# Talk:Leaning tower illusion

I have a handful of comments on this interesting article.

In the opening paragraph, the authors say "Because our retinae are planar surfaces, the images cast upon them are in perspective". The retinae are not planes. The point is that they are surfaces, so the 3d coordinates of points in the world get collapsed into 2d in the projection onto the retinal surface. It's also vague to say that the retinal images "are in perspective". I think the authors want to focus on the loss of one dimension in the projection. And to say that the geometry of perspective drawings (line convergence, vanishing points, etc.) is thereby contained in the retinal images.

The pictures of the Pisa Tower and the Petronas twin towers are great. The illusion is very compelling in both. In the paragraph describing the Petronas towers, the authors say "our brain compensates so that we perceive the towers rise at the same angle". You could be clearer in what you mean by "the same angle". "Receding" is misspelled in the next sentence.

My only real complaint with the article is that the authors don't really say what they mean by compensation. So I was left wondering what it means for compensation to be applied to the whole image as opposed to part of the image. Maybe this is beyond the spirit of Scholarpedia, but I'd like to see "compensation" fleshed out. There's clearly something important about the camera axis being non-perpendicular to the axis of the structure being photographed.

The test done by Kitaoka is a good one. I created some images in a similar, but simpler way. 1) One tilted line in a square frame. When viewed next to a copy of itself, the leaning tower illusion exists, but is small. 2) Two converging lines in a square frame. Viewed next to a copy, the illusion is stronger. 3) Multiple lines converging on a vanishing point in a square frame. The illusion is yet stronger. This is consistent with the authors' argument that the illusion is most compelling when the object appears to be a real object viewed such that truly parallel lines converge because of the perspective viewpoint.

The tram lines demo is a good one. "Receding" is misspelled again.

I found the discussion around Fig. 8 confusing. I thought you were saying that the perspective images of buildings will make the sides of the building look parallel to one another. Here the sides really are parallel, so why don't we see them as parallel? This probably goes back to not really understanding the compensation theory.

## Reviewer B

This is a nice contribution to Scholarpedia. It is a modern example of an article following the Helmholtz line of thought, which is largely untestable and inherently incomplete. That is, we see things because we compensate, the Helmholtzians aver. How did we learn to compensate? No answer. Perhaps this was because at one time we saw things correctly? But if so, why? Because we do not need to compensate under some circumstances? If so, which? No answer. The Helmholtz enterprise is flawed. As a nice example of the Helmholtz train of thought, this article should be accepted. The article also mentions in passing the correct way to frame the issues raised, as follows. The notion of compensation is simply unnecessary, as far as this article goes. The article points out that receding parallels converge in the picture plane. We can see both the parallelism in the z-dimension and the convergence in the picture plane to some extent. It follows that if two edges recede in the z-dimension but do not converge in the picture plane, they must be divergent in the z-dimension. Hence the appearance that is here called an “illusion”.

## Question

Why do we say that the image on the right side angles outward, rather than the image on the left angling inward? Is it because this is what we see, or simply how we express it? If it is what we see, anyone have an idea why? Is it simply because we saw the one on the right first? Has anyone seen what happens if the image on the left is presented first? Trottier 02:06, 15 October 2009 (EDT)