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PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration

Abolfazl Babanazari, Carson Cramer, Tyler Summers, Carlos Nieto, Kaveh Fathian

arXiv:2609.25375v2cs.ROcs.CV

TL;DR

PARTE tackles ambiguous point correspondences in planar scenes by using planar patches as complementary registration evidence. It represents patch context with PCH and jointly processes plane and point matches; across the evaluated benchmarks, it reports the highest mean success rate on the four principal robotics benchmarks while maintaining low runtime.

  • Problem

    Planar regions produce ambiguous point matches, and existing strategies that suppress or discard them also discard useful structural cues.

    Source: §I · p. 2

  • Method

    PARTE describes planar patches with PCH and jointly processes plane and point correspondences for outlier rejection and rigid-transformation estimation.

    Source: §I · p. 2

  • Results

    PARTE achieves the highest mean success rate across the four principal robotics benchmarks while maintaining low end-to-end runtime, and the highest overall success rate on ETH and partial-to-full RESSO.

    Source: §I · p. 2

  • Takeaways & Limitations

    When useful plane correspondences are unavailable, PARTE naturally reduces to point-only registration.

    Source: §VI · p. 13

    PCH is sensitive to changes in geometry and density around a plane, including context changes in partial-to-full registration and large LiDAR density variations.

    Source: D. Limitations · p. 13

Abstract

from arXiv · show

Global point-cloud registration remains challenging when limited overlap, repetitive geometry, and sensor noise produce correspondence sets dominated by outliers. Planar regions are particularly difficult for conventional point descriptors and are therefore often suppressed or discarded before matching. We present PARTE (Plane-Assisted Robust Transformation Estimation), a global registration method that instead treats planar structure as complementary registration evidence. PARTE extracts planar patches and represents them using our novel Plane Context Histogram (PCH), a descriptor that encodes the geometry surrounding each patch, while a two-level matching procedure identifies reliable plane correspondences. Candidate point and plane correspondences are combined in a confidence-weighted compatibility graph for joint outlier rejection, followed by rigid transformation estimation. When no usable plane correspondences are available, PARTE naturally reduces to point-only registration. We evaluate PARTE on 8,097 registration pairs across six indoor and outdoor benchmarks spanning dense RGB-D and sparse LiDAR measurements. Evaluations show PARTE achieves the highest overall success rate against 13 standard and state-of-the-art methods while maintaining low runtime. An open-source C++ implementation with Python bindings is provided at https://ariarobotics.github.io/parte/.

I. INTRODUCTION

PARTE addresses ambiguous point matches in planar, noisy, or limited-overlap scenes by using planar patches alongside point correspondences. It introduces PCH and joint point–plane outlier rejection, and reports the highest mean success rate on four principal benchmarks while maintaining low runtime.

I. INTRODUCTION

  • Planar points can make point-based matches ambiguous, yet discarding them also removes structural cues and can leave too few neighbors for reliable descriptors.PARTE’s premise is that a planar patch can itself provide a distinctive feature and constrain relative pose.Source: §I · p. 2
  • PCH describes each planar patch through surrounding scene geometry, and a two-level matching procedure establishes plane correspondences for joint processing with point matches.Planar patches are extracted while remaining points are matched with conventional point features; plane matches receive confidence weights in graph-based outlier rejection.Source: §I · p. 2
  • PARTE achieves the highest mean success rate across four principal robotics benchmarks and the highest overall success rate on ETH and partial-to-full RESSO.The evaluation covers 8,097 registration pairs across six benchmarks spanning dense RGB-D and sparse LiDAR measurements.Source: §I · p. 2
  • PARTE combines point and planar-patch correspondences in graph-based outlier rejection and rigid-transformation estimation.Its contributions also include geometry-dependent compatibility constraints that account for uncertainty in extracted planes.Source: §I · p. 2

II. RELATED WORK

  • Earlier approaches suppress planar or low-curvature regions to reduce ambiguous matches, whereas PARTE uses planar patches as complementary registration evidence.Related approaches also use geometric primitives or richer plane representations, but PCH describes each patch using surrounding geometry.Source: §II · pp. 2–3

III. NOTATION

This section establishes notation for set cardinality and norms, source and target quantities, correspondence indexing, and symmetric-matrix eigenvalues and eigenvectors.

III. NOTATION

  • For a finite set X, |X| denotes its cardinality, and the section defines ℓ1, ℓ2, and χ2 distance notation.The supplied notation passages also identify source and target quantities with superscripts P and Q and index matched point and plane features by correspondence.Source: §III · pp. 3–4
  • Matched point and plane features are reindexed by correspondence, with (pi, qi) denoting the ith point correspondence and (πPj, πQj) the jth plane correspondence.Superscripts P and Q identify quantities associated with the source and target point clouds.Source: §III · pp. 3–4
  • For a symmetric 3×3 matrix, λi(A) and vi(A) denote its eigenvalues and corresponding unit eigenvectors, ordered by eigenvalue.The accompanying equation gives the descending eigenvalue ordering and eigenvector relation.Source: §III · p. 4

IV. PROPOSED APPROACH

PARTE combines planar patches and non-planar point features for joint registration. Its preprocessing downsamples the clouds, estimates normals, and grows planar patches using tests that account for both point-to-plane fit and normal agreement.

IV. PROPOSED APPROACH

  • PARTE uses planar patches alongside point features in a joint registration pipeline, reducing to point-only registration when suitable planes are unavailable.The pipeline includes feature extraction, matching, outlier rejection, and transformation estimation.Source: §IV · p. 4

A. Preprocessing and Feature Extraction

  • Downsampling, normal estimation, and planar-patch segmentation prepare the planar patches and remaining points for later joint registration.Voxel downsampling replaces points in each occupied voxel with their centroid; normals are estimated from local PCA.Source: A. Preprocessing and Feature Extraction · p. 4
  • Region growing initializes patches from locally planar neighborhoods, merges neighboring patches when their union remains planar, and discards patches below the minimum support.Patch statistics are updated from constituent patches during merging.Source: A. Preprocessing and Feature Extraction · pp. 4–5
  • Patch planarity is checked using both mean squared point-to-plane distance and disagreement between the patch normal and support-point normals.The normal choice must satisfy both conditions; the covariance-based and normal-based estimates can each fail one of them alone.Source: A. Preprocessing and Feature Extraction · p. 5, Figure 3 · p. 5

B. Descriptor generation and matching

PARTE computes point descriptors on non-planar points while retaining planar points as neighborhood context, and represents planar patches with PCH descriptors. Plane matching first groups coplanar patches, then refines ambiguous matches within groups.

Point descriptor and matching

  • FPFH descriptors are computed at non-planar points, while planar points remain in the neighborhoods used to compute those descriptors.Point matches are mutual nearest neighbors under the ℓ2 distance.Source: B. Descriptor generation and matching · p. 5

Plane descriptor and matching

  • PCH encodes nearby points by signed distance to a patch plane and normal agreement, accumulating them into a normalized 192-dimensional histogram.The histogram uses 16 distance bins and 12 normal-agreement bins.Source: B. Descriptor generation and matching · p. 6, Figure 5 · p. 6
  • Disconnected patches on the same plane are grouped into a plane-level descriptor and matched across clouds using mutual nearest neighbors under χ2-distance.When a match contains multiple coplanar patches, localized PCHs are rematched within the groups using oriented bounding boxes.Source: B. Descriptor generation and matching · p. 6
  • For ambiguous plane matches, oriented bounding boxes restrict each patch's PCH support before a second matching stage distinguishes patches within the matched group.Direct and refined matches form the candidate plane-correspondence set.Source: B. Descriptor generation and matching · p. 6

Descriptor confidence

  • Plane-match confidence reflects how much closer the selected descriptor match is than the next-best alternatives, approaching zero when either patch is ambiguous.This score later weights plane correspondences during graph-based outlier rejection.Source: B. Descriptor generation and matching · p. 6

C. Outlier Rejection

PARTE rejects candidate point and plane matches by finding a mutually consistent subset in a compatibility graph. It uses point–point, plane–plane, and plane–point geometric tests, then selects a maximum-weight clique that accounts for plane-match confidence.

C. Outlier Rejection

  • Plane–point consistency thresholds account for normal uncertainty, with the bound increasing for points farther from the plane centroid.This accommodates the larger effect of normal uncertainty at greater centroid distances.Source: C. Outlier Rejection · p. 7
  • A compatibility graph connects candidate point or plane correspondences when they satisfy the applicable pairwise consistency test, so each clique is mutually consistent.The tests use preserved point distances, angles between plane normals, and signed point-to-plane distances.Source: C. Outlier Rejection · pp. 6–7
  • The method selects a maximum-weight clique, assigning unit weights to point matches and confidence-derived weights to plane matches.This favors distinctive plane matches without relaxing geometric consistency tests; the cited example contrasts it with a larger, incorrect clique chosen by cardinality.Source: C. Outlier Rejection · p. 7

D. Transformation Estimation

PARTE estimates a rigid transformation from retained point and plane correspondences by jointly fitting points and aligning plane normals and offsets. Block Coordinate Descent alternates rotation and translation updates, initialized with an extended Arun rotation estimate.

D. Transformation Estimation

  • The transformation objective minimizes point distances and aligns corresponding plane normals and translated offsets, weighting each plane correspondence by its confidence.The retained mixed correspondences are used for this joint estimate.Source: D. Transformation Estimation · p. 7
  • Block Coordinate Descent alternates rotation and translation updates because the joint problem does not have a straightforward simultaneous solution.Each update optimizes one variable while fixing the other, so the objective cannot increase between iterations.Source: D. Transformation Estimation · pp. 7–8
  • Initialization sets translation to the centroid of matched target points, yielding an extended Arun rotation estimate that also uses matched plane normals.Subsequent BCD updates refine the transformation.Source: D. Transformation Estimation · p. 8
  • The alignment illustration contrasts the initial mismatch, the first rotation update with fixed translation, and the final result after full nonlinear BCD optimization.The first rotation update is equivalent to the classical Arun rotation estimate.Source: Figure 8 · p. 8

V. EXPERIMENTAL EVALUATION

The evaluation proceeds from direct plane-descriptor and matching assessment to complete registration benchmarks, then examines design choices and runtime. Its datasets and protocols are summarized in Table II.

V. EXPERIMENTAL EVALUATION

  • The evaluation covers plane matching, complete registration across indoor RGB-D, outdoor LiDAR, and partial-to-full tasks, then ablations and runtime analysis.Table II reports dataset protocols and average point and plane counts per unique scan after voxel downsampling.Source: §V · p. 8, Table II · p. 8
  • Ablation studies examine planar-patch extraction and plane-weight selection, alongside analysis of complete-pipeline runtime.The ablations are presented in Appendices A and B.Source: §V · p. 8

A. Experimental Setup

The experiments use established registration benchmarks spanning indoor RGB-D, outdoor LiDAR, terrestrial LiDAR, and partial-to-full scans. They report descriptor and registration metrics under stated comparison and implementation protocols.

A. Experimental Setup

  • The benchmark set includes 3DMatch and lower-overlap 3DLoMatch, two KITTI protocols, ETH terrestrial LiDAR, and partial-to-full RESSO scans.3DMatch pairs have at least 30% overlap; 3DLoMatch pairs have 10–30% overlap.Source: A. Experimental Setup · p. 8
  • PCH is compared with geometric, local, global, and segment-level plane descriptors, while registration comparisons span classical, robust, geometry-based, plane-based, and learning-based methods.The plane baselines include patch area and perimeter; the registration baselines include RANSAC, FGR, TEASER++, MAC, CLIPPER+, QUATRO, G3Reg, PLADE, VPFBR, PREDATOR, PointDSC, and VBReg.Source: A. Experimental Setup · p. 8
  • Plane matching is evaluated by F1, average precision, and true-positive correspondences per pair; registration uses success rate, average rotation and translation errors, and runtime.Success rate counts pairs meeting dataset-specific rotation- and translation-error criteria.Source: A. Experimental Setup · p. 9
  • Most geometric parameters are fixed across experiments or scaled by voxel size, including plane extraction, FPFH and PCH neighborhoods, and outlier-rejection tolerances.PCH uses a radius of 20v; the stated base spatial and angular tolerances are v and 5°.Source: A. Experimental Setup · p. 9

B. Plane Descriptor Evaluation

PCH distinguishes planar patches using surrounding scene geometry, and the two-level matcher improves plane-correspondence performance over competing descriptors. Its confidence also tracks the likelihood that a plane match is correct.

B. Plane Descriptor Evaluation

  • Plane correspondences are established by mutual nearest-neighbor matching, with descriptor-specific distance measures selected for the highest overall MNN F1 across datasets.The evaluation tests multiple reasonable distance choices for applicable descriptors.Source: B. Plane Descriptor Evaluation · p. 9
  • PCH-2L outperforms competing descriptors across most datasets, with especially large gains on 3DLoMatch and both KITTI benchmarks.The full two-level matcher further improves on the one-level PCH matcher.Source: B. Plane Descriptor Evaluation · p. 9
  • PCH describes each plane using surrounding scene geometry rather than the patch alone, providing a more distinctive cue where patch shape or extent is weak.Descriptors are compared on the same extracted planar patches; PCH additionally uses surrounding geometry.Source: B. Plane Descriptor Evaluation · p. 9
  • On 3DMatch and KITTI-LC, PCH remains above competing precision–recall curves throughout the plotted recall range.The figure also plots descriptor-match confidence against empirical inlier ratio.Source: B. Plane Descriptor Evaluation · p. 9
  • For PCH on both datasets, higher confidence corresponds to a strongly increasing empirical inlier ratio, making confidence a basis for weighting plane matches.The highest-confidence correspondences are correct in the large majority of cases.Source: B. Plane Descriptor Evaluation · p. 9

C. Global Registration Performance

PARTE achieves the highest mean success rate across the four principal benchmarks while maintaining low runtime, and leads overall on ETH and partial-to-full RESSO. Performance varies with correspondence quality, displacement, and the availability of reliable plane context.

C. Global Registration Performance

  • PARTE records 89.6% success on 3DMatch and 55.8% on 3DLoMatch, ranking second only to PREDATOR on both benchmarks.It has the lowest rotation error on both and the lowest translation error on 3DMatch; 3DLoMatch is especially difficult because of low overlap.Source: C. Global Registration Performance · p. 10, Table V · p. 11
  • PARTE achieves the highest success rate with both FPFH variants and remains the highest-performing non-learned method with MNN-matched FCGF, while MAC leads geometric methods with 1,000 FCGF matches.Consistently camera-oriented normals improve FPFH matching; the larger FCGF set contains more competing mutually consistent structures.Source: C. Global Registration Performance · p. 10, Table VI · p. 11
  • On KITTI-10m, PARTE matches PREDATOR for the highest overall success rate at 99.8%, a benchmark the authors describe as largely saturated.G3Reg also performs strongly at 99.1%.Source: Table VII · p. 11, C. Global Registration Performance · p. 11
  • KITTI-LC success rates decrease substantially with displacement; at 20–30 m, G3Reg leads on four of five sequences.The evaluation separates results into 0–10 m, 10–20 m, and 20–30 m translation ranges.Source: C. Global Registration Performance · p. 11, Table VIII · p. 12
  • On ETH, PARTE recovers 40 of the 43 registrations missed by TEASER++, with plane correspondences participating in 39 recoveries, all involving the ground plane.TEASER++ success rises from 72.7% to 94.0% with consistently oriented FPFH normals; a single reliable plane can complement insufficient point correspondences.Source: C. Global Registration Performance · p. 12
  • PARTE has the highest overall RESSO success rate at 59.6%, ahead of CLIPPER+ at 58.6%; changing scan context reduces PCH's discriminative advantage.PARTE fails on 40 of 99 registrations, 28 of which every other method also misses; incorrect plane matches can bias the selected clique toward outliers.Source: C. Global Registration Performance · pp. 11–12, Table IX · p. 12
  • On Gazebo Winter, PARTE recovers 95 of 96 registrations missed by QUATRO, using the matched ground plane in the compatibility graph to filter inconsistent point matches before pose estimation.The relative motion has a maximum tilt of 5.48°; the plane supplies evidence during correspondence selection, not only a final pose constraint.Source: C. Global Registration Performance · pp. 12–13
  • Across the four main benchmarks, PARTE achieves the highest mean success rate while maintaining low runtime, showing consistently strong performance on both indoor and outdoor registration problems.Source: C. Global Registration Performance · p. 13

D. Limitations

PARTE combines point and planar-patch evidence and achieves the best overall success rate among evaluated methods. Its performance depends on useful planes and surrounding geometry, while point matching remains a computational bottleneck.

D. Limitations

  • Reliable plane correspondences can improve registration particularly when point correspondences contain few inliers, but PARTE approaches point-only behavior when few useful planes are available.The conventional point-matching stage remains the main computational bottleneck.Source: D. Limitations · p. 13
  • Changes in geometry or density around a plane can reduce PCH effectiveness, including partial-to-full registration shifts and large LiDAR density variations.Source: D. Limitations · p. 13

VI. CONCLUSION

  • Across diverse indoor RGB-D and outdoor LiDAR benchmarks, PARTE achieves the best overall success rate among evaluated methods.Fig. 10 reports mean success rate and runtime across four benchmarks, weighted equally.Source: §VI · p. 13, Figure 10 · p. 13

APPENDIX A ABLATION STUDIES

The ablations examine conservative plane extraction, plane-match weighting, and runtime. They report strong extraction-backend performance, more robust clique selection with PCH-confidence weighting, and a runtime bottleneck that remains in point matching.

APPENDIX A ABLATION STUDIES

  • Initialization excludes approximately 40% of 3DMatch, 50% of KITTI-10m, and 65% of ETH points from region growing; FPFH inlier ratios generally rise with normal dispersion.Rejected points remain available as point features, and the 12° threshold helps preserve distinctive regions while reducing region-growing work.Source: Appendix A · p. 15, Figure 12 · p. 16, Figure 11 · p. 16
  • PARTE provides the strongest registration performance while remaining faster than most reliable segmentation baselines.The reported PARTE segmentation time includes KNN construction, although those neighborhoods are reused elsewhere in the pipeline.Source: Appendix A · p. 15, Table XI · p. 15

(a) PCL RANSAC [43]

  • PCH-confidence weighting is considerably less sensitive to the plane-weight multiplier than fixed weighting, maintaining strong performance over a broader range.The weights affect plane correspondences during clique selection relative to unit-weight point matches.Source: (a) PCL RANSAC [43] · p. 16, Figure 13 · p. 16

APPENDIX B RUNTIME ANALYSIS

  • Separating and matching planar patches can reduce total runtime by lowering point-descriptor, matching, and outlier-rejection costs, though point matching remains the main bottleneck.The comparison covers 3DMatch and KITTI-10m under multithreaded and sequential execution.Source: Appendix B · p. 16, Figure 14 · p. 16

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