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You want to use the distanceTransform function. It gives you the distance to the closest 0 pixel, so you'll have to pre- and post-process the image.
Pre process by copying the image as a mask, and make everything not white equal to 1 or something. Then put a single black pixel around the edges.
Post-process by getting rid of the edge and taking everything not in the mask,setting it to whatever your no good value is. -1 you say.
