Expansion/inversion of binary image

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Below I've segmented some cells, but I am trying now to essentially make the cells white and the rest black.The problem really is the white area around the cells - I'm not sure what the best approach would be. Any suggestions? I've been trying some morphological approaches but they don't seem to help.

My current attempts basically have been using erosion/opening. I could do some contour work, but I would like to avoid that if possible.