One photograph cannot fix scale.

Demonstration

Perspective projection maps a 3D point to an image point by dividing by depth. Double every distance in a scene and double every object’s size and the projection is unchanged, pixel for pixel. The scene and its scaled copy are indistinguishable from one viewpoint.

So a network predicting metres from a single image is not solving a well-posed problem. What it can do is exploit the regularities of the world it was trained on — doors are about two metres, corridors have known proportions, this camera has this focal length — and those regularities are priors about the training distribution, not geometry.

The literature is unusually honest about this and the terminology records it. Relative depth predicts ordering. Scale-invariant losses score a prediction after fitting the best scale, so the model is never penalised for the part it cannot know. Metric depth models exist and are explicitly restricted to a domain and camera, because that is the extra information that resolves the ambiguity.

MiDaS’s contribution was to train across many datasets whose depth annotations are in incompatible units — some metric, some stereo disparity, some structure from motion — by using a loss invariant to scale and shift. Giving up on the unknowable is what let the data be pooled.

Genuine resolution comes from adding information: a second camera at a known baseline, motion between frames, an object of known size, or a sensor that measures distance directly.

Corollary

When a monocular depth model reports metres, ask what fixed the scale. If the answer is the training set, the number is a prediction about how similar your scene is to that dataset, and it will be wrong in exactly the way that assumption is wrong.