Affine homography computation

Suppose you have an homography H between two images. The first image is the reference image, where the planar object cover the entire image (and it is parallel to the image). The second image depicts the planar object from another abritrary view (run-time image). Now, given a point in the reference image p=(x,y), i have a rectangular region of pixels of size SxS (with S<=20 pixel) around p (call it patch). I can unwarp this patch using the pixels in the run-time image and the inverse homography H^(-1).

Now, what i want to do is to compute, given H, an affine homography H_affine suitable for the patch around the point p. The naive way that i am using is to compute 4 point correspondences: the four corners of the patch and the corresponding points in the run-time image (computed using the full homography H). Given this four point correspondences (all belonging to a small neighborhood of the point p), one can compute the a开发者_开发知识库ffine homography solving a simple linear system (using the gold standard algorithm). The affine homography so computed will approximate with reasonable precision (below .5 pixel) the full projective homography, since we are in a small neighboorhood of p (if the scale is not too unfavorable, that is, the patch SxS does not correspond to a big image region in the run-time image).

Is there a faster way to compute H_affine given H (related to the point p and the patch SxS)?

You say that you already know H, but then it sounds like you're trying to compute it all over again but this time call the result H_affine. The correct H would be a projective transformation and it can be uniquely decomposed into 3 parts representing the projective part, the affine part and the similarity part. If you already know H and only want the affine part and below, then decompose H and ignore its projective component. If you don't know H, then the 4 point correspondence is the way to go.