Re: Correction of Perspective Distortion

"OkinawaDolphin " <OkinawaDolphin@xxxxxxxxxxx> wrote in message
<fnpft6$lod$1@xxxxxxxxxxxxxxxxxx>...
I have to analyze images that are distorted because the
optical axis is not perpendicular to the plane being
imaged. Therefore, lines that are parallel in the real
world are not parallel in the image and rectangular objects
appear as parallelograms. How can I correct for this?

Is the any Matlab function that calculates the images that
would have been taken perpendicular to the plane to be
imaged?
-------------
There are two kinds of image "distortion" that you might have in mind here.
You could be thinking of a draftsman-like image as viewed from an infinite
distance above a plane. Then a parallel projection onto a tilted plane would
be a simple stretching along the direction orthogonal to the intersection of
the two planes. Rectangles would change to parallelograms and parallel lines
would always remain parallel. This is not usually what is referred to as a
"perspective distortion".

Or you might be talking about a projection from a fixed perspective point
above one plane onto a tilted plane. In that case parallel lines in the one
plane do not, in general, translate to parallel lines in the other, and rectangles
become quadrilaterals which are not, in general, parallelograms. (Think of
parallel train rails and railroad ties seeming to converge to an infinitely
distant point.)

Which do you have in mind? If you have this second circumstance in mind,
there are five different parameters that enter into the situation. First, there is
the position in the first plane at the base of an orthogonal line (optical axis)
from the given perspective point, which takes two parameters. Next, is the
distance above the plane to that perspective point, a third parameter. The
fourth and fifth parameters are the direction and amount of tilt to the second
plane relative to the first one.

It isn't clear to me just how you would go about determining all these
necessary parameters before carrying out the kind of correction you are
seeking. It is quite possible to give a transformation which could make the
necessary correction that you ask for, once these five parameters are known.
As I recall from some work I did a very long time ago, the equations involved
are simple rational functions. However, (perhaps out of laziness,) I am
reluctant to go to the trouble of again working it all out without having some
kind of assurance that you have devised a method for finding the necessary
five parameters.

Roger Stafford

.

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