Fourier Transform Plate Solver

Blind plate solving combining roll scan and Fourier correlation methods.

A blind plate solver correlates a night sky image with a star catalog to determine the camera pose (two pointing direction angles plus a roll angle about that direction) and to identify the stars appearing in the image. It is sensible to start with a star detector to find the pixel coordinates of star candidates in the image, reducing the correlation problem to a minimal noise geometric problem. A number of methods can be used to tackle this problem with and without estimates of the pose or image scale. (See references.) These include asterism shape matching and brute force comparisons using bright image stars as pivots tested on every catalog star below some magnitude limit. Another method expands both the image, projected onto the sky, and the catalog in spherical harmonics and correlates the two.

This educational Live Script explores yet another method. It creates a geographic projection of the catalog and of the star candidates for various trial roll angles, replaces each point by a Gaussian kernel spot to account for errors, and performs a cross correlation, the maximum value indicating the solution. A singularity at the poles of the projection is avoided by using three north poles.

The script runs a star detector on real mobile wide-field phone night sky images, uses for each a known field of view, and presents the solution method one stage at a time. The plate solver is a Python package which can be run independently. The Live Script reads prerecorded records for the included images. One parameter switches the solve from the stored record to a live run.

This script may interest students of physics and astronomy and others interested in image processing. Try this blocks, Challenges, and references are included for further exploration. Additional educational Live Scripts by the author are here.