Context without Commitment: Robust Dense Correspondence under Non-Rigid Deformation

Yuzhen He; Sara Homscheid

cs.CVSep 29, 2026

Context without Commitment: Robust Dense Correspondence under Non-Rigid Deformation

Authors: Yuzhen He, Sara Homscheid

Organizations: Mannheim Institute for Intelligent Systems in Medicine (MIISM) Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany

Abstract

Non-rigid point-cloud registration aims to find the corresponding target point for each point on a deforming source surface. Point-level matching keeps the full target cloud available, but correspondence becomes ambiguous when different regions have similar local geometry. Regional or coarse-to-fine methods provide broader spatial context, but an incorrect regional match can exclude the correct correspondence before dense matching. We propose CoCo-Reg, which uses regional patches to enrich dense point features without allowing patch predictions to restrict the final point-level search. CoCo-Reg constructs farthest-point-sampled patches, exchanges geometric information within and between source and target, supervises patch similarity using identity-corrected point overlap, and projects the resulting regional information back to dense point features. The final registration stage still scores the full target cloud before global point-level candidate selection. On 726 held-out ModelNet10 objects across nine deformation levels, two established learning-based baselines obtain mean correspondence errors of 0.1993 and 0.1921, whereas CoCo-Reg obtains 0.0547. Relative to its point-level baseline, this is a 72.6% reduction. CoCo-Reg achieves lower correspondence error on 92.3% of paired test objects and reduces the mean fraction of points with error above 0.1 from 47.3% to 17.3%. Chamfer distance and HD95 decrease in the same direction, and CoCo-Reg remains lower across all tested deformation levels. These results support using regional context for dense non-rigid correspondence without imposing a hard patch-level restriction on the final search. Because evaluation uses one checkpoint per method, the reported gains characterize the complete systems rather than the isolated causal contribution of an individual component. Code will be made publicly available.

Figures & tables

Figure 1: Overview of CoCo-Reg. Top: The proposed method extracts dense point features from the source and target point clouds, constructs geometric patches, and exchanges information between source and target patches through geometry-aware interaction. The resulting patch information is projected back to the dense point features through a residual refinement. Final correspondence estimation is then performed at the point level using the global sLBP search, which scores the complete target cloud before retaining the Top-128 candidates. Bottom: Comparison with hard patch-based matching. In a hard coarse-to-fine strategy, an incorrect patch match can remove the correct point correspondence from the subsequent search. CoCo-Reg instead uses patch information to enrich the point representation without applying a hard patch-level restriction to the final correspondence search.

Method	MCE	Median	P95	Objects with MCE $>0.1$	Points with error $>0.1$ (%)	Chamfer	HD95
Robust-DefReg	$0.1921\pm 0.2001$	0.1188	0.6287	402/726 (55.4%)	$48.4\pm 35.6\%$	$0.0178\pm 0.0100$	$0.1066\pm 0.0608$
DefTransNet	$0.1993\pm 0.2165$	0.1180	0.6865	389/726 (53.6%)	$47.3\pm 35.9\%$	$0.0170\pm 0.0094$	$0.1015\pm 0.0575$
CoCo-Reg	$\mathbf{0.0547\pm 0.0693}$	0.0379	0.1529	90/726 (12.4%)	$\mathbf{17.3\pm 21.1\%}$	$\mathbf{0.0108\pm 0.0061}$	$\mathbf{0.0682\pm 0.0381}$

Table 1: Overall results on 726 held-out objects. Mean-valued quantities are reported as mean

\pm

SD across test objects. Median and P95 are quantiles of the 726 per-object MCE values. “Objects with MCE

>0.1

” reports the number and percentage of test objects whose mean correspondence error exceeds 0.1. “Points with error

>0.1

” reports the mean within-object percentage of points whose identity-specific correspondence error exceeds 0.1. Lower is better for all metrics.

Metric	Mean $\Delta$ [95% CI]	$r_{rb}$	CoCo-Reg win rate [95% CI]	Wilcoxon $p$
MCE	$-0.1447\;[-0.1585,-0.1314]$	0.960	92.3% [90.1, 94.1]	$2.89\times 10^{-111}$
Chamfer	$-0.00623\;[-0.00657,-0.00588]$	0.964	93.1% [91.0, 94.8]	$3.17\times 10^{-112}$
HD95	$-0.03328\;[-0.03569,-0.03096]$	0.934	89.5% [87.1, 91.7]	$1.83\times 10^{-105}$
Point failure rate	$-0.2994\;[-0.3200,-0.2789]$	0.973	88.8% [86.3, 91.0]	$1.10\times 10^{-106}$

Table 2: Paired CoCo-Reg vs. DefTransNet statistics.

\Delta

is CoCo-Reg

-

DefTransNet; negative values favor CoCo-Reg. Mean-difference CIs are 20,000-resample paired bootstrap intervals; win-rate CIs are exact binomial intervals.

r_{rb}

is oriented so positive values favor CoCo-Reg.

Figure 2: Qualitative registration under increasing deformation. Representative source, target, and CoCo-Reg registrations are shown at deformation levels 0.2, 0.5, and 0.8. Colors indicate the identity-specific correspondence error associated with each source-point identity and are propagated across the corresponding source, target, and registered points for spatial comparison.

Level	$N$	Robust-DefReg	DefTransNet	CoCo-Reg	$\Delta$ [95% CI]	Win	Holm $p$
0.1	63	$0.1111\pm 0.1841$	$0.1205\pm 0.2055$	$\mathbf{0.0293\pm 0.0934}$	$-0.0913[-0.1381,-0.0504]$	84.1%	$3.05\times 10^{-9}$
0.2	80	$0.1436\pm 0.2104$	$0.1485\pm 0.2212$	$\mathbf{0.0382\pm 0.0967}$	$-0.1103[-0.1530,-0.0713]$	85.0%	$5.43\times 10^{-11}$
0.3	74	$0.1346\pm 0.2128$	$0.1477\pm 0.2366$	$\mathbf{0.0336\pm 0.0887}$	$-0.1142[-0.1640,-0.0704]$	90.5%	$5.43\times 10^{-11}$
0.4	92	$0.1115\pm 0.1221$	$0.1167\pm 0.1440$	$\mathbf{0.0309\pm 0.0288}$	$-0.0858[-0.1156,-0.0600]$	94.6%	$2.57\times 10^{-14}$
0.5	88	$0.1676\pm 0.1625$	$0.1768\pm 0.1798$	$\mathbf{0.0438\pm 0.0312}$	$-0.1330[-0.1688,-0.1004]$	92.0%	$1.13\times 10^{-14}$
0.6	80	$0.2143\pm 0.1870$	$0.2245\pm 0.2097$	$\mathbf{0.0537\pm 0.0341}$	$-0.1708[-0.2152,-0.1292]$	92.5%	$8.98\times 10^{-14}$

Table 3: Deformation-stratified mean correspondence error (MCE). Means are mean

\pm

SD across objects.

\Delta

is the paired CoCo-Reg

-

DefTransNet mean difference with bootstrap 95% CI; negative values favor CoCo-Reg.

	Chamfer distance (CD)			HD95
Level	Robust	DefTransNet	CoCo-Reg	Robust	DefTransNet	CoCo-Reg
0.1	$0.0097\pm 0.0087$	$0.0093\pm 0.0083$	$\mathbf{0.0056\pm 0.0046}$	$0.0558\pm 0.0485$	$0.0534\pm 0.0457$	$\mathbf{0.0358\pm 0.0293}$
0.2	$0.0114\pm 0.0085$	$0.0113\pm 0.0086$	$\mathbf{0.0066\pm 0.0048}$	$0.0670\pm 0.0508$	$0.0682\pm 0.0541$	$\mathbf{0.0422\pm 0.0308}$
0.3	$0.0112\pm 0.0084$	$0.0108\pm 0.0080$	$\mathbf{0.0069\pm 0.0049}$	$0.0678\pm 0.0494$	$0.0652\pm 0.0463$	$\mathbf{0.0447\pm 0.0313}$
0.4	$0.0146\pm 0.0070$	$0.0139\pm 0.0067$	$\mathbf{0.0084\pm 0.0039}$	$0.0863\pm 0.0398$	$0.0822\pm 0.0380$	$\mathbf{0.0547\pm 0.0239}$
0.5	$0.0178\pm 0.0077$	$0.0170\pm 0.0073$	$\mathbf{0.0105\pm 0.0044}$	$0.1070\pm 0.0440$	$0.1019\pm 0.0431$	$\mathbf{0.0667\pm 0.0260}$

Table 4: Deformation-stratified set-level geometry. Values are mean

\pm

SD across objects. CD is symmetric unsquared Chamfer distance and HD95 is the 95th-percentile bidirectional Hausdorff distance. Lower is better.

Rotation	$N$	Robust-DefReg	DefTransNet	CoCo-Reg	Win vs. Def.
$0$ – $30^{\circ}$	234	$0.0792\pm 0.1018$	$0.0771\pm 0.1030$	$\mathbf{0.0354\pm 0.0465}$	80.3%
$>30$ – $60^{\circ}$	240	$0.1160\pm 0.1101$	$0.1127\pm 0.1112$	$\mathbf{0.0487\pm 0.0547}$	96.7%
$>60^{\circ}$	252	$0.3693\pm 0.2134$	$0.3954\pm 0.2324$	$\mathbf{0.0783\pm 0.0898}$	99.2%

Table 5: Rotation-stratified descriptive analysis of the final test set. Values are MCE

\pm

SD across objects. The last group contains observed rotations above

60^{\circ}

up to

91.7^{\circ}

Category	DefTransNet	CoCo-Reg	$\Delta$ [95% CI] / Win
Bathtub	$0.2807\pm 0.2607$	$\mathbf{0.0863\pm 0.0947}$	$-0.1943[-0.2628,-0.1327]$ / 92.9%
Bed	$0.2334\pm 0.2806$	$\mathbf{0.0518\pm 0.0666}$	$-0.1816[-0.2415,-0.1257]$ / 93.7%
Chair	$0.1785\pm 0.1720$	$\mathbf{0.0457\pm 0.0381}$	$-0.1328[-0.1656,-0.1021]$ / 90.1%
Desk	$0.2502\pm 0.2476$	$\mathbf{0.0620\pm 0.0578}$	$-0.1881[-0.2466,-0.1364]$ / 95.4%
Dresser	$0.2048\pm 0.1943$	$\mathbf{0.0677\pm 0.0951}$	$-0.1371[-0.1784,-0.1002]$ / 94.1%

Table 6: Category-stratified CoCo-Reg vs. DefTransNet MCE. Mean

\pm

SD are across objects;

\Delta

is CoCo-Reg

-

DefTransNet with bootstrap 95% CI. All ten categories are shown.

Explore similar work

DINE: Distance Is Not Enough -- Learning Global Deformation Priors for Robust Soft-Tissue Point Cloud Registration
Jul 16, 2026Sara Monji-Azad, Rohit Beer, Marvin Kinz +2Point Cloud Registration Deformable Cnn
Mannheim Institute for Intelligent Systems in Medicine (MIISM), Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany · Department of Radiation Oncology, Brigham and Women’s Hospital, Dana-Farber Cancer Institute, Harvard Medical School, Boston, Massachusetts, USA · Department of Otorhinolaryngology, Head and Neck Surgery, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany +4
Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy
Jun 26, 2026Rixon Crane, Fahira Afzal Maken, Nicholas Lawrance +4Point Cloud Registration Image Registration
Data61, CSIRO, Brisbane, Australia · Data61, CSIRO, Sydney, Australia · Work done while at Data61, CSIRO, Brisbane, Australia +3
BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration
Sep 10, 2026Qianliang Wu, Haobo Jiang, Guangwei Gao +5Point Cloud Registration Image Registration
Nantong University · Nanyang Technological University · Nanjing University of Science and Technology +2

Jul 16, 2026, cs.CVJ/K move · Enter open · S save

DINE: Distance Is Not Enough -- Learning Global Deformation Priors for Robust Soft-Tissue Point Cloud Registration

Sara Monji-Azad, Rohit Beer, Marvin Kinz, Claudia Scherl+1

Mannheim Institute for Intelligent Systems in Medicine (MIISM), Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany · Department of Radiation Oncology, Brigham and Women’s Hospital, Dana-Farber Cancer Institute, Harvard Medical School, Boston, Massachusetts, USA · Department of Otorhinolaryngology, Head and Neck Surgery, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany+4

Point Cloud Registration Deformable Cnn Deformation Point Clouds Distance Principal Component Analysis

Open paper AskPDF arXiv

Non-rigid point cloud registration is central to soft-tissue shape analysis, but large deformations, noise, and outliers make correspondence estimation challenging. Most learning-based methods rely on local objectives such as Chamfer distance, which encourage point-wise proximity but do not constrain the global plausibility of the predicted deformation field. We address this limitation with DINE, a maximum a posteriori framework that augments distance-based registration with a learned statistical prior over displacement vector fields. DINE is applied to two registration backbones, Robust-DefReg and DefTransNet, using a two-stage strategy: a first-stage model is trained with Chamfer distance, its predicted deformation fields are used to estimate a prior, and the model is then refined with a combined distance and negative log-prior objective. We compare a full-field PCA Gaussian prior with a per-vector normalizing-flow prior. Experiments on DeformedTissue and SynBench show lower mean Chamfer distance under deformation and corruption. On DeformedTissue, DINE-PCA reduces Chamfer distance by approximately 27--69% relative to the corresponding Stage-1 backbone across deformation levels, and improves robustness by up to 66% for outliers and 83% for Gaussian noise. On SynBench, improvements are modest at the smallest deformation levels and reach approximately 59--79% from moderate to severe deformation. These results suggest that global deformation plausibility is an important constraint for reliable soft-tissue point cloud registration. (The code will be published soon.)

Abstract

Explore similar work

DINE: Distance Is Not Enough -- Learning Global Deformation Priors for Robust Soft-Tissue Point Cloud Registration

Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration