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Extract lines from output of sobel filter

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I'm using the sobel filter for extract the contours of an image.
It work.
Now i must extract lines from the contours the lines can be with two type first point- second point or with the lines equation or ???.
But i dont know a good method for extract the lines, in c++ or cuda from a texture or vector of points(that is the output of the sobel filter).
Can you help me?

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