The whole idea of producing a precisely rectangular image of a known rectangle in the real world is suspect, and actually a distortion of reality. I say this because a rectangular object cannot truly appear as precisely rectangular.
At first blush this sounds counter-intuitive. You might say: "Of course rectangular objects look rectangular- what else would they look like?!" But do they? Under most circumstances, rectangular objects appear mostly rectangular, but widen the view that a rectangular object encompasses, and the picture becomes clearer.
Imagine that you are standing in front of a very large one story building- let's say that it is 10 feet high, 200 feet wide, and you are 20 feet away from it. The left end of the building stretches way off to the left, and the right end to the right. Those ends of the building appear very small, while the middle of the building right in front of you appears quite large. How then, can the front of the building appear as a rectangle?
In fact, the top of the building and the bottom of the building must actually appear as curved edges, with the two curves farthest apart in the middle, and closer together at the two distant ends. This is a simple consequence of the fact that closer objects appear larger and distant objects appear smaller. For a rectangular object centered on the direct axis of view, this causes all sides of the rectangle to appear slightly bulged out away from the center.
While this scenario is certainly an extreme example, it is still true for all other situations, just to a lesser degree. This is the effect that the built-in distortion in a camera lens attempts to mitigate. This lens design tries to force the object to actually be imaged as a rectangle, when, as we've already seen, it can't really look that way.
For the most part, this purposeful distortion in a camera lens is actually a benefit (why else would lens designers go to such great lengths to design them this way?). But when attempting to reconstruct a panoramic image from separate camera images this built-in distortion makes the effort problematic. I'll look at this issue in my next post.
|Image by camera lens with built-in distortion to|
produce precisely rectangular shape
|View of rectangular object as it might actually|
appear as a consequence of geometry