How photographs become geometry

Triangulation

Photogrammetry works by finding the same physical point in several photographs and intersecting the rays that must have produced it. Seen from above: drag the cameras, and watch how the angle between rays — not the number of photographs — decides how well the point is pinned down.

The capture —

Cameras 8

Arc covered 300°

Match precision 0.12°

Some surfaces are textureless Respect occlusion

Drag any camera in the scene. Match precision is the angular error in locating the same feature in two images — a real pipeline's accuracy is limited by this long before it is limited by pixel count.

Top-down view — drag the cameras —

cameras well-constrained point uncertain point seen by fewer than two cameras — no reconstruction

Points reconstructed

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Best baseline angle

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Median uncertainty

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Surface coverage

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Photographs needed

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Uncertainty against baseline angle why two cameras side by side are nearly useless

Depth uncertainty scales as 1 / sin θ, where θ is the angle between the two rays. At 90° it is at its best. At 5° it is more than ten times worse — the rays are so nearly parallel that a tiny error in matching slides the intersection a long way along the line of sight. This is why photogrammetry guides insist on moving around the subject rather than zooming in on it.

Every reconstructed point needs at least two cameras that can both see it. Drop the arc to 40° and watch the far side of the object go red: those surfaces face away from every camera, so no amount of resolution or processing recovers them. Photogrammetry's first constraint is not algorithmic, it is logistical — you have to walk around the thing.

Texture is not decoration, it is the measurement. Matching means recognising the same physical speck in two photographs. A blank white wall offers nothing to recognise, so every point along it is equally consistent with what the cameras saw and the surface simply fails to reconstruct. This is why scanning rigs project random dot patterns onto featureless objects — they are adding, quite literally, the information the geometry needs.

And this is exactly the gap NeRFs step into. Photogrammetry insists on explicit correspondence: this pixel and that pixel are the same point, therefore the point is here. Where that fails — textureless surfaces, transparency, reflections, fur — there is nothing to triangulate. A neural radiance field never asks the question. It optimises a volume until its rendered images match the photographs, so it can represent whatever reproduces the observations, including things that have no well-defined surface at all.