[task #15637] Match RA and Dec catalog to X and Y catalog to find WCS

[Sachin Kumar Singh]

Follow-up Comment #4, task #15637 (project gnuastro):

I read the paper introducing astrometry.net
<https://arxiv.org/pdf/0910.2233.pdf> and also went quickly through its
repository on github <https://github.com/dstndstn/astrometry.net>. One thing
that really bugged me was their documentation. It is not complete and whatever
is written in more or less subtle. Anyway, the paper introduced the idea
fairly well, though it was more theoretical oriented than software-oriented.
Here are the basic steps that it employs for matching and wcs calculations:

* Firstly, all the objects(stars or galaxies) in the files are detected. They
use a method which is based on flux differences and peak/threshold filtering.
But noisechisel provides an easy and efficient way for the same and is already
present for our disposal. So object detection can easily be done:-).

* Next, they use a quad(a set of 4 stars) to make unique geometric hash codes
which is quite fast and efficient for storage and matching neighbours. It also
provides invariant to translation, rotation and scaling of the star positions
so that it can be computed using only the relative positions of the four stars
in any conformal coordinate system.

* The index/reference catalogue is pre-computed for fast retrievals. For
reference catalogues, they use an all-sky(or near all-sky) surveys (like
USNO-B1, infrared  2MASScatalo, and ultraviolet catalogue from GALEX). They
then pre-process these catalogues by making a HEALPix grid and choosing the
brightest stars in those HEALPixes to make a large number of geometric hashes.
 These hashes are then stored in a kd-tree along with the star positions(for
verification). kd-tree provides fast retrieval of query hashes present in the
neighbourhood of the hashes in the reference catalogue.

* Finally, a verification step is also done which used a bayesian decision
model to calculate a threshold for a match to be passed or failed.


Now we have detected objects and made catalogues with them. But we need to
make HEALix grid in our reference catalogue and then create a kd-tree to store
these predefined hashes. We also need a structure to store the hashes for
invariance. Then we'll need to match the hashes in our x-y catalogues to that
reference catalogue (ra-dec). Maybe verification can be done later on when all
these are done. What is your suggestion?

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