Algorithm to stack astronomical images I'm looking for a simple algorithm to compare astronomical images (of the same sky region) against each other, compute their movement and rotation, to finally stack them.

At the moment I'm already having a more or less working algorithm. First I extract all the stars out of an image (including information like brightness and FWHM), and then I walk through all the resulting "points" and create triangles out of the current point and those two other stars that have the shortest distance to this star.

This list of triangles is created for every image. After this I take one image as a reference and then I walk through the list of triangles in the reference image to find a triangle in the other image with the same length of each side of the triangle (I also "allow" some tolerance due minimal relative differences of the star positions in each image). For this matches I calculate movement and rotation relative to the reference image. The last step is to find the matched triangles that have to same relative movement and rotation like the other matches. This is done by calculating the standard deviation, sorting out triangles that are not within 1 or 2 sigma and repeat this process until I have a very small standard deviation.

The last part, finding "valid" triangles with the same movement/rotation, is working fine. The problem is that sometimes I have only like 2 or 3 "valid" triangles out of 300 initial triangles. All other triangles have side lengths different to those of the reference image. 

So I assume it's the way I generate my initial triangles which causes the problem. Sortings stars by their brightness and using this data to generate the triangles also doesn't work. So is there a better way to create the initial triangles in all the images?
This page about a commercial product goes into some detail about their algorithm.  It does the triangle matching you describe, with something like simulated annealing to get a more optimal solution.

The accepted answer to this closely related question recommends Hugin panorama software; it's open source, so you should be able to glean the algorithms used.