On "perspective distortion" and "distance compression"

Often, we see such effects such as the convergence, in an image, of lines that are actually parallel in the three-dimensional space of the subject (the edges of a rectangular building, for example) called "perspective distortion".

I have criticized this usage, pointing out that this result of the "projection of a three-dimensional scene onto a two dimensional plane" should not be characterized as distortion. I point out that, for example, exactly the same result occurs in live human viewing of the same scene from the same vantage point. Thus we should not "criticize" the photographic process for essentially capturing the same view of the scene that the human eye would have captured directly.

However, recently, in a discussion in another branch of this forum, our colleague Bart van der Wolf called my attention to the fact that there is a related matter than can reasonably be spoken of as "perspective distortion".

Bart points out that if the image is viewed at a size and from such a distance that the angular size of objects is different than for direct human viewing from the vantage point of the camera, the impact of the geometric effects of perspective will be different to the viewer of the image than to that direct viewer.

And it is that discrepancy that perhaps deserves the label "perspective distortion".

We often draw upon our expectation that the viewing will be done that way for artistic effect, such as the "distance compression" of a group of objects shot from an extreme distance. (More on that shortly.)

If the magnification from the "sensor or film" image to the viewed image is M, then this "distortion" is averted when the image is viewed from a distance, d, given by:

d = Mf,

where f is the focal length used for the shot. (This relies on an approximation valid if the distance to the subject is "many times" the focal length.)

Thanks to Bart for illuminating this situation.

Returning to "distance compression", I have often pointed out that this effect is not, as commonly said, a creature of large focal length but rather only of the distance from the camera to the group of objects (noting that we often of course use a large focal length in such a situation to allow us to appropriately fill the frame with our "composition")

But I now realize that this is in fact not the whole story.

Indeed, the geometric relationships we characterize as "distance compression" result only from the subject distance, not to focal length. But those geometric relationships only look "unnatural" to us when we observe the object group, in the viewed image, at a significantly-greater angular size than they would have subtended if we had viewed the scene from the camera (just as discussed above).

Now, assuming a certain common range of "camera-to-print" magnification, M, and a certain common range of viewing distance, d, the image compression effect, as perceived by the viewer of the print, will in fact be greater for greater values of focal length.

We can express this criterion algebraically, using the same notation as above, as:

f>>d/M

So I now see that I need to be more cautious in wagging my finger at those who speak of distance compression as being produced by large focal lengths!

Best regards,

Doug

it's just a matter of using the correct technical term. Usually when someone uses the incorrect term, everyone still knows what they are trying to say.

After shooting large format for a year or so, I've come to really understand how distance to subject makes a big difference in how the subject is perceived on the film. Sure lenses add a bit of their own distortion to the view before it hits the film, but really understanding how distance affects things is something I just didn't really pay much attention to before shooting large format! Maybe it's because I think more about my shot before I take it now, because of all the work required for just one shot in large format. Same thing with DOF, focal length, and other things, I understood how they worked, but I have a better understanding now. Maybe it's because large format cameras are very simple in design (just holding the lens infront of the film!) and it makes certain things more obvious.