I thouhgt that, having opened the door by my "tedious" language above. I would comment a little on the matter of "perspective".
We have a tendency to speak of perspective as the phenomenon in which lines that are parallel in space show up as converging lines in our image.
In that state of mind, imagine that we consider a situation in which we shoot "head on" at a small rectangular billboard, behind which is a larger billboard (whose plane is parallel to the first).
We see no converging lines in the image, and thus have a tendency to say "there is no perspective in this image".
In fact, perspective refers to the entire result of projecting this three dimensional "scene" onto a two dimensional image, as a result of viewing the scene from a particular location of the viewer (the "point of perspective").
In the example above, although the larger billboard might have twice the linear dimensions of the smaller one, it will not be twice as large in the image (owing to its greater distance from the viewer). That is a manifestation of the perspective situation here.
Now, a typical common concern with perspective is when we have taken a shot of nice plane building facade when we cannot aim the camera directly at the center of the facade. (To be really precise, the problem arises when the film plane isn't parallel to the facade.) So we stand in the street, and aim the camera upward so as not to waste half the frame with street in the image.
As a result, the building facade (which we will assume has a rectangular outline) shows up on the image as a trapezoid (with the vertical edges at the sides of the facade now converging); if all the windows are actually the same size and square, on the image they will all be trapezoids; the upper ones will be smaller than the lower ones; and the upper ones will be "squashed" vertically in aspect ratio compared to the lower ones.
Now the image we get is exactly what the eye, regarding the building from that same spot, with that same "aim point", would record. There is no anomaly in the camera image.
But our client would like the building facade to look rectangular, with all windows square and the same size, just like on the architect's rendering.
This is what we would have gotten if we had shot the subject building straight on out of the window of the 4th floor ladies' restroom in the CIA office in the building across the street. But we were't able to do that.
(Of course there would have been perspective effects there too - they just wouldn't include "the vertical edges of the facade coming out convergent" and "the windows having different sizes". There are perspective effects in any photograph.)
So we seek to modify the image "so the perspective effects resulting from the oblique shot are changed to be the same as the perspective effects we would have had in the straight-on shot".
Not to "remove perspective".
Not to "correct perspective".
But rather to change it from what we got in our shot to what we would have had in a shot that produced the result the client wanted.
Best regards,
Doug
