Talk:Perspective projection distortion

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"An example is a view where one is standing facing north towards a road which runs perfectly east-west. In an artificial perspective projection, every car on the road would be drawn at the same size, even though it is clear in reality that the farther away from the center of the picture that a car is, the farther away from the viewer that car would be."

Agree...I am this original poster of this article .... it has been mangled beyond recognition....I am going to try to repost with improved version all around.....But rather than anyone trying to "correct" or who challenges the technology, please lets talk it out before editing the orginal...thanks Patkelso 14:39, 7 September 2006 (UTC) ..Pat Kelso

This is simply untrue. The more distant cars will be painted on more distant parts of the canvas, and will therefore appear smaller to the viewer, despite being painted at the same size.

There seems to me to be much confusion arising from the notion that perspective in some way emulates the behaviour of the retina. It doesn't: it allows a canvas (screen, etc) to emulate a window on the world, when viewed from a given point (and if you move your viewpoint with respect to the canvas, the correct perspective will be a different linear perspective, not a queer 'spherical' one.

The article currently says

Imagine that on an infinite plane there is an infinitely long and infinitely straight railroad, and that you are standing between the parallel rails. As you peer down the track in one direction the rails appear to intersect (on the horizon). As you peer in the opposite direction they again appear to intersect. ... You similarly test the other rail and discover it too is straight. How can this happen?
...
This conclusively demonstrates that the retina itself is spherical in shape.

I really like this "thought experiment" and "picture sphere" illustrations. However, the conclusion does not follow. I can take photographs with a camera (let's say it's a pinhole camera) in all the locations and directions mentioned in the "thought experiment". After I develop the film, I can take a ruler and put it on the photographs and see that the image of the rail in each image appears straight, and intersects the image of the other rail in both directions. Does this conclusively demonstrate that the film is spherical in shape ? (The retina does happen to be almost perfectly spherical, but that fact is irrelevant to this article).

I agree completely. Simply put, stuff that is farther away from the point where it is viewed from looks smaller since there is more to be seen. Think of the fact that the moon and the sun appear to be the same size, yet the moon is hundreds of times smaller. This is because it is also hundreds of times closer. Likewise, the parallel tracks appear to converge since the distance between them appears smaller at a distance - converging to zero as the distance aproaches infinity. The retina does distort images, but this is taken care of by the visual cortex. Convergence of the tracks is in no way related to the retina since, as you point out, any camera (no matter the lense, projected image shape, etc.) captures this effect. Evilrho 23:48, 23 September 2005 (UTC)

(It is, of course, impossible to assemble all my photographs in a collage on a flat surface, such that the images of one rail are in a straight line from one vanishing point to the other, and also the images of the other rail are in a straight line).

-- DavidCary 19:56, 18 Jun 2004 (UTC)

Proving mathematically that all retinas and perhaps even all cube-map textures containing railway lines are spherical was a bit much for me... The article is probably less readable, but more accurate now. Κσυπ Cyp   2004年11月25日 (木) 20:23 (UTC)

The article mentions "the correct way to project the image", implying that any other method is "incorrect". But I fail to see (no pun intended) any difference. What advantage is there to using a sphere (hemisphere ?) ?

The article specifically mentions:

* when someone stands somewhere *other* than at the "station point" in front of the flat image, there will be distortion.

That's true, but don't we get just as much distortion when someone stands somewhere *other* than at the center of the image sphere ?

I see that the image must somehow "wrap around" the viewer to properly show the intersection directly to his left and directly to his right, which is impossible with a single flat picture. But what's so wrong with using several flat pictures, left-front-right etc. ?

-- DavidCary 19:56, 18 Jun 2004 (UTC)

Nothing. I think the 2nd half of this article is flawed. The spherical shape of the retina is completely unrelated to the phenomenon of the converging tracks. Also, the fact that they seem to converge twice but that you can't seem them converge twice without turning 180 degrees is irrelevant. Actually, if you were in a hot air balloon a hundred feet above the center of the tracks you could. Big deal! See my note about the moon and the sun above. This is a case of over-complicating a simple geometric phenomenon occurring with light as viewed by any singular point. Evilrho 23:48, 23 September 2005 (UTC)


Where are Figures 1, 2 and 3?

this article is fundamentally muddled and misinformed; it should be deleted immediately. the discussion here is misguided. i refer discussants to m.h. pirenne: "optics, photography and painting" (1970), which contains empirical demonstrations that clarify the important issues.

provided an image surface is viewed monocularly from the center of projection (viewpoint, station point) and with the same direction of view used to create it, a central projection image (perspective image) will *always exactly* recreate the visual facts of the original viewpoint, regardless of the physical shape of the image surface or angle of view to the image surface. from the center of projection in the original direction of view, an image on a sphere and an image on a plane surface appear exactly the same.

ALL perspective "distortions" are entirely compensated for by the projective geometry of the original projection, and ALL perspective images demonstrate "distortions" if the original viewing geometry is not replicated. for example, the "great circles" on a spherical image surface appear as ellipses when the viewpoint is not at the center of the sphere.

the fallacy in the argument for "railroad tracks that converge yet seem to be parallel" is that the eye is allowed to change its direction of view while implicitly holding the image surface perpendicular to the direction of view; the perspective geometry is permitted to change dynamically. this in effect says that one perspective view must be "wrong" because a different perspective view is possible. the sphere represents as it were the average or aggregate of an infinite number of different directions of view, each with a plane surface perpendicular to it at constant viewing distance. this metaphor may be ecologically relevant to spatial intuitions but it has little to do with the geometry of perspective distortions. indeed, this argument is discussed explicitly in panofsky's "Perspective as symbolic form" (1924) and was originally advanced (and refuted) in the 17th century.

the curvature of the retina has absolutely nothing to do with the subjective form of visual experience, for the simple reason that a projective image, viewed from the center of projection, cannot give any information about the form of the image surface in the image itself. again, this myth is dispelled by pirenne's empirical examples.

finally, "perspective distortions" have been discussed in the artistic literature since leonardo's surviving notebooks, and in nearly every case the "distortion" is judged as such either by comparing geometrically a plane projection surface to a curved projection surface from an abstract ("god's eye") point of view, or by judging a physical projective image from different viewpoints (as nearly all paintings are viewed under normal conditions). the traditional artistic solution to the problem of multiple viewpoints has been to restrict the widest visual angle comprised by the painting (traditions vary, but the consensus is usually a visual angle of less than 30 degrees, or a 6' man viewed from 12'), a method that is taught in the academic tradition as "increasing the distance between the diagonal vanishing points in relation to the width or height of the image".

the author of the original article (pat kelso) appears to be familiar with the book on curvilinear perspective by flocon and barré (1967), but is unaware of how their informal and essentially intuitive justifications for curvilinear perspective relate to perspective geometry and the optics of human vision.



There are 3 fundamental rules that apply to perspective projection –

1 The object must be viewed with one eye. 2 The line of sight must remain fixed 3 The station point must not move.

These rules are observed whenever a still photograph is taken.

There is always an element of distortion when the object is not the centre of attention. I suggest that it is not right to refer to “distortion” because this is the actual path of the light from object to eye. The further from the centre of vision the more “unfamiliar” the image becomes.

A more interesting phenomenon  :-

If you draw a circle on a horizontal surface directly in front of you and imagine that it is the base of a cylinder extending vertically. Observing the rules above:-

We know that the circle will be viewed as an ellipse - but there will be a horizontal cross section of the cylinder at some point that will be viewed as true circle (before the axes of the ellipse interchange).

More generally, a family of an infinite number of circles can be sited, each centred on the centre of vision but of ever increasing radius and centred ever further from eye level but with the bottom of the curve ever closer to it.

And - there will be another family, (the mirror image), the same distances below eye level as the first lot are above it.

It also follows that if the centre of vision is on eye level a further two families can be sited left and right of centre.

Any of these circles can be tested if we draw a quadrilateral round it and construct the diagonals. For the perspective to be consistent both sides and diagonals must project to their respective vanishing points.

The origin of the circles is the point where the lines from the vanishing points meet the centre of vision at right angles. At this point the radius of the circle is zero and the limit is when the circumference becomes a straight line at eye level and the centre at infinity!

These circles of course are beyond the normal cone of human vision but a camera with a very wide angle lens will show what is going on if a circle is positioned horizontally and photographed at the extremity of the frame.

Dalgoma 10:26, 28 May 2007 (UTC)


I'm fairly certain on this correction, but wasn't bold enough to edit the article. In the section stating:

Both types of projection involve a distortion; parallel lines never intersect in nature, but they always intersect in perspective projections—with the rare exception wherein a) the surface of projection is planar and b) a plane of the projected object is parallel to the plane of projection.


I first believe that the "always" should be taken out since it is misleading. Furthermore, I believe the case where the plane defined by the (world) parallel lines is perpendicular to the projection plane also results in non-intersecting lines. In fact, the lines are projected as points in this case. Buttlumpy 17:28, 20 July 2007 (UTC)


-- muhe001 18 Jun 2007

There are so many flaws in this article. If you are to be talking about a "true projection", where a projection of a projection is the same as the second projection only, then most of this article is rubbish.