Posted by Dave on May 7, 2010 | 4 Comments
Take a look at this video (Click on the image to play, QuickTime required):
Which ellipse is rotating faster?
While at first it seems quite obvious that the ellipse on the right is rotating faster, if you download the movie and play in loop mode, by counting rotations you should be able to convince yourself that they are actually rotating at the same speed.
The next question, of course, is why. Gideon Caplovitz, Po-Jang Hsieh, and Peter Tse systematically studied the question in a paper they published in 2005. They showed viewers dozens of movies like the one above, with one ellipse always the same fatness always rotating at the same speed (126 degrees per second). In each movie, the width and speed of the second ellipse was systematically varied, and viewers judged which ellipse seemed to be rotating faster. This graph shows the results:
There’s a lot going on here, so I’m going to take some time to explain it. The four ellipses at the bottom are the different shapes used in the study. One of the two ellipses being shown was always like ellipse a, outlined in green. Sometimes both ellipses were the same shape (a), and sometimes the second ellipse was skinnier (b, c, or d). Angular velocity is the rotational speed of the second ellipse. The first ellipse always rotated at 126 degrees per second. The graph charts how frequently the second ellipse was perceived as spinning faster than the first ellipse. The color of the line corresponds to the shape of the ellipse — a is green, b is black, and so on. As you can see, when the green ellipse was spinning at 126 degrees per second, it was judged to be spinning faster than the reference ellipse 50 percent of the time (participants weren’t allowed to say the ellipses were spinning the same speed — they had to choose faster or slower). For ellipse b, this threshold occurred at a slower speed — even when it was spinning at just 105 degrees per second, most respondents saw it as moving faster than the fatter reference ellipse spinning at 126 degrees per second. The thinner ellipses were seen as spinning even faster, as you can clearly see in the example movie.
Does the illusion work for any shape? The researchers repeated the study with rectangles and found no effect — respondents were accurate at judging which rectangle spun faster, regardless of how fat or skinny it was.
But when they used rectangles with rounded corners rather than true ellipses, the illusion returned. The less rounded the corners, the faster the rectangles seemed to rotate.
Caplovitz’s team also tried adding dots to the end points of the ellipses, like this:
While the effect was diminished, skinnier ellipses were still perceived as spinning faster. So even when there is a readily-trackable part of the ellipse, viewers still see skinny ones as spinning faster than fat ones.
So we must not base estimates of rotational speed solely on trackable features like corners or dots on an image. Instead, the researchers conclude, we probably combine inputs from multiple sources. Fortunately, we don’t see a lot of spinning ellipses in day-to-day life, or we’d have a lot of trouble making sense of their movements.
Caplovitz, G., Hsieh, P., & Tse, P. (2006). Mechanisms underlying the perceived angular velocity of a rigidly rotating object Vision Research, 46 (18), 2877-2893 DOI: 10.1016/j.visres.2006.02.026