Newsgroups: sci.image.processing
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From: ndevilla@eso.org (Nicolas Devillard)
Subject: Re :  WARPING: need help with solution options on distorted images...
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Message-ID: <1995Jun23.132157.6182@eso.org>
Keywords: warping, resampling, deformations
Sender: news@eso.org
Reply-To: n.devillard@eso.org
Organization: European Southern Observatory
Date: Fri, 23 Jun 1995 13:21:57 GMT
Lines: 37

Warping is an operation on images that operates in 2 passes :
 
1. Calculation of a model of deformation
2. Resampling of the image according to previous transformation

Q: What is a model of deformation ?
A: Any (x, y, z) -> (x', y', z') function could be estimated. The simplest are linear
(of course), which model only scale change, translations, and rotations.
2nd degree polynomials can be used to fit a quadric surface.
In your case, modelling a lens distortion is usually a polynomial of 6th degree
in radius, or 12th degree in cardinal coordinates.
Of course, such deformations are not always global for the whole image. Local functions can be used to model local deformations.

Q: How do you estimate such models ?
A: For a global transformation on the image, such as lenses warps, the only way
is to indicate couples of points between a deformed image, and a correct one. If the number of points is sufficient, the model can be derived from a least squares calculation and thus feeded into a resampling routine. In your case, you may
not have a correct image. Make some ! If you take pictures of a regular grid for example, you can easily appariate points from one image to another, and use these points to compute the model.
This assumes your lens always keeps the same deformation through time.
 
Q: What about resampling ?
A: Resampling can be performed by many different algorithms (nearest neighbor, bilinear, bicubic, B-splines, etc.). Your choice only depends on the computing power you have, and the image quality you need (the highest quality, the highest computing power needed).
 
Q: Is there any software available ?
A: In many private labs were such softwares created. I just know warping softwares exist for Windows, but I cannot tell the name or even the company. Khoros may do the job, thus I do not know enough of it to tell if it is easy or not to perform generic warpings with it.
 
Q: Which is the literature reference ?
A: The most complete is
    Digital Image Warping
    George Wolberg
    IEEE computer press society
 
Hope it gives you answering clues.
Nicolas Devillard




