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From: "OkinawaDolphin " <OkinawaDolphin@Hotmail.com>
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Subject: Re: Correction of Perspective Distortion
Date: Thu, 31 Jan 2008 07:37:01 +0000 (UTC)
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>   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.)

It seems that it is the second kind of distortion. In 
Matlab there are the functions such as maketform and 
cp2tform for defining spatial transformations. Both affine 
and projective transforms can be performed using these 
functions. Parallel lines seem to converge and rectangles 
are changed to rectangles or quadrilaterals. Therefore I 
think that a projective transformation is suitable.

If I had a photograph taken above the imaged area, I could 
use it as a reference image. However, such an image does 
not exist. So there are two possibilities:

1. Creating a simplified artificial reference image.

2. Arbitrarily define mappings between points on converging 
lines in an image to points on a rectangle.

Can you recommend a method of chosing or defining pairs of 
points?