# The structure of visual space

Mark Changizi has an interesting post “The Visual Nerd in You Undestands Curved Space” where he explains that spherical geometry is relevant for the visual perception.

At some point he writes a paragraph which triggered my post:

Your visual field conforms to an elliptical geometry!

(The perception I am referring to is your perception of the projection, not your perception of the objective properties. That is, you will also perceive the ceiling to objectively, or distally, be a rectangle, each angle having 90 degrees. Your perception of the objective properties of the ceiling is Euclidean.)

Is it true that our visual perception senses the Euclidean space?

Look at this very interesting project

The structure of optical space under free viewing conditions

and especially at this paper:

The structure of visual spaces by J.J. Koenderink, A.J. van Doorn, Journal of mathematical imaging and vision, Volume: 31, Issue: 2-3 (2008), pp. 171-187

In particular, one of the very nice things this group is doing is to experimentally verify the perception of true facts in projective geometry (like this Pappus theorem).

From the abstract of the paper: (boldfaced by me)

The “visual space” of an optical observer situated at a single, fixed viewpoint is necessarily very ambiguous. Although the structure of the “visual field” (the lateral dimensions, i.e., the “image”) is well defined, the “depth” dimension has to be inferred from the image on the basis of “monocular depth cues” such as occlusion, shading, etc. Such cues are in no way “given”, but are guesses on the basis of prior knowledge about the generic structure of the world and the laws of optics. Thus such a guess is like a hallucination that is used to tentatively interpret image structures as depth cues. The guesses are successful if they lead to a coherent interpretation. Such “controlled hallucination” (in psychological terminology) is similar to the “analysis by synthesis” of computer vision.

So, the space is perceived to be euclidean based on prior knowledge, that is because prior controlled hallucinations led consistently to coherent interpretations.