Learning Where to Trust: Reliability-Guided Expert Routing and Velocity Gating for 3D Deformable Registration

Chenyu Guo; Wenjie Dai; Yiqian Chang; Zhiyuan Zhang; Yunfan Wei; Shuhan Qi

cs.AIOct 27, 2026

Learning Where to Trust: Reliability-Guided Expert Routing and Velocity Gating for 3D Deformable Registration

Authors: Chenyu Guo, Wenjie Dai, Yiqian Chang, Zhiyuan Zhang, Yunfan Wei, Shuhan Qi

Organizations: Harbin Institute of Technology, Shenzhen, Guangdong, China · Peng Cheng Laboratory, Shenzhen, Guangdong, China

Abstract

Deformable image registration relies on accurate anatomical correspondences. However, explicitly coupling local matching reliability with spatial context selection and deformation update strength remains insufficiently explored in learning-based registration. This challenge is particularly pronounced in homogeneous, weakly textured, and severely deformed regions, where ambiguous matches may induce erroneous deformation updates. We propose ReliMorph, a reliability-routed symmetric framework for 3D deformable registration that couples correspondence assessment with spatial context selection and update strength.Local correlation distributions characterize correspondence ambiguity using shared anatomical features with modality-specific adaptation. These reliability cues guide spatial expert fusion and gate residual velocities during coarse-to-fine refinement. Updated inverse-inconsistency feedback guides routing and gating at finer pyramid levels. To our knowledge, ReliMorph is the first 3D deformable registration framework to jointly condition spatial expert routing and residual velocity gating on correspondence reliability. Extensive experiments demonstrate that ReliMorph consistently outperforms competing methods in anatomical overlap, highlighting its effectiveness across unimodal and multimodal registration tasks.

Figures & tables

Figure 1: Motivation and validation of reliability-routed registration. (a) Conventional uniform processing applies identical context modeling and deformation updates despite spatially varying matching ambiguity. (b) In contrast, ReliMorph leverages correspondence statistics and inverse-consistency cues to adaptively route complementary experts and regulate residual updates according to matching reliability.

Figure 2: Overview of ReliMorph. Stage I (shared encoding) extracts multiscale anatomical features using a shared encoder with modality-specific adaptation. Stage II (reliability-routed estimation) uses correspondence and registration-state cues to guide expert fusion and residual-velocity gating at each pyramid level. Stage III (symmetric refinement) integrates gated velocities via scaling and squaring, then composes the resulting residual transformations with the accumulated transformations in both directions. Updated inverse-inconsistency maps feed back to Stage II at the next finer level.

Figure 3: Reliability-conditioned expert routing and velocity modulation. Correspondence and registration-state cues guide voxel-wise fusion of local, axial, and dilated convolutional experts. A confidence-based gate with a positive lower bound scales the residual stationary velocity field decoded from the fused features.

	IXI			OASIS			AbdomMRCT
Method	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	$\mathcal{L}_{\mathrm{MIND\text{-}SSC}}\downarrow$
SyN	0.7460	3.157	0	0.7454	2.350	0	0.8212	8.746	0	0.0894
TransMorph	0.7934	2.257	0.2879	0.7965	2.009	0.7456	0.8798	9.542	20.73	0.0315
CorrMLP	0.8070	2.136	0.4508	0.8017	1.855	0.0115	0.8591	18.517	17.74	0.0412
AC-CAR	0.7857	2.363	0.1860	0.8080	1.895	0.1819	0.8557	13.124	18.02	0.0445
SACB-Net	0.7911	2.327	0.0189	0.8132	1.824	0.6495	0.8588	13.553	4.740	0.0426

Table 1: Registration performance on IXI, OASIS, and AbdomMRCT. HD95 is measured in millimeters. Fold denotes the percentage of voxels with

\det(\nabla\phi)\leq 0

. OASIS results are reported on the labeled validation pairs.

Figure 4: Qualitative comparison of inter-subject brain MRI registration on IXI. For each method, rows show the warped moving image with selected anatomical contours, the signed intensity residual $I_{\mathrm{warp}}-I_{\mathrm{fixed}}$ , the displacement field (RGB encodes $d_{x},d_{y},d_{z}$ ), and the Jacobian determinant $J$ . The panels on the right show the fixed and moving images and their intensity difference before registration. Residual maps share the color scale shown below. In the Jacobian maps, red indicates folding ( $J\leq 0$ ), gray indicates near-unit volume change ( $|J-1|\leq 0.02$ ), green indicates compression, and blue indicates expansion.

Figure 5: Qualitative comparison of deformable registration on OASIS and abdominal images. The first two columns show the moving and fixed images; the remaining columns show results from the compared methods. For OASIS, the top two rows show the warped images and color-coded deformation fields. For the abdominal case, the bottom two rows show the warped images and corresponding propagated segmentation masks.

Figure 6: Comparison of registration accuracy (DSC), inference time, and peak GPU memory usage across methods on the IXI dataset.

Variant	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$
		(mm)	(%)
Full model	0.8093	2.040	0.0032
w/o ambiguity statistics	0.7911	2.317	0.0001
w/o correlation descriptors	0.7875	2.356	0.0001
Uniform expert fusion	0.7907	2.312	0.0001
w/o velocity gating	0.7919	2.314	0.0001

Table 2: Ablation experiments on the IXI dataset for ReliMorph.

	Mean routing weight			$\Delta e$ (pp)
Ambiguity	Local	Axial	Dilated	Local	Axial	Dilated
Low	0.468	0.314	0.218	+1.42	+0.76	+0.38
Medium	0.338	0.369	0.293	+0.85	+1.09	+0.74
High	0.219	0.353	0.428	+0.41	+1.14	+1.56

Table 3: Expert specialization on IXI.

\Delta e

denotes the increase in regional anatomical label disagreement (pp) after suppressing each expert at the finest matching level of the frozen model.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Parameter	IXI/OASIS	AbdomMRCT
$(r_{L},\ldots,r_{1})$	$(3,2,1)$
$(\tau_{L}^{(0)},\ldots,\tau_{1}^{(0)})$	$(0.07,0.07,0.07)$
$\lambda_{\mathrm{ms}}$	0.25
$\lambda_{\mathrm{str}}$	0.05	0
$\lambda_{\mathrm{vel}}$	0.02
$\lambda_{\mathrm{inv}}$	0.05

Appendix

Table S1 : Default hyperparameters. Merged entries apply to all datasets. Per-level vectors are ordered from coarse to fine.

Temperature	DSC $\uparrow$	HD95 $\downarrow$ (mm)	Fold $\downarrow$ (%)	$\bar{H}_{1}$
Fixed $0.5\tau_{l}^{(0)}$	0.7958	2.241	0.0046	0.412
Fixed $\tau_{l}^{(0)}$	0.8026	2.134	0.0029	0.684
Fixed $2\tau_{l}^{(0)}$	0.7931	2.285	0.0014	0.876
Learned (default)	0.8093	2.040	0.0032	0.618

Appendix

Table S2 : Temperature ablation on IXI.

\bar{H}_{1}

summarizes distribution concentration and has no preferred direction.

Figure S1 : Comparison of DSC and HD95 distributions across registration methods.

Figure S2 : Qualitative registration comparison on IXI, OASIS, and AbdomMRCT. For each dataset, method columns show warped images with segmentation overlays (top) and signed intensity residuals for IXI/OASIS or label disagreement maps for AbdomMRCT (bottom).

Figure S3 : Qualitative comparison of IXI registration.

Method	DSC $\uparrow$	Jaccard $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	DSC $\uparrow$	Jaccard $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	DSC $\uparrow$	Jaccard $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$
	IXI				OASIS				AbdomMRCT
UTSRMorph	0.7867	0.6552	2.346	0.0320	0.7943	0.6822	2.012	0.0709	0.8215	0.7038	8.528	0
TransMatch	0.7966	0.6673	2.155	0.0136	0.7886	0.6756	2.203	0.0527	0.8303	0.7162	8.136	0
DySNet	0.7683	0.6308	2.889	0.0582	0.7845	0.6654	2.084	0.0739	0.8476	0.7404	20.402	8.2127
SHMoAReg	0.8005	0.6729	2.230	0.5839	0.8113	07017	1.950	0.7721	0.8631	0.7614	13.33	7.7402
ReliMorph (ours)	0.8093	0.6845	2.040	0.0032	0.8258	0.7222	1.709	0.0423	0.8868	0.7894	6.970	0.0298

Appendix

Table S3 : Complete registration comparisons on IXI, OASIS, and AbdomMRCT. DSC and Jaccard are reported on a

0

–

1

scale, HD95 in millimeters, and Fold as a percentage. Values are averaged over the evaluated image pairs. OASIS results are obtained on the labeled validation pairs.

$c_{\min}$	DSC $\uparrow$	HD95 $\downarrow$ (mm)	Fold $\downarrow$ (%)	ICE $\downarrow$ (mm)
IXI
$0$	0.7745	2.460	0	0.6387
$0.1$	0.7732	2.497	0	0.4745
$\mathbf{0.25}$	0.8093	2.040	0.0032	0.4412
$0.5$	0.7875	2.456	0	0.5126
$1$	0.7919	2.314	0.0001	0.4748

Appendix

Table S4 : Gate-floor sensitivity on IXI and OASIS. Fold denotes the percentage of voxels with

\det(J_{\phi})\leq 0

; ICE denotes bidirectional inverse-consistency error. The default gate floor is highlighted in bold.

Configuration	Expert set	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	Params	FLOPs
			(mm)	(%)	(M)	(G)
Full model	$\{L,A,D\}$	0.8093	2.040	0.0032	0.431	123.61
w/o local expert	$\{A,D\}$	0.7890	2.343	0	0.427	123.612
w/o axial expert	$\{L,D\}$	0.7878	2.341	0	0.428	123.713
w/o dilated expert	$\{L,A\}$	0.7891	2.330	0.0007	0.422	123.612
Homogeneous experts	$\{L_{1},L_{2},L_{3}\}$	0.7873	2.361	0.0001	0.431	124.335

Appendix

Table S5 : Effect of expert composition on IXI. All configurations use soft routing and are trained independently.

L

A

, and

D

denote the local, axial, and dilated experts, respectively.

L_{1}

L_{2}

, and

L_{3}

have identical architectures but independent parameters.

D_{r}

denotes a dilated expert with dilation rate

r

Policy	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	Time $\downarrow$	Mem. $\downarrow$
		(mm)	(%)	(s/pair)	(GB)
Uniform	0.7907	2.312	0.0001	$0.77\pm 0.12$	1.73
Soft	0.8093	2.040	0.0032	$0.78\pm 0.12$	1.75
Top-1	0.7942	2.264	0.0048	$0.79\pm 0.12$	1.76
Top-2	0.8018	2.151	0.0039	$0.79\pm 0.12$	1.76

Appendix

Table S6 : Comparison of routing policies on IXI using the same local, axial, and dilated experts. Inference time and peak GPU memory are measured for full bidirectional inference at batch size one.

Variant	DSC $\uparrow$	HD95 $\downarrow$	Fold $\downarrow$	AURC $\downarrow$
			(mm)	(%)
Full model	0.8093	2.040	0.0032	0.0642
w/o conf. supervision	0.7984	2.208	0.0024	0.1185
Identity gates	0.7919	2.314	0.0001	0.0718
Constant gates †	0.7956	2.254	0.0019	0.0689

Appendix

Table S7 : Confidence supervision and velocity modulation on IXI. The first three variants are trained independently; † denotes a frozen full-model intervention with mean-matched constant gates. Fold: voxels with

\det(J_{\phi})\leq 0

. AURC evaluates final confidence against foreground anatomical label disagreement.

	Foreground			Anatomical boundary
Reliability score	AUROC $\uparrow$	AP $\uparrow$	AURC $\downarrow$	AUROC $\uparrow$	AP $\uparrow$	AURC $\downarrow$
Raw confidence $s_{\mathrm{raw}}$	0.796	0.384	0.0695	0.742	0.578	0.2184
Adjusted confidence $s_{\mathrm{adj}}$	0.824	0.432	0.0642	0.768	0.619	0.2065
Inverse consistency $s_{\mathrm{inv}}$	0.718	0.289	0.0894	0.605	0.492	0.2562
Matching entropy $s_{\mathrm{ent}}$	0.684	0.246	0.0982	0.691	0.518	0.2448
Local dissimilarity $s_{\mathrm{res}}$	0.765	0.341	0.0768	0.719	0.546	0.2310

Appendix

Table S8 : Voxel-level error detection and risk–coverage evaluation of reliability scores on IXI using the same full-model transformations. Voxels with anatomical label disagreement form the positive class for AUROC and AP.

Score	AUROC $\uparrow$	AP $\uparrow$	Flag	Rec. $\uparrow$	Prec. $\uparrow$
			(%)	(%)	(%)
Raw conf. $s_{\mathrm{raw}}$	0.858	0.672	10.4	35.7	83.3
Adj. conf. $s_{\mathrm{adj}}$	0.894	0.746	10.4	39.3	91.7
Inv. cons. $s_{\mathrm{inv}}$	0.762	0.528	9.6	25.0	53.8
Entropy $s_{\mathrm{ent}}$	0.715	0.464	11.3	25.0	53.8
Local dissim. $s_{\mathrm{res}}$	0.819	0.605	10.4	32.4	75.0

Appendix

Table S9 : Inference-time detection of low-quality pairs on IXI. The DSC cutoff is determined on validation data and fixed during evaluation. Score thresholds target a 10% validation flag rate; evaluation flag rates are reported. Recall and precision refer to the low-quality class.

Method	Device	Time $\downarrow$ (s/pair)	GPU memory $\downarrow$ (GiB)
SyN	CPU	$151.6\pm 12.3$	N/A
TransMorph	GPU	$0.31\pm 0.04$	4.89
CorrMLP	GPU	$2.39\pm 0.22$	6.80
AC-CAR	GPU	$0.65\pm 0.08$	3.66
SACB-Net	GPU	$3.34\pm 0.87$	2.42
ShiftMorph	GPU	$\boldsymbol{0.07\pm 0.02}$	1.41

Appendix

Table S10 : Inference efficiency on IXI with an input size of

160\times 192\times 224

and batch size one. Time is reported as mean

\pm

standard deviation across image pairs. GPU memory is the largest observed peak allocated memory.

Medical Image Registration

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ACorD: Adaptive Correspondence Discovery for Medical Image Registration

Arghavan Rezvani, Kun Han, Xiaohui Xie

University of California, Irvine

Medical Image Registration Deformable Image Registration Deformable Attention

Open paper AskPDF arXiv

Medical image registration is a fundamental task for aligning anatomical structures across images. Exhaustively searching for point-wise correspondences is prohibitively expensive in both computation and memory, particularly for high-resolution 3D medical images. Most recent learning-based methods directly predict correspondences in a coarse-to-fine manner, but often propagate intermediate estimates across scales without explicitly weighting correspondence evidence, which can allow coarse-scale errors to persist during refinement. To address these challenges, we propose ACorD, an adaptive correspondence discovery framework designed to mitigate error propagation with an attention-guided process. ACorD first predicts multiple potential correspondence candidates through Correlation-guided Cross-scale Offset Prediction (CCOP), which combines correlation maps as spatial matching priors with cross-scale features as global deformation context. Then, Multi-Head Deformable Aggregation (MHDA) aggregates these candidate correspondences using attention, producing a learned, non-uniform weighting over competing matches rather than treating them equally. The multi-head design further captures complementary deformation patterns, ensuring both global alignment and local precision. By integrating adaptive offset prediction with selective, attention-based aggregation of correspondence evidence, ACorD enables accurate deformation refinement. Extensive experiments on four public medical registration benchmarks demonstrate that adaptive correspondence discovery within a multi-scale refinement framework improves registration robustness across diverse anatomical structures.

Abstract

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