How to warpPerspective a large image based on transform inferred from small region

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basically yes.

for a proper description of how, you'd need to demonstrate your problem more precisely. I'd suggest illustrations/pictures or very precise textual description.

at the very least, you can construct 3x3 matrices for translation and scaling and matrix-multiply them (from the left) onto the homography you calculated. that has the effect of moving the data in "screen space", i.e. in the result. to construct one such operation, you start with an identity matrix. for translation you change the top two values of the third column. for scaling you'd change the first two values on the diagonal. use separate matrices for each operation, then multiply them.