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There are multiple functions to do it. If you have a list of points, perspectiveTransform() is what you're looking for.

std::vector<cv::Point> inPts, outPts;
inpPts.push_back(cv::Point(3, 5));
perspectiveTransform(inPts, outPts, homography);

// now, you have the x', y' stored in outPts[0];

You may also want to convert an entire picture from one space to another - if you want to match pairs of points in two pictures, this is a common task.

So, given the currentPicture, and pictureReference, both declared as cv::Mat, you can

warpPerspective(currentPicture, pictureReference, homography);

Here you can find docs for warpPerspective