reprojection_error — 3D pose_estimation op

• Data kinds: points × keypoints → measurement

• Call: import fullseye as fs; fs.ledger.reprojection_error(points_3d, points_2d, K, R, t) (to call the implementation directly, import pnp3d; pnp3d.reprojection_error(points_3d, points_2d, K, R, t); from the registry, ops3d.get("reprojection_error"))

Usage

Reprojection error (RMS pixels). For judging how well a pose fits. → scalar.

Raises ValueError: points_2d is not (N,2) / point counts mismatch / non-finite.

Computation: projects each 3D point with x = K (R X + t), takes u = x0/x2, v = x1/x2, and returns the RMS sqrt(mean(d_i²)) of the Euclidean distances d_i [px] to the observed 2D points.

• points_3d (N,3), points_2d (N,2) (pixel coordinates, same convention as project_points), K (3,3), R (3,3), t (3,). R, t map world → camera (Xc = R X + t).

• Points with negative depth x2 (behind the camera) are also divided and projected as they are, so with a wrong pose, points flipped front-to-back can appear "close". x2 = 0 gives inf/NaN from the division and is not checked.

• The unit is pixels. If the correspondences are correct and K matches, it is on the order of pixel noise (sub-pixel).

• Typical: evaluate the result of dlt_pose / pnp_ransac. info["rms"] of pnp_ransac is the same quantity (over the inlier set). Compare with a GT pose using pose_error.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• pnp_pose_outliers — py -3.11 examples_3d/pnp_pose_outliers.py

• pose_estimation — py -3.11 examples_3d/pose_estimation.py

Ops the type connects to (they accept measurement as input)

vol_gaussian_psf · fuse_to_voxel · fresnel_reflectance · snell_angle

Same category (pose_estimation)

dlt_pose · pnp_ransac


*Provenance: pnp3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.