Relative Motion Illusions – Orthogonal Dotted Lines Sway

from Michael’s Visual Phenomena & Optical Illusions


What to see & do

When you inspect the above image you may notice that the central diamond moves, shifts or “swims” within / above the background. I call this the Orthogonal Dotted Lines Sway.


You are seeing your own eye movement here. The phenomenon belongs to the class of relative motion illusions, including the Ōuchi, the “Spine drift” illusion and examples by Akiyoshi Kitaoka, namely “Kite” and “Kite 2”. With the pop-up that defaults to Orthogonal Dotted Lines Sway, these and various other patterns can be selected. They all evoke shifting, swimming or swaying relative motion illusions, to different degrees; the Orthogonal Dotted Lines Sway is possibly the simplest arrangement to evoke it, yet quite strong.

An explanation, probably correct

The “integration bias hypothesis” goes back to Hine (1997) but is best explained (and supported by data) by Mather (2000). Basically, if an rectangle is moved obliquely, its short and long edges generate motion signals, which have to be vectorially combined to recover the correct direction. Any bias leads to misestimation of the correct direction. Here motion direction along the dotted line sees high edge contrast (evoking a strong motion signal), while orthogonal to it the contrast is lower (grey background), causing a weaker motion signal. When the full pattern is moved (e.g. by eye movements), the misestimation of the central disk is orthogonal to the one of the surround, leading to relative displacement, thus to the illusion. As a test: When the background is darkened (use the lower of the 3 “color wells”), leading to more equal motion signals from all edges, the illusion is gone.

A former explanation attempt with incorrect prediction

I built the present figure based on this hypothesis to explain this rather beautiful phenomenon (unfortunately, this hypothesis does not explain the “maximal sway direction”, so it fails):

  1. We are making rapid eye movements about 3× per second, mostly without noticing it
  2. It is known that rapid movement of visual patters on the retina leads to motion blur, which is perceptually suppressed (Burr and Morgan, 1997; Land, 1999)
  3. Motion blur reduces contrast in different parts of the stimulus pattern differently
  4. It is known that reduction of contrast reduces perceived speed (Thompson, 1982). This is actually predicted when quantitively considering standard motion detector models (Bach & Atala-Gérard, 2020)
  5. All factors above, combined, lead to actual relative displacement of the neural correlate of the stimulus parts with different motion blur response.
  6. Irregular eye movements thus lead to perceived irregular shift of the stimulus parts, causing the “swimming” percept.

While nothing seems actually wrong with the above :), the motion blur hypothesis predicts the wrong sway/shift angle. In the case of “Orthogonal Dotted Lines Sway”, along or 90° orthogonal to the lines is predicted, but (easy to test) a 45° shift (relative to lines, here corresponds to 0° or 90°) produces the strongest illusion. Bummer.