## Repeatability of finding center and radius of the lunar disc.

Error budgetPosted by Peter Thejll Aug 21, 2012 12:33PMA required image analysis step is the determination of lunar disc centre and radius.

We currently use a hybrid method: First we fit circles to points on the BS rim (found as an image by using edge-detection image-analysis methods: SOBEL filters!) of the lunar disc image - this is done many times using different points and then the median is extracted for x0,y0 and radius. These values are then used as starting guesses for a more refined method that searches a range of possible values near the starting guesses and determines a 'winner' based on how well a synthetic circle matches the 'rim image' generated above.

We compare the statistics of the starting guesses and the final adopted values. In two separate runs on 88 different images we assemble these values:

Run 1:

x0 start guess: 311.82352 +/- 2.7447506

x0 final guess: 310.44694 +/- 2.3127377

y0 start guess: 248.49938 +/- 1.1339389

y0 final guess: 248.70556 +/- 1.0812740

radius start guess: 136.32425 +/- 0.98834739

radius final guess: 136.90833 +/- 0.44461002

Run 2:

x0 start guess: 311.78076 +/- 2.9802184

x0 final guess: 310.46767 +/- 2.3079720

y0 start guess: 248.51968 +/- 1.0747726

y0 final guess: 248.70327 +/- 1.1017349

radius start guess: 136.42162 +/- 1.2634192

radius final guess: 136.90870 +/- 0.40265642

x0 is found slightly more precisely with the final method (2.3 pixels vs 2.8).

y0 is found with similar precision in the two methods (about 1.1 pixels).

radius is found better with the final method (0.4 vs about 1 pixels).

We seem to be able to determine the centre of the lunar disc with image analysis techniques to the 1-2 pixel level, and radius to better than half a pixel.

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