register_cpd_rigid — 3D `deform` op

• Data kinds: points × points → pose

• Call: import fullseye as fs; fs.ledger.register_cpd_rigid(src, dst, iters=50, w=0.0, tol=1e-08) (to call the implementation directly, import deform3d; deform3d.register_cpd_rigid(src, dst, iters=50, w=0.0, tol=1e-08); from the registry, ops3d.get("register_cpd_rigid"))

Usage

EM-estimate rotation and translation with the rigid version of Coherent Point Drift (CPD).

Aligns src (moving Y, M points) to dst (fixed X, N points) by a rigid transform. CPD regards dst in terms of an isotropic Gaussian mixture whose centroids are placed at src; the E step updates the soft correspondences (posterior), and the M step updates the maximum-likelihood rigid transform and variance. Unlike ICP, correspondences are not decided hard, so it is robust to initial misalignment and partial outliers. Scale is fixed at 1 (pure rigid).

Reference: Myronenko & Song, "Point Set Registration: Coherent Point Drift", 2010.

Args:

src: (M,3) moving point cloud.

dst: (N,3) fixed point cloud.

iters: maximum number of EM iterations.

w: outlier (uniform distribution) mixing ratio 0≤w<1. 0 means no outliers.

tol: stop as converged when the relative change of the variance σ² is below this value.

Returns:

R: (3,3) rotation (dst ≈ src @ R.T + t).

t: (3,) translation.

info: dict. "sigma2" (final variance), "iters", "converged", "rmse"

(nearest-neighbour RMSE of the transformed src).

Raises:

ValueError: invalid shape, too few points, w out of range, or N*M exceeding

CPD_MAX_PAIRS (25M) (because a dense (N,M) responsibility matrix is built every iteration;

decimate both point clouds before passing them).

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)

• motion_scene — py -3.11 examples_3d/motion_scene.py

Ops the type connects to (they accept `pose` as input)

fuse_to_voxel · pose_error · bundle_adjust · mean_reprojection_error · optimize_pose_graph · relative_pose · mean_edge_error · rotation_translation_error

Same category (`deform`)

tps_fit · tps_warp · register_nonrigid

*Provenance: deform3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

register_cpd_rigid — 3D deform op