rmse_correspondence — 3D metrics op

• Data kinds: points × points → measurement

• Call: import fullseye as fs; fs.ledger.rmse_correspondence(a, b) (to call the implementation directly, import metrics3d; metrics3d.rmse_correspondence(a, b); from the registry, ops3d.get("rmse_correspondence"))

Usage

RMSE over known correspondences (same index) = sqrt(mean |a_i − b_i|²). → scalar. For judging the registration residual.

Computation: convert a, b to float arrays, average the per-row Euclidean distance to the power 2 sum((a - b)**2, axis=1) and take the square root. No nearest-neighbour search is done — the caller guarantees that a[i] and b[i] correspond to the same point (e.g. src @ R.T + t transformed by registration and the corresponding dst point list, or the GT correspondence of synthetic data).

Arguments and validation: ValueError if a.shape != b.shape. There is no other check:

two empty (0, 3) arrays give a NaN (with a warning) because mean is empty, and shapes other than (N, 3) still return a value if they can be summed with axis=1. Pass 3-column point clouds.

Returns: Python float, unit = the coordinate unit, [0, inf). 0 if identical.

Note: used on clouds whose correspondence is off (index reordered), it gives a large value even if the pose is correct. If the correspondence is unknown use chamfer_distance / fscore; to compare the pose itself with GT use pose_error.

Background guides (the physics and conventions behind this op)

• blender_interop — Using Blender alongside — build the shape, measure it with fullseye (pitfalls: axes, units, ground truth)

• measurement_uncertainty — Measurement uncertainty and calibration — what it takes to claim you are measuring

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)

• metrics_eval — py -3.11 examples_3d/metrics_eval.py

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

vol_gaussian_psf · fuse_to_voxel · fresnel_reflectance · snell_angle

Same category (metrics)

chamfer_distance · hausdorff_distance · m3c2_distance · fscore · normal_consistency · voxel_iou · pose_error


*Provenance: metrics3d.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.