Why would we rotate the right image (Image 2) by R (and not the left image)? Isn't the relationship that x' = R(x-t), where x' is from Image 2? If we consider Image 1 to be in the "normal" orientation, then Image 2 is already a rotated version of Image 1. I'm confused why we would then want to rotate Image 2 again by R.
motoole2
The goal of step 1 is to find a rotation matrix $R$ such that the image planes of both cameras are parallel; as a result, we only need to apply this rotation matrix $R$ to one image.
The goal of steps 2 and 3 is to find a second rotation matrix $R_{\text{rect}}$ to reorient the common image plane such that it is parallel to the stereo baseline / translation vector, making the epipolar lines horizontal.
nssampat
I understand, but my question was more about why in step 1 we choose to rotate the right camera by R rather than the left camera.
motoole2
We could actually rotate either the right camera by $R$ or the left camera by $R^T$. Or, we can even rotate both cameras. So long as the final result has both cameras pointed in the same direction.
Why would we rotate the right image (Image 2) by R (and not the left image)? Isn't the relationship that x' = R(x-t), where x' is from Image 2? If we consider Image 1 to be in the "normal" orientation, then Image 2 is already a rotated version of Image 1. I'm confused why we would then want to rotate Image 2 again by R.
The goal of step 1 is to find a rotation matrix $R$ such that the image planes of both cameras are parallel; as a result, we only need to apply this rotation matrix $R$ to one image.
The goal of steps 2 and 3 is to find a second rotation matrix $R_{\text{rect}}$ to reorient the common image plane such that it is parallel to the stereo baseline / translation vector, making the epipolar lines horizontal.
I understand, but my question was more about why in step 1 we choose to rotate the right camera by R rather than the left camera.
We could actually rotate either the right camera by $R$ or the left camera by $R^T$. Or, we can even rotate both cameras. So long as the final result has both cameras pointed in the same direction.