What is a Good Threshold?

If we're going to identify objects in the night sky, we need to find a grayscale threshold that means: Above this value, the pixels are probably part of an object.  Below it they are probably not.

A threshold is just an integer -- the pixels in our image, brought to us by the miraculously excellent Proline camera, are 16-bit integers, whose possible values range from 0 to 65,535.

The reason we need to think about a threshold is because the background -- the dark between the stars -- is not perfectly black.  If it were perfectly black, then its pixel values would all be zero, and our threshold would always be "anything above zero".  But it's not.  In the images I have taken, the dark between the stars tends to be around gray value 1000.  The darkest sky I have seen so far (on March 5th, 2016) had a background around 650.

And that background is never perfectly smooth.  It has noise.  It has a standard distribution of values, so that, if you brighten it enough and zoom in enough, it looks like this:

Further, if we just wanted to find nice, reasonable stars, we wouldn't have to worry about setting a good threshold.  Nice, reasonable stars are so much brighter than the background noise that you could choose practically any threshold at all and it would work just fine.

But we want to see the faintest things that hide right down in the noise, so we need the best threshold that can possibly be found.

How do we know if we have a good one?

Here are a couple examples, from the lovely dark sky of 5 March 2016, above Siding Spring, Australia.

 

The image on the left has been thresholded at 500, the one on the right at 600.

Look at the trapezoid of 4 faint stars near the upper left of both images.  They are just as discernable in the right image as in the left.  In fact, there are no faint stars visible in the left image that are not also visible in the right.

If we go too far into the noise with our threshold, we are not making any new faint stars visible.  We are only brightening the noise.

What we want is the highest threshold we can get -- and thus the darkest background we can get -- that does not lose those faintest stars.  That will be our criterion for a good threshold.

It's easy to find a good threshold 'by hand', by slicing the 16-bit image at many levels and inspecting the results -- but we need to automate the process.  Next week we will look at a method of doing that.