Finding closest non-black pixel in an image fast

Question

I have a 2D image randomly and sparsely scattered with pixels.
given a point on the image, I need to find the distance to the closest pixel that is not in the background

Answer 1

I would do a simple lookup table - for every pixel, precalculate distance to the closest non-black pixel and store the value in the same offset as the corresponding pixel. Of course, this way you will need more memory.