Perceived pattern regularity computed as a summary statistic: implications for camouflage

Why do the equally spaced dots in figure 1 appear regularly spaced? The answer 'because they are' is naive and ignores the existence of sensory noise, which is known to limit the accuracy of positional localization. Actually, all the dots in figure 1 have been physically perturbed, but in the case of the apparently regular patterns to an extent that is below threshold for reliable detection. Only when retinal pathology causes severe distortions do regular grids appear perturbed. Here, we present evidence that low-level sensory noise does indeed corrupt the encoding of relative spatial position, and limits the accuracy with which observers can detect real distortions. The noise is equivalent to a Gaussian random variable with a standard deviation of approximately 5 per cent of the inter-element spacing. The just-noticeable difference in positional distortion between two patterns is smallest when neither of them is perfectly regular. The computation of variance is statistically inefficient, typically using only five or six of the available dots.