I am facing the challenge to recover the Z coordinate from an inverse disparity map and the instinct matrix K. The Z coordinate does not have to be metric but it has to be scale aware.
$$ K_{3\times 3} = \left[ {\begin{array}{cccc} 721 & 0 & 596 \\ 0 & 721 & 149 \\ 0 & 0 & 1 \\ \end{array} } \right] $$
I know that $z=f\frac{T}{d}$ where T is the distance between two coplanar cameras, f is the focal length, and d is the disparity. However, I am not told any extrinsic other than the camera is 1.5m up from the floor. The disparity is already an inverse disparity so I guess $z=f \times d$? Also, what do I do with the other parameters in my K matrix (596, 149)? Any help is welcome.