Can't compute homography

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I'm quite inexperienced with Matlab and image processing, and I've been struggling with this problem for the past few days.

I have a 12 point correspondence between coplanar plane coordinates and their image projections. I also know the intrinsics of the camera. From what I understood, this is enough to compute the homography. (My final goal is to obtain the extrinsic parameters of the camera, which I believe is straightforward after computing the homography H.)

I've tried different methods to obtain H, but I get a different matrix with each method/function I try, when apparently they all have the same input/output. For example, using vgg_H_from_x_lin(X1,X2) found here http://www.robots.ox.ac.uk/~vgg/hzbook/code/ and homography_solve from http://www.mathworks.com/matlabcentral/answers/26141-homography-matrix gives me 2 completely different matrices.

I've tried this as well, https://cseweb.ucsd.edu/classes/wi07/cse252a/homography_estimation/homography_estimation.pdf , which led me to another different H.

What am I doing wrong here? This should be quite simple as I have the point correspondence and the camera intrinsics, but I can't understand how to compute H correctly.

Thanks in advance.

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