How Astrometry.net works (plate solving)

[furrysocks2]

I found this paper, titled "Astrometry.net: Blind astrometric calibration of arbitrary astronomical images"

https://arxiv.org/pdf/0910.2233.pdf

Quote

We have built a reliable and robust system that takes as input an astronomical image, and returns as output the pointing, scale, and orientation of that image (the astrometric calibration or WCS information). The system requires no first guess, and works with the information in the image pixels alone; that is, the problem is a generalization of the “lost in space” problem in which nothing—not even the image scale—is known.

Lots of diagrams and explanation of how it works and how the indices were put together:

Interesting, if you're interested in the internals.

[furrysocks2]

These are the bits I found most interesting on first read, explaining what a "quad" is and how it is used to generate potential matches.

Quote

Given a set of stars (a “quad”), we compute a local description of the shape—a geometric hash code—by mapping the relative positions of the stars in the quad into a point in a continuous-valued, 4-dimensional vector space (“code space”). Figure 1 shows this process. Of the four stars comprising the quad, the most widely-separated pair are used to define a local coordinate system, and the positions of the remaining two stars in this coordinate system serve as the – 8 – hash code. We label the most widely-separated pair of stars “A” and “B”. These two stars define a local coordinate system. The remaining two stars are called “C” and “D”, and their positions in this local coordinate system are (xC, yC) and (xD, yD). The geometric hash code is simply the 4-vector (xC, yC, xD, yD). We require stars C and D to be within the circle that has stars A and B on its diameter. This hash code has some symmetries: swapping A and B converts the code to (1−xC, 1−yC, 1−xD, 1−yD) while swapping C and D converts (xC, yC, xD, yD) into (xD, yD, xC, yC). In practice, we break this symmetry by demanding that xC ≤ xD and that xC + xD ≤ 1; we consider only the permutation (or relabelling) of stars that satisfies these conditions (within noise tolerance).

...

Noise in the image and distortion caused by the atmosphere and telescope optics lead to noise in the measured positions of stars in the image. In general this noise causes the stars in a quad to move slightly with respect to each other, which yields small changes in the hash code (i.e., position in code space) of the quad. Therefore, we must always match the image hash code with a neighborhood of hash codes in the index.

...

When presented with a list of stars from an image to calibrate, the system iterates through groups of four stars, treating each group as a quad and computing its hash code. Using the computed code, we perform a neighborhood lookup in the index, retrieving all the indexed codes that are close to the query code, along with their corresponding locations on the sky. Each retrieved code is effectively a hypothesis, which proposes to identify the four reference catalog stars used to create the code at indexing time with the four stars used to compute the query code.

...

The task of the verification procedure is to reject the large number of false matches that are generated, and accept true matches when they are found. Essentially, we ask, “if this proposed alignment were correct, where else in the image would we expect to find stars?” and if the alignment has very good predictive power, we accept it.