rustcpd

Coherent Point Drift point-set registration — rigid, affine, deformable, constrained deformable, and statistical-shape-model/atlas — powered by a fast, deterministic, pure-Rust core (no BLAS, no compiled dependencies at install time: wheels ship for Linux, macOS, and Windows, CPython ≥ 3.9).

pip install rustcpd

import numpy as np
import rustcpd as cpd

# Rigid: recover the similarity transform mapping source onto target.
result = cpd.register_rigid(target, source)          # (N,3)/(M,3) arrays
aligned = result.points                              # (M, 3)
R, t, s = result.rotation, result.translation, result.scale

# Deformable with landmark constraints and an exact full-rank solve.
result = cpd.register_deformable(
    target, source,
    alpha=2.0, beta=2.0, low_rank=None,
    constraints=[(0, 0), (25, 25)],
)

# Large clouds: rank-300 kernel via pivoted Cholesky (much cheaper to
# build than the default "eigen" method as the source grows).
result = cpd.register_deformable(
    target, source, low_rank=300, low_rank_method="pivoted_cholesky",
)

# Statistical shape model (atlas): modes is (M*3, rank), point-major.
result = cpd.register_atlas(target, mean, modes, eigenvalues)
b = result.coefficients
posed = result.scale * (mean @ result.rotation) + result.translation

# Global pose search for atlas initialization (3-D).
init = cpd.pose_initialize(source, target, modes, eigenvalues)

After a deformable fit, apply the learned continuous warp to points it was never trained on — drive a dense mesh from a coarse registration, or move landmarks:

fit = cpd.register_deformable(target_subsample, source_subsample, beta=2.0)
warped_full = fit.transform(full_resolution_points)   # any (P, D) array

Read off soft correspondences from any registration — the best target match per source point and its confidence, plus the full posterior:

match = cpd.correspondences(target, result.points, result.sigma2)
match.matches        # (M,) best target index per source point
match.probability    # (M,) confidence in [0, 1]
match.posterior      # (M, N) full soft assignment matrix

Complete a partial shape and get per-point uncertainty. The atlas is a linear-Gaussian shape model, so a partial observation yields a closed-form posterior over its coefficients:

fit  = cpd.register_atlas(partial_target, mean, modes, eigenvalues)
post = fit.posterior(partial_target, mean, modes, eigenvalues, completeness=0.55)
completed  = post.predict()               # (M, D) filled-in shape
confidence = post.predictive_variance()   # (M,) per-point uncertainty
ensemble   = post.sample_shapes(200, seed=0)   # plausible completions

Visibility is inferred from the fitted correspondence; the optional completeness ∈ (0, 1] anchors it (roughly what fraction of the object was observed). Calibrate the uncertainty to nominal coverage with the rustcpd.calibration submodule (split-conformal). None of this touches the complete-data registration paths.

Shared keyword arguments on every registration: sigma2 (initial variance; estimated when omitted), max_iterations (default 100), tolerance, outlier_weight (uniform-outlier mixture weight in [0, 1)), k (k-nearest-neighbor sparse E-step; None = exact), parallel (default True; results are bitwise-identical to serial execution), and single_precision (opt-in f32 E-step, ~1e-7 accuracy, faster on large 2-D/3-D clouds).

Two more on rigid, affine, and deformable (atlas already had the first): normalize=True conditions the fit in an internal unit-scale frame and maps the result back to your coordinates — recommended for clouds in large physical units, where the absolute beta/sigma2 defaults would otherwise be mis-scaled. callback= is a per-iteration hook receiving {"iteration", "sigma2", "difference", "points"}; return False to stop early, True or None to continue:

result = cpd.register_deformable(
    target, source, normalize=True,
    callback=lambda s: s["sigma2"] > 1e-8,   # custom stopping rule
)

The heavy lifting happens in Rust with the GIL released, so other Python threads keep running. Invalid inputs raise ValueError. Bundled type stubs give editors and type checkers full signatures.

Parameter-selection guidance: see docs/TUNING.md in the repository.

Source, benchmarks, and the Rust API: see the repository.

License: BSD 2-Clause.

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Newer release available (4.0.0)

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Author: Arthur Porto

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BSD-2-Clause
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Requires

Python >=3.9

Tags

point-cloud registration cpd rustcpd alignment

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