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I need a Windows application that will allow an image to be loaded and then a polygon drawn on that image (or identified by way points) and automatically filled. The application will then report the area of the polygon.

Units don't matter (could be pixels, cm, inches) as it is only going to be used for relative comparisons.

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    Have you looked at imageJ? – Eric Shain Jul 20 '18 at 1:41
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On API level you can do it with PolygonRoi from ImageJ: https://imagej.nih.gov/ij/developer/api/ij/gui/PolygonRoi.html

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