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how to make canny edge detection invariant to image size?

I'm trying to implement a document scanner following http://www.pyimagesearch.com/2014/09/01/build-kick-ass-mobile-document-scanner-just-5-minutes/

however, I found out that the method is very sensitive to image size.

when the image is very large, the canny edge detector tends to draw very thin edge lines, so thin that at certain areas, the edge lines disjoint.

And then the next step findContour function would fail.

how to make canny edge detection invariant to image size? Thanks.