Recover metric scale and triangulate

Level: Compose · Input: accepted pose direction and bearing matches

Calibrated two-view geometry cannot recover translation magnitude by itself. Choose and record a metric source before calling the result metric:

• a calibrated physical baseline;

• surveyed camera centres;

• a known camera/tripod height with an observable floor;

• another independently measured scene constraint.

If t = s * t_direction, every triangulated point and stereo range scales by the same s. A unit translation therefore produces baseline-normalized, not metric, structure.

Use only accepted matches with adequate parallax. Retain angular reprojection residual, cheirality and conditioning with every sparse point; these refined tracks are the useful bridge to multiview reconstruction and semantic association.

Scale propagation

Let the estimator return $\hat{t}$ with unit norm and let an external measurement provide baseline $s$. Then $t=s\hat{t}$. Triangulation solves depths $\rho_a,\rho_b$ such that

$$\rho_b b_b = R(\rho_a b_a) + t.$$

Multiplying $s$ by a factor multiplies both depths and every reconstructed coordinate by the same factor. A later algorithm cannot infer the missing unit from those points alone.

Sparse-point acceptance

For every triangulated correspondence, require positive depth in both views, sufficient parallax, a finite condition measure and a bounded angular reprojection residual. Keep rejected tracks with their reason when auditing a pipeline, but do not use them as precise anchors for semantic association.

A known-height floor constraint can estimate scale only when the floor model, camera height and corresponding bearings are independently justified. It is not a generic substitute for a measured baseline.

See the scale, floor-intersection and triangulation stages in two-view geometry. Then continue to dense spherical stereo.