Scale ambiguity of perspective projection

Scale ambiguity of perspective projection means that image coordinates alone cannot determine absolute scene size and distance. In an ideal camera with focal length $f$ and centered image coordinates,Replacing $(X,Y,Z)$ by $(sX,sY,sZ)$ for any positive $s$ leaves $(u,v)$ unchanged. A geometrically similar scene twice as large and twice as far away therefore produces the same projection.^[ref]

For example, a $0.10\mathrm{m}$ object at depth $1\mathrm{m}$ and a $1\mathrm{m}$ object at depth $10\mathrm{m}$ subtend the same image height under this model. Extra metric information, such as a known object length or a measured camera baseline, supplies a scale. In stereo vision, scaling the reconstructed scene and the assumed baseline together preserves the image observations; measuring the baseline breaks that freedom. Camera calibration of focal length alone does not provide an absolute length for an otherwise unknown scene.