There is considerable interest in how humans estimate the number of objects in a scene in the context of an extensive literature on how we estimate the density (i.e., spacing) of objects. Here, we show that our sense of number and our sense of density are intertwined. Presented with two patches, observers found it more difficult to spot differences in either density or numerosity when those patches were mismatched in overall size, and their errors were consistent with larger patches appearing both denser and more numerous. We propose that density is estimated using the relative response of mechanisms tuned to low and high spatial frequencies (SFs), because energy at high SFs is largely determined by the number of objects, whereas low SF energy depends more on the area occupied by elements. This measure is biased by overall stimulus size in the same way as human observers, and by estimating number using the same measure scaled by relative stimulus size, we can explain all of our results. This model is a simple, biologically plausible common metric for perceptual number and density.psychophysics | vision | texture | numerical cognition

To judge the overall direction of a shoal of fish or a crowd of people, observers must integrate motion signals across space and time. The limits on our ability to pool motion have largely been established using the motion coherence paradigm, in which observers report the direction of coherently moving dots amid randomly moving noise dots. Poor performance by autistic individuals on this task has widely been interpreted as evidence of disrupted integrative processes. Critically, however, motion coherence thresholds are not necessarily limited only by pooling. They could also be limited by imprecision in estimating the direction of individual elements or by difficulties segregating signal from noise. Here, 33 children with autism 6 -13 years of age and 33 age-and ability-matched typical children performed a more robust task reporting mean dot direction both in the presence and the absence of directional variability alongside a standard motion coherence task. Children with autism were just as sensitive to directional differences as typical children when all elements moved in the same direction (no variability). However, remarkably, children with autism were more sensitive to the average direction in the presence of directional variability, providing the first evidence of enhanced motion integration in autism. Despite this improved averaging ability, children with autism performed comparably to typical children in the motion coherence task, suggesting that their motion coherence thresholds may be limited by reduced segregation of signal from noise. Although potentially advantageous under some conditions, increased integration may lead to feelings of "sensory overload" in children with autism.

Compared to unaffected observers patients with schizophrenia (SZ) show characteristic differences in visual perception, including a reduced susceptibility to the influence of context on judgments of contrast – a manifestation of weaker surround suppression (SS). To examine the generality of this phenomenon we measured the ability of 24 individuals with SZ to judge the luminance, contrast, orientation, and size of targets embedded in contextual surrounds that would typically influence the target’s appearance. Individuals with SZ demonstrated weaker SS compared to matched controls for stimuli defined by contrast or size, but not for those defined by luminance or orientation. As perceived luminance is thought to be regulated at the earliest stages of visual processing our findings are consistent with a suppression deficit that is predominantly cortical in origin. In addition, we propose that preserved orientation SS in SZ may reflect the sparing of broadly tuned mechanisms of suppression. We attempt to reconcile these data with findings from previous studies.

It has been suggested that numerosity is an elementary quality of perception, similar to colour. If so (and despite considerable investigation), its mechanism remains unknown. Here, we show that observers require on average a massive difference of approximately 40% to detect a change in the number of objects that vary irrelevantly in blur, contrast and spatial separation, and that some naive observers require even more than this. We suggest that relative numerosity is a type of texture discrimination and that a simple model computing the contrast energy at fine spatial scales in the image can perform at least as well as human observers. Like some human observers, this mechanism finds it harder to discriminate relative numerosity in two patterns with different degrees of blur, but it still outpaces the human. We propose energy discrimination as a benchmark model against which more complex models and new data can be tested.

These findings indicate that motion perception in the participants with migraine was limited by an inability to exclude visual noise. We suggest that this is a defining characteristic of visual dysfunction in migraine, a theory that has the potential to integrate a wide range of findings in the literature.