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Obstructed Rectangle Detection

Hi, I am trying to detect 4 corners of a regular paper sheet. i have tried all the ways canny/sobel/polygon detection/line detection they all work fine

if and only if the whole paper is visible

if one or more of the corner is obstructed by users hand (if he is trying to write something on paper) one of the corners get lost and i really need all four or an estimation of all four

so is there a way if i know three points of a polygon and i can calculate/guess where the fourth one will be if its obstructed found this article which seems to do the opposite of what i want -> http://stackoverflow.com/questions/17087446/how-to-calculate-perspective-transform-for-opencv-from-rotation-angles

or is there a way to remove the hand from the image by using some tech color detection etc?

any help will be appreciated