One viewpoint
A single image has no depth in it
This is a working excavation: a terraced pit, haul vehicles on the benches, and spoil heaps built up outside the workings. You can see it is a pit because you already know what pits look like, and because the shadows fall in a way your eye reads as depth.
The sensor has none of that. From one viewpoint every point on the ground is a single brightness and nothing in the file says how far away it was. The picture could as easily be painted on a flat sheet.
Two viewpoints, one pass
Move sideways and things shift by different amounts
Now the sensor moves along its track and looks at the same ground from a second position. Everything in the frame appears to slide, but not equally: the pit floor and the tops of the spoil heaps travel one way relative to the ground around them, and the flat land at the edges barely moves at all.
That difference is called parallax, and it is not a nuisance to be corrected. It is the entire signal. How far a point appears to shift between two known viewpoints tells you how far away it was, which on a nadir-looking sensor means how high it stands.
From parallax to elevation
Match every point in both images and you have a height model
Do that matching for every point rather than one, and instead of a picture you have a surface: a value in metres for each patch of ground. This is a digital surface model, and it is the actual deliverable behind most of what follows.
Nothing here is interpreted. Two viewpoints, a known separation between them, and triangulation, which is the same geometry a surveyor has used for two centuries.
Two dates
Subtract last year's surface from this year's and you have a volume
Two height models of the same site, months apart, subtracted from each other. Ground that has dropped shows warm, ground that has risen shows cool, and everything untouched sits near neutral. The pit has deepened and widened, and the spoil heaps have grown.
Multiply each pixel's change in height by the ground it covers and add them up. The figures beside the picture are worked out in your browser from the two surfaces, not typed into this page: material out of the pit, material onto the heaps, and the difference between them, which is what left the site.
That third number is usually the interesting one. It is the basis of production reconciliation, and it is measurable from orbit without anyone's cooperation on the ground.
The error bar
What decides whether the number is any good
Three things, mostly. The separation between the two viewpoints, because too narrow a baseline gives you noise and too wide a one makes the two images too dissimilar to match. The texture of the ground, because matching needs something to match and smooth featureless surfaces such as still water or fresh snow defeat it. And the accuracy of the sensor's own position, which sets the floor on everything else.
So a volume from stereo comes with a range, not a single figure, and the honest way to quote it is with that range attached. Anyone handing you a cubic metre count to five significant figures is not telling you how it was made.
