how to calculate area of objects in certain region of an image.

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Hi i have an grayscale image which has objects all over the image. I want to know the area of the objects in certain regions of the image. I have divided the image in four quadrants using hline and vline and applied in polygon to define each rectangle region. but now i want to calculate the total area of objects residing in each rectangle. but regionprops() doesn't seem to cut it. I'm at a loss about how to do so.
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KSSV
KSSV 2017-6-5
Attach an image so that people can help you around. Simply a question might not give an idea.

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