Monocular Depth Estimation — From Relative Order to Metric Distance

Monocular depth estimation predicts a per-pixel distance from one RGB image. A single image does not uniquely distinguish a small nearby object from a large distant one with the same apparent size. Therefore the first question is whether a model predicts relative depth—front-to-back ordering—or metric depth with a physical unit such as metres.

In brief

• A monocular image generally does not determine absolute scale. Relative depth describes ordering and shape; metric depth aims at unit-bearing distance.
• Even a model that outputs metric depth can show scale drift or local failures outside the camera, scene, and training distribution it learned from.
• An image without ground truth cannot establish depth accuracy. Separate depth error, relative ordering, occlusion boundaries, and whether scale alignment was used.

Why the image does not fix scale

For a pinhole camera, a 3D point (X,Y,Z) projects approximately as u=fX/Z, v=fY/Z. Scaling all coordinates and depth by the same factor leaves the image position unchanged. This is monocular scale ambiguity. A depth model resolves it statistically using object size, perspective, shading, texture, and learned scene priors.

Diagram 1 · Use the button to switch views

If a model output \hat D is only relative, evaluation may align it with a\hat D+b. A low post-alignment error does not prove that the model can directly recover metres. Never mix unaligned metric evaluation with aligned relative evaluation.

Separate the output types

When metric depth drives an obstacle distance or dimension, fix the domain ground truth, sensor synchronization, camera intrinsics, valid range, and invalid-value policy. A model name or plausible-looking image does not establish real-world accuracy.

A minimal evaluation protocol

Compare ground-truth depth D and prediction \hat D over the same valid-pixel set. Common measures include absolute relative error \mathrm{AbsRel}=\mathrm{mean}(|\hat D-D|/D), RMSE, and threshold accuracy \delta. Record invalid pixels, occlusion handling, excluded far ranges, and the number of valid pixels.

For a relative model, state whether scale alignment is estimated separately for every test image or fixed from training data. Per-image alignment is useful for comparing relative shape, but it can hide the model's inability to recover a stable physical scale.

Common failure conditions

• Mirrors, transparent objects, sky, and textureless walls provide few reliable visual cues.
• Unfamiliar lighting, cameras, regions, objects, or fields of view can break scale and boundaries.
• Thin structures and occlusion boundaries can contain safety-critical local errors despite a low average metric.
• Video predictions can flicker from frame to frame. Single-image metrics do not guarantee temporal stability.

Summary

Monocular depth is an inference problem that combines image evidence with visual priors; it is not simply a distance sensor in software. Separate relative depth, metric depth, and scale alignment, and record ground-truth and valid-pixel conditions before comparing results. A model-specific Lab should wait until licensed inputs, fixed versions, reference depth, and hardware conditions are available.

References

• Eigen et al., Depth Map Prediction from a Single Image using a Multi-Scale Deep Network
• Ranftl et al., Vision Transformers for Dense Prediction