-order distributions. Such texture pairs could not be discriminated from each other by the human visual system without scrutiny. Unfortunately, Markov processes are inherently one-dimensional while the general processes underlying visual texture discrimination are two-dimensional. Here three new methods are introduced that generate two-dimensional non-Markovian textures with different third-order but identical first- and second-order statistics. All three methods generate texture pairs that cannot be discriminated from each other. The lack of texture discrimination is the more astonishing since the individual elements that form the texture pair are clearly perceived as being very different. However, a counterexample was found that yields discrimination although the texture pair has approximately identical second-order statistics. This case can be explained by assuming that early feature extractors do some preprocessing. These new demonstrations give support to a model of texture discrimination in which the stimulus is first analyzed by local feature extractors that can detect only simple features such as dots and edges of given sizes and orientations. Then the outputs of these simple extractors are evaluated by a global processor that can compute only second- or first-order statistics (that is can compare at most two such outputs).