Areas of Voronoi cells from an image file

Question

I have a binary image with non-point objects.

Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (the goal is area distribution)?

Sample image

Are you asking how to calculate a Voronoi diagram for non-point objects? — Dr. belisarius, Oct 8 '14 at 12:16
They started and finished with images. I found difficult for me to derive numerical areas. — Yuriy, Oct 8 '14 at 12:21

ybeltukov · Accepted Answer · 2014-10-08 12:35:43Z

13

There is a one-liner (if you have wide enough screen)

Histogram@ComponentMeasurements[#, "Area"][[;; , 2]] &@
   WatershedComponents@DistanceTransform@Import@"http://i.stack.imgur.com/k0EUJ.png"

enter image description here

answered Oct 8 '14 at 12:35

ybeltukov

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$\begingroup$ Now, that's terseness :D $\endgroup$
– Dr. belisarius
Oct 8 '14 at 12:45
$\begingroup$ It's a One Line Mathematica Lesson®. $\endgroup$
– DumpsterDoofus
Oct 8 '14 at 15:04

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