Motion perception

Motion perception is the process of inferring the speed and direction of elements in a scene based on visual, vestibular and proprioceptive inputs. Although this process appears straightforward to most observers, it has proven to be a difficult problem from a computational perspective, and extraordinarily difficult to explain in terms of neural processing.
First-order motion perception
Two or more stimuli that are switched on and off in alternation can produce two different motion percepts. The first, demonstrated in the figure to the right is "Beta movement", often used in billboard displays, in which an object is perceived as moving when, in fact, a series of stationary images is being presented. This is also termed "apparent motion" and is the basis of movies and television. However, at faster alternation rates, and if the distance between the stimuli is just right, an illusory "object" the same colour as the background is seen moving between the two stimuli and alternately occluding them. This is called the phi phenomenon and is an example of "pure" motion detection uncontaminated, as in Beta movement, by form cues. (Read Beta movement and Phi phenomenon here).
Second-order motion perception
Second-order motion is motion in which the moving contour is defined by contrast, texture, flicker or some other quality that does not result in an increase in luminance or motion energy and produces a weaker motion aftereffect.

The aperture problem

The aperture problem. The grating appears to be moving down and to the right, perpendicular to the orientation of the bars. But it could be moving in many other directions, such as only down, or only to the right. It is impossible to determine unless the ends of the bars become visible in the aperture. Each neuron in the visual system is sensitive to visual input in a small part of the visual field, as if each neuron is looking at the visual field through a small window or aperture. The motion direction of a contour is ambiguous, because the motion component parallel to the line cannot be inferred based on the visual input. This means that a variety of contours of different orientations moving at different speeds can cause identical responses in a motion sensitive neuron in the visual system.
(Excerpts from Wikipedia)

A barber pole with spiral stripes rotates around its vertical axis, so the colors move horizontally, but the stripes appear to move upwards vertically. (newworldencyclopedia.org)

Image source

An example of the barberpole illusion. The grating is actually drifting downwards and to the right at 45 degrees, but its motion is captured by the elongated axis of the aperture.

Image source

Barberpole illusion

The barberpole illusion is a visual illusion that reveals biases in the processing of visual motion in the human brain. This visual illusion occurs when a diagonally striped pole is rotated around its vertical axis (horizontally), it appears as though the stripes are moving in the direction of its vertical axis (downwards in the case of the animation to the right) rather than around it.

The barber's pole is commonly found outside barber shops.
In 1929, psychologist J.P. Guilford informally noted a paradox in the perceived motion of stripes on a rotating barber pole. The barber pole turns in place on its vertical axis, but the stripes appear to move upwards rather than turning with the pole. Guilford tentatively attributed the phenomenon to eye movements, but acknowledged the absence of data on the question.
In 1935, Hans Wallach published a comprehensive series of experiments related to this topic, ... Wallach's analysis focused on the interaction between the terminal points of the diagonal lines and the implicit aperture created by the edges of the pole.(Wikipedia)

Roget's ‘Palisade’ Illusion

The illusion is seen when a spoked wheel rolls behind a picket fence or palisade. The spokes are observed to be bent into a family of curves as illustrated below. Roget's studies showed that the effect was independent of the forward speed of the wheel, and required both the forward and rotational motion. The effect is strongest when the palisade periodicity and the periodicity of the spokes at the rim are equal or nearly equal.

Wagon-wheel effect

The wagon-wheel effect (alternatively, stagecoach-wheel effect, stroboscopic effect) is an optical illusion in which a spoked wheel appears to rotate differently from its true rotation. The wheel can appear to rotate more slowly than the true rotation, it can appear stationary, or it can appear to rotate in the opposite direction from the true rotation. This last form of the effect is sometimes called the reverse rotation effect. .(Wikipedia)

This animated GIF demonstrates the wagon-wheel effect. The speed of the "camera", moving towards the right, constantly increases at the same rate with the objects sliding to the left. Halfway through the 24-second loop, the objects appear to suddenly shift and head backwards. .(Wikipedia)

The Windmills of your Mind Illusion

Best Illusion of The Year Contest 2017, Top 10 finalists. BY Michael Pickard and Gurpreet Singh, The University of Sunderland. UK

Author description: How is it possible to see simultaneous forward and backwards rotation in the windmill when it is turning at constant speed and direction? Key factors in this illusion include: symmetry in the windmill design; the amount of rotation per frame; persistence of vision; and the propensity in vision to group together things that are in close proximity. The schematics provided show how differences in pitch together with the careful positioning of the windmill arms determines how visual groupings can be formed one way or the other and it is these that determine the direction of motion seen.

Optical Illusion - Which way is the train going?

Is the train going forwards or backwards?

The Train at London Underground Moves Both Ways

The two-way train animated GIF is made of following four frames.

Slow motion of four-framed sequences.

Fast motion of four-framed sequences.