Do concise depth cues eliminate the Müller-Lyer illusion?

Jeremy Ma

The Muller Lyer illusion is a well known and simple illusion. The illusion consist of two straight lines of the same length with different arroqs in the ends. One with arrows pointing inwards, and one pointing outwards. Despite being the same length, line with arrows pointing outwards is perceived to be shorter than one with arrows pointing inwards.

One hypothesis suggest that the arrows are perceived with perspective - so they are perceived as corners of a rectilinear object, which gives the lines a sense of depth. According to Emmert's law, since these lines subtend the same visual angle, they would be perceived as a different size.

To confirm this hypothesis, I created a realistic 3d version of the Müller-Lyer illusion, which include depth cues such as shading and perspective, in order to suggest that the lines are indeed in the same plane and eliminate the illusory depth.

The arrow angles are 60 degrees from the horizontal and the ratio between the arrow length and the line length is 1.5:4.

In addition to the 3d version, I also put a 2D outline on the render to show that the illusion does persist if an additional outline is added.

Depth version


2D normal version


Comments


Jeremy Ma

c) This shows that perspective is not the primary reason of the muller lyer illusion, as most subjects seem to still be able to perceive the illusion despite the cues obviously suggesting the lack perspective.
d) There is an alternative hypothesis to the muller lyer illusion which is the centroid explaination which suggests that the centroid of the luminance affects our perception of distance and endpoints, and that the fact that the centroid of luminance is different in the two arrows affect out perception. This is kind of what Cesar was saying about changing the angle to see if that affects perceived length, which would be a great way to test the centroid hypothesis!

Cesar Duran

a) With the 3D structure, I definitely still experienced the illusion that the middle "wall" was longer in the outward pointing structure.

b) This does show that the illusion is still consistent whenever the illusion is made 3 dimensional with the addition of depth. I noticed that the used angle was 60 degrees, so I wonder whether there may be an angular threshold where the illusion will be destroyed? And whether there's a different threshold in 3D and 2D

Emily Huang

a) Even with the added depth cue, I still see the left line as being shorter than the right line.
b) This definitely confirms the hypothesis you were trying to test - since the added depth didn't change the illusion, it is probable that we are perceiving the arrows to to be the corners of rectilinear objects that give the lines a sense of depth.

Maddie C

I get the difference in length very strongly in both of these. I wonder if anyone has 3D printed these...?

Malinda

I still get the illusion with the added 3D structure (top image), but it's definitely stronger to me when you add the lines.