I am measuring object width with a monocular camera. I have done the necessary calibration to remove lens distortions and to get the intrinsic parameters.
Now i used a calibration plane to define the homography matrix as accurately as possible. I understand if the measured objects are exactly on the same plane that is defined by homography the error should be minimal.
The problem is that the measured objects can be thicker and thinner so the homography matrix of the original plane is not good for all objects.
Is it possible to calculate a new homography matrix for a plane that is moved by some depth z if you know the thickness of the object (the depth you would want to move the original plane).
If so how would this transformation be described with an equation.
Is it a viable option to define (for the sake of the question) 3 homography matrices for thin, normal and thick objects to reduce the overall error from the displacement.
Thanks in advance.
From my understanding since the homography is scalable this should be possible.
Your question is unclear: you do not specify what errors are important for your problem, hence the "accuracy" of interest.
If your setup is monocular (one camera) and with calibrated intrinsic parameters, absolute distances can be determined only for objects of known shape and size (for example, the calibration target you used), regardless of whether they are on any plane.
For objects of unknown size, one can make weaker statements, for example ordering in distance. Many such cases were analyzed and solved by A. Criminisi in his Ph.D. thesis at Oxford years ago. Look it up.