A stationary pattern with asymmetrical luminance gradients can appear to move. We hypothesized that the source signal of this illusion originates in retinal image motions due to fixational eye movements. We investigated the inter-subject correlation between fixation instability and illusion strength. First, we demonstrated that the strength of the illusion can be quantified by the nulling technique. Second, we concurrently measured cancellation velocity and fixation instability for each subject, and found a positive correlation between them. The same relationship was also found within a single observer when the visual stimulus was artificially moved in the simulation of fixation instability. Third, we confirmed the same correlation with eye movements for a wider variety of illusory displays. These results suggest that fixational eye movements indeed play a relevant role in generating this motion illusion.

Most people see movement in Figure 1, although the image is static. Motion is seen from black 3 blue 3 white 3 yellow 3 black. Many hypotheses for the illusory motion have been proposed, although none have been tested physiologically. We found that the illusion works well even if it is achromatic: yellow is replaced with light gray, and blue is replaced with dark gray. We show that the critical feature for inducing illusory motion is the luminance relationship of the static elements. Illusory motion is seen from black 3 dark gray 3 white 3 light gray 3 black. In psychophysical experiments, we found that all four pairs of adjacent elements when presented alone each produced illusory motion consistent with the original illusion, a result not expected from any current models. We also show that direction-selective neurons in macaque visual cortex gave directional responses to the same static element pairs, also in a direction consistent with the illusory motion. This is the first demonstration of directional responses by single neurons to static displays and supports a model in which low-level, first-order motion detectors interpret contrast-dependent differences in response timing as motion. We demonstrate that this illusion is a static version of four-stroke apparent motion.

The cerebral cortex predicts visual motion to adapt human behavior to surrounding objects moving in real time. Although the underlying mechanisms are still unknown, predictive coding is one of the leading theories. Predictive coding assumes that the brain's internal models (which are acquired through learning) predict the visual world at all times and that errors between the prediction and the actual sensory input further refine the internal models. In the past year, deep neural networks based on predictive coding were reported for a video prediction machine called PredNet. If the theory substantially reproduces the visual information processing of the cerebral cortex, then PredNet can be expected to represent the human visual perception of motion. In this study, PredNet was trained with natural scene videos of the self-motion of the viewer, and the motion prediction ability of the obtained computer model was verified using unlearned videos. We found that the computer model accurately predicted the magnitude and direction of motion of a rotating propeller in unlearned videos. Surprisingly, it also represented the rotational motion for illusion images that were not moving physically, much like human visual perception. While the trained network accurately reproduced the direction of illusory rotation, it did not detect motion components in negative control pictures wherein people do not perceive illusory motion. This research supports the exciting idea that the mechanism assumed by the predictive coding theory is one of basis of motion illusion generation. Using sensory illusions as indicators of human perception, deep neural networks are expected to contribute significantly to the development of brain research.

The neural basis of illusory motion perception evoked from static images has not been established well. We examined changes in neural activity in motion sensitive areas of the human visual cortex by using functional magnetic resonance imaging (fMRI) technique when a static illusory-motion image ('Rotating Snakes') was presented to participants. The blood-oxygenation-level dependent (BOLD) signal changes were compared between the test stimulus that induced illusory motion perception and the control stimulus that did not. Comparison was also made between those stimuli with and without eye movements. Signal changes for the test stimulus were significantly larger than those for the control stimulus, if accompanied by eye movements. On the other hand, the difference in signal changes between test and control stimuli was smaller, if steady fixation was required. These results support the empirical finding that this illusion is related to some component of eye movements.

We propose an explanatory approach to Café Wall type illusions that is simple yet fairly comprehensive. These illusions are constructed out of basic elementary units in a jigsaw-like manner. Each unit, in general, contains both a solid body and a thin tail: the contrast polarity between the two determines the direction of the contributory illusory tilt produced by that element-according to a heuristic rule illustrated in figure 1. Ensembles of these elements exhibit illusory tilts only when the tails of the elements align along a common line in an additive manner. When elements of opposing polarity alternate, the illusion is cancelled. This approach extends and supersedes those presented in Pinna's illusion of angularity and Kitaoka's 'acute' corner effect. Furthermore, it appears to be, in part, compatible with existing mechanisms proposed to account for the emergence of local tilt cues, and it suggests several novel variations on the Café Wall theme.