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Width dissecting with a line on masked image

Dear all,

I am currently working with OpenCV 3.2.0 on Python.

Suppose I have a colored object that is centered against a white backdrop, and that I've filtered it to produce a B&W image, I wish to retrieve information on the respective length of the two sides of the object as well as the width (in pixels) of the object in the image.

Example: image description

As above, the object is white in colour.

May I know the general approach I should adopt in solving this?

Thank you!