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

You didn't specify how you want to measure distance. I'll assume L1 (rectilinear) because it's easier; possibly these ideas could be modified for L2 (Euclidean).

If you're only doing this for relatively few pixels, then just search outward from the source pixel in a spiral until you hit a nonblack one.

If you're doing this for many/all of them, how about this: Build a 2-D array the size of the image, where each cell stores the distance to the nearest nonblack pixel (and if necessary, the coordinates of that pixel). Do four line sweeps: left to right, right to left, bottom to top, and top to bottom. Consider the left to right sweep; as you sweep, keep a 1-D column containing the last nonblack pixel seen in each row, and mark each cell in the 2-D array with the distance to and/or coordinates of that pixel. O(n^2).

Alternatively, a k-d tree is overkill; you could use a quadtree. Only a little more difficult to code than my line sweep, a little more memory (but less than twice as much), and possibly faster.