How to correlate 2D mask with noisy image?

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I have a matrix 'A' with two columns which contains 2D points ( coordinates 'x' and 'y'). These points earlier were projected onto the plane from 3d cloud, so they create a 2d shape of some object. For the second I have a noisy image 'B'(4k x 4k matrix) with similar (but translated and scaled) shape. What I want to do is to correlate points from matrix 'A' and use them as a binary mask for the object on the image 'B'. Currently i dont have a slightest idea how to do it. Thanks for all help.

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HoneyBadger17 On

Following off of what AnonSubmitter85 suggested with the pattern recognition method, something like a SIFT (Scale Invariant Feature Transformation) detector might be helpful in the case of the scaled and rotated object. Similarly, matlab has a set of functions that do SURF (Speeded Up Robust Features) detection:

http://www.mathworks.com/help/vision/examples/find-image-rotation-and-scale-using-automated-feature-matching.html

Hopefully this can stimulate some new ideas.