Re: [APML]: Image registration [Was: Latest Tony Hallas Images]

[Axel Mellinger <axm2@canopus.physik.uni-potsdam.de>]

The Astro-Photography Mailing List
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On Tue, 8 Sep 1998, Eric Royer wrote:

> Could you explain in a few words how you managed to align the images ?
> What kind of transformation did you apply to each image to compensate for the
> deformation of the wide angle lens ? (I suppose it is a function of the distance
> from the center of the photo)

Well, it's hard to do it in just a few words, but I'll give it a try... 
Basically, the Milky Way panorama is plotted in a coordinate system with
galactic longitude and latitude as x and y axis, respectively. 
I had to work out the transformation from galactic
coordinates to (x,y) coordinates in the film plane.  It's a little
exercise in spherical trigonometry - in 2D the relation would simply be
x = 2*f*tan(alpha/2), where x is the pixel coordinate, f the focal length
and alpha the angle between the star and the optical axis. Of course the
camera might be rotated with respect to the galactic frame, so I had to
put in a rotation angle, too, and also allow for the fact that the
optical axis might not be exactly in the center of the image (this could
happen if the image was cropped asymmetrically when scanned onto Photo
CD). All in all I had 6 adjustable parameters, which were determined in a
nonlinear least squares fit. For each image I picked about 12-15 evenly
distributed reference stars, looked up their coordinates (RA and Dec,
which were then transformed to galactic coordinates), and measured their
pixel positions.

If this sounds like a little too much math for the moment, I'll try to get
an article with some illustrations on my web site soon. 

Clear skies,

Axel

-- 
Axel Mellinger  <http://canopus.physik.uni-potsdam.de/~axm/astrophot.html>