A long tradition of psychological research has lamented the systematic errors and biases in people's perception of the characteristics of sequences generated by a random mechanism such as a coin toss. It is proposed that once the likely nature of people's actual experience of such processes is taken into account, these "errors" and "biases" actually emerge as apt reflections of the probabilistic characteristics of sequences of random events. Specifically, seeming biases reflect the subjective experience of a finite data stream for an agent with a limited short-term memory capacity. Consequently, these biases seem testimony not to the limitations of people's intuitive statistics but rather to the extent to which the human cognitive system is finely attuned to the statistics of the environment.

The vast majority of research on optic flow (retinal motion arising because of observer movement) has focused on its use in heading recovery and guidance of locomotion. Here we demonstrate that optic flow processing has an important role in the detection and estimation of scene-relative object movement during self movement. To do this, the brain identifies and globally discounts (i.e., subtracts) optic flow patterns across the visual scene-a process called flow parsing. Remaining motion can then be attributed to other objects in the scene. In two experiments, stationary observers viewed radial expansion flow fields and a moving probe at various onscreen locations. Consistent with global discounting, perceived probe motion had a significant component toward the center of the display and the magnitude of this component increased with probe eccentricity. The contribution of local motion processing to this effect was small compared to that of global processing (experiment 1). Furthermore, global discounting was clearly implicated because these effects persisted even when all the flow in the hemifield containing the probe was removed (experiment 2). Global processing of optic flow information is shown to play a fundamental role in the recovery of object movement during ego movement.

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SummaryDuring smooth pursuit eye movement, observers often misperceive velocity. Pursued stimuli appear slower (Aubert-Fleishl phenomenon [1, 2]), stationary objects appear to move (Filehne illusion [3]), the perceived direction of moving objects is distorted (trajectory misperception [4]), and self-motion veers away from its true path (e.g., the slalom illusion [5]). Each illusion demonstrates that eye speed is underestimated with respect to image speed, a finding that has been taken as evidence of early sensory signals that differ in accuracy [4, 6–11]. Here we present an alternative Bayesian account, based on the idea that perceptual estimates are increasingly influenced by prior expectations as signals become more uncertain [12–15]. We show that the speeds of pursued stimuli are more difficult to discriminate than fixated stimuli. Observers are therefore less certain about motion signals encoding the speed of pursued stimuli, a finding we use to quantify the Aubert-Fleischl phenomenon based on the assumption that the prior for motion is centered on zero [16–20]. In doing so, we reveal an important property currently overlooked by Bayesian models of motion perception. Two Bayes estimates are needed at a relatively early stage in processing, one for pursued targets and one for image motion.

A moving observer needs to be able to estimate the trajectory of other objects moving in the scene. Without the ability to do so, it would be difficult to avoid obstacles or catch a ball. We hypothesized that neural mechanisms sensitive to the patterns of motion generated on the retina during self-movement (optic flow) play a key role in this process, "parsing" motion due to self-movement from that due to object movement. We investigated this "flow parsing" hypothesis by measuring the perceived trajectory of a moving probe placed within a flow field that was consistent with movement of the observer. In the first experiment, the flow field was consistent with an eye rotation; in the second experiment, it was consistent with a lateral translation of the eyes. We manipulated the distance of the probe in both experiments and assessed the consequences. As predicted by the flow parsing hypothesis, manipulating the distance of the probe had differing effects on the perceived trajectory of the probe in the two experiments. The results were consistent with the scene geometry and the type of simulated self-movement. In a third experiment, we explored the contribution of local and global motion processing to the results of the first two experiments. The data suggest that the parsing process involves global motion processing, not just local motion contrast. The findings of this study support a role for optic flow processing in the perception of object movement during self-movement.

We have recently suggested that the brain uses its sensitivity to optic flow in order to parse retinal motion into components arising due to self and object movement (e.g. Rushton, S. K., & Warren, P. A. (2005). Moving observers, 3D relative motion and the detection of object movement. Current Biology, 15, R542-R543). Here, we explore whether stereo disparity is necessary for flow parsing or whether other sources of depth information, which could theoretically constrain flow-field interpretation, are sufficient. Stationary observers viewed large field of view stimuli containing textured cubes, moving in a manner that was consistent with a complex observer movement through a stationary scene. Observers made speeded responses to report the perceived direction of movement of a probe object presented at different depths in the scene. Across conditions we varied the presence or absence of different binocular and monocular cues to depth order. In line with previous studies, results consistent with flow parsing (in terms of both perceived direction and response time) were found in the condition in which motion parallax and stereoscopic disparity were present. Observers were poorer at judging object movement when depth order was specified by parallax alone. However, as more monocular depth cues were added to the stimulus the results approached those found when the scene contained stereoscopic cues. We conclude that both monocular and binocular static depth information contribute to flow parsing. These findings are discussed in the context of potential architectures for a model of the flow parsing mechanism.

Contextual preference reversals occur when a preference for one option over another is reversed by the addition of further options. It has been argued that the occurrence of preference reversals in human behavior shows that people violate the axioms of rational choice and that people are not, therefore, expected value maximizers. In contrast, we demonstrate that if a person is only able to make noisy calculations of expected value and noisy observations of the ordinal relations among option features, then the expected value maximizing choice is influenced by the addition of new options and does give rise to apparent preference reversals. We explore the implications of expected value maximizing choice, conditioned on noisy observations, for a range of contextual preference reversal types—including attraction, compromise, similarity, and phantom effects. These preference reversal types have played a key role in the development of models of human choice. We conclude that experiments demonstrating contextual preference reversals are not evidence for irrationality. They are, however, a consequence of expected value maximization given noisy observations.

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