When matching two images, say L and R, of the same scene from different perspectives, sometimes it is useful to assume that the images are related by a homography, either because the observed object is planar, or because the images cover a small portion of the object, which can be considered planar in first approximation:

So I will search for nine coefficients of the homography, determined up to a factor, which minimize some target function – difference of squares or anything else.

If the images come from a calibrated system, then I know the pencil of epipolar planes and its intersections with the images; I know, say, that the straight line in image L is transformed by the homography I am looking for into the corresponding straight line in image R.

Here is how I can exploit this constraint to help determine the homography.

Assuming and I can write

whence

Therefore it must be

Being the homography determined up to a factor, I can safely assume and use these three linear equations in nine unknowns as constraints for my search of the homography.

Note however that the three equations are not linearly independent, as .

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