computer vision - Depth error due to triangulation in stereo systems

Question

I have a question trying to understand the definition of the depth error due to triangulation from a pair of stereo rectified images.

The formula is as follows:

eps_z = bf/d - bf/(d+eps_d)

Where b is the baseline between left and right camera and d the disparity (pixel difference) between a reprojected point from 3D into both left and right camera planes. If everything was ideal eps_z and eps_d should be zero and the depth measured from both cameras should be the same.

My question is: why eps_d is only present in the right image? Shouldn't the disparity between L and R be the same as the one from R to L therefore the error should be the same or doesn't it have to be like that? I know if they are the same there is no depth error but for me seems counter intuitive that it changes depending on the direction.

question from:https://stackoverflow.com/questions/65848584/depth-error-due-to-triangulation-in-stereo-systems

Answer 1

"why eps_d is only present in the right image"

It isn't. You're dealing with measurement errors here. If you knew exactly whether to add or subtract this from the left or right side, it wouldn't be an error term, but a correction term. An error term represents uncertainty. That's also why by convention it doesn't have a sign.