Let image $x$ be an original (non-warped) image. Let $I_1$ be $I_1'$ having suffered some projective transformation and possibly some noise. Suppose we have computed SIFT descriptors for both images.
Can you explain how RANSAC is concretely used to find the homography that aligns image $x$ and $y$?
More concretely, I understand we give to the RANSAC function the keypoints ($I_1$) and keypoints ($I_1'$).
My understanding (from various papers/tutorials I've read) is that it will take the positions of keypoints in $I_1$, which I denote as $(x,y)$, and the positions of keypoints $I_1'$, $(x', y')$, i.e. RANSAC($(x,y),(x',y')$), and then take randomly pairs of $(x',y')$ and $(x,y)$, and then compute the homography by trying to solve for each $x_i', y_i'$: $$[x'_i, y'_i]=H*[x_i, y_i]$$
But then how to estimate inliers? I guess by looking at the Euclidean distance between each pair of points found in the homography.
However, I don't really see the 'big picture'. I don't completely link this process of 'finding homography' and checking inliers etc.
It would be great if someone could summarize that in a clear way?
P.S. In general, tutorials say that they "find the homography" and then check for inliers - in some way - but they don't explain in a more pragmatic way what really happends.... w.r.t sift descriptors