SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation

Niklas Schwarz; Jens Kleesiek; Moritz Rempe

eess.IVAug 28, 2026

SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation

Authors: Niklas Schwarz, Jens Kleesiek, Moritz Rempe

Organizations: Institute for AI in Medicine (IKIM), University Hospital Essen, Girardetstraße 2, 45131 Essen, Germany · Cancer Research Center Cologne Essen (CCCE), University Medicine Essen, Hufelandstraße 55, 45147 Essen, Germany · RACOON Study Group, Site Essen, Essen, Germany · Department of Physics, Technical University Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany ·

Abstract

Ultrasound-guided interventions can require localization of an untracked 2D frame within a 3D anatomical reference. Rigid slice-to-volume registration (SVR) estimates this six-degree-of-freedom pose but remains challenging because of limited anatomical context, acoustic artifacts, and view-dependent appearance. Existing methods often use dense cross-attention, whose cost scales with the product of slice and volume token counts, or direct pose regression without explicit correspondence constraints. We introduce SCoPE-Reg, combining state-space slice--volume interaction, dense 3D coordinate prediction, and parameter-free weighted Kabsch estimation. On SVR tasks from CAMUS and $μ$ -RegPro, SCoPE-Reg yields mean target registration errors of $0.73$ mm and $2.27$ mm against $1.24$ mm and $2.63$ mm for the state of the art (SOTA), reduces peak error on CAMUS by 56% below SOTA ( $12.5\!\to\!5.5$ mm), and registers $100\%$ and $80\%$ of frames within $3$ mm. On CAMUS at $128^2$ it retains the lowest error at increasing pose-perturbation magnitude. It holds $6.49$ M parameters independent of resolution, sustaining $51$ FPS at $512^2$ . SCoPE-Reg establishes a SOTA in rigid ultrasound SVR: by coupling correspondence-based accuracy with bounded worst-case error and resolution-independent cost, it becomes viable at native acquisition resolution during intervention, where prior methods trade accuracy, reliability, or frame rate against one another. Supplementary code provided and will be open-sourced upon acceptance.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of SCoPE-Reg. 2D/3D encoders extract features, which Correlation-Weighted Coordinate Decoder (CWCD) fuses with grids to predict dense coordinates $\mathbf{q}$ and evidence weights $\mathbf{w}$ . Weighted Kabsch then estimates rigid pose $\hat{\mathbf{T}}$ in closed form.

Panel of Figure 2 — Figure 2: SSVF and depth reduction. Slice/volume features and coordinate grids are fused across four spatial orderings. DI-SSM feature scans yield $\mathbf{Y}_{f}$ and coordinate scans accumulate weighted locations into $\mathbf{Z}$ ; depth reduction on ( $\mathbf{Y}_{f},\mathbf{Z}$ ) then yields coordinate numerator $\mathbf{Y}$ and evidence weights $\mathbf{w}$ .

		mTRE (mm) $\downarrow$			TransErr $\downarrow$	RotErr $\downarrow$	$\leq 3$ mm $\uparrow$	Dice $\uparrow$	HD95 $\downarrow$	NCC $\uparrow$	SSIM $\uparrow$
	Method	mean	p95	max	(mm)	( ∘ )	(%)		(%)
CAMUS	Initial (identity)	$8.17\pm 0.05$	$10.71$	$13.55$	$5.93\pm 0.05$	$9.64\pm 0.11$	$0.1\pm 0.0$	–	–	–	–
	FVR-Net [ 19 ]	$4.90\pm 0.56$	$10.89$	$15.12$	$3.31\pm 0.55$	$6.36\pm 0.27$	$3.0\pm 0.8$	$0.942\pm 0.011$	$5.56\pm 0.70$	$0.731\pm 0.052$	$0.436\pm 0.021$
	CU-Reg [ 31 ]	$2.46\pm 1.19$	$6.30$	$15.15$	$1.67\pm 0.81$	$3.88\pm 2.02$	$69.5\pm 32.8$	$0.979\pm 0.011$	$2.62\pm 1.62$	$0.923\pm 0.051$	$0.666\pm 0.107$
	EUReg [ 44 ]	$1.24\pm 0.15$	$2.01$	$12.47$	$0.58\pm 0.07$	$1.64\pm 0.25$	$97.2\pm 0.6$	$0.986\pm 0.003$	$1.63\pm 0.20$	$0.964\pm 0.006$	$0.789\pm 0.029$
	DreamReg [ 28 ]	$6.50\pm 0.05$	$9.10$	$11.78$	$4.31\pm 0.02$	$8.95\pm 0.12$	$1.1\pm 0.2$	$0.928\pm 0.003$	$7.20\pm 0.27$	$0.669\pm 0.007$	$0.303\pm 0.005$

Table 1: Slice-to-volume registration accuracy. Mean

\pm

std over 5 folds. mTRE, TransErr, HD95 in mm; RotErr in ∘ ;

\leq

3 mm in %. Dice/HD95 show label overlap under unified protocols. Bold / underlined : best/second-best.

Panel of Figure 3 — Figure 3: Qualitative comparison. Outer columns: the volume centre frame at the identity pose (left) and the 2D target frame at ground-truth pose (right). Between: each method’s resampled slice at its predicted pose and its absolute difference to the target (black: agreement, red: error; shared scale). Top: CAMUS [ 30 ] , echocardiography; bottom: $\mu$ -RegPro [ 2 ] , transrectal prostate. Median-error test cases.

Panel of Figure 4 — Figure 4: Robustness to pose perturbations on CAMUS ( $128^{2}$ ). Log DistErr (mm) across 6-DoF ranges. Lines and shading denote mean $\pm$ std; dashed line shows zero-pose baseline.

	Res.	Params (M)	GFLOPs	FPS	Mem (MiB)
FVR-Net [ 19 ]	$128^{2}$	$67.80$	$61.2$	$33$	$378$
	$192^{2}$	$76.19$	$137.7$	$33$	$546$
	$384^{2}$	$151.68$	$550.8$	$18$	$1561$
	$512^{2}$	$243.96$	$979.2$	$13$	$2670$
CU-Reg [ 31 ]	$128^{2}$	$98.82$	$38.7$	$35$	$531$
	$192^{2}$	$98.82$	$93.2$	$35$	$1068$

Table 2: Computational efficiency vs. resolution on CAMUS. Single-frame (batch 1) inference. GFLOPs exclude custom selective_scan kernels; FPS and memory are end-to-end.

Variant	mean	p95	max	(MiB)	FPS
	mTRE (mm) $\downarrow$			Mem
Cross Att. + Direct Heads	$1.91\pm 0.30$	$4.64$	$13.69$	$\mathbf{75}$	$\mathbf{281}$
SSVF + Direct Heads	$\mathbf{0.68\pm 0.02}$	$1.57$	$10.04$	$82$	$274$
CWCD + Direct Heads	$0.72\pm 0.04$	$1.61$	$11.61$	$81$	$153$
CWCD + Kabsch Solver	$0.89\pm 0.04$	$1.95$	$5.59$	$79$	$150$
CWCD + WKPS (Ours)	$0.73\pm 0.04$	$\mathbf{1.37}$	$\mathbf{5.49}$	$79$	$150$

Table 3: Ablation on CAMUS (

128^{2}

). mTRE in mm reported as 5-fold mean

\pm

std, with p95 and max pooled across test frames. Memory and FPS measured at batch size 1. Best results in bold .

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Optimizer	CAMUS	$\mu$ -RegPro	WD	CAMUS	$\mu$ -RegPro	Warm-up	Batch	CAMUS	$\mu$ -RegPro
		LR			LR schedule				Epochs
FVR-Net [ 19 ]	Adam	$10^{-4}$	$5{\times}10^{-5}$	$0$	step ( $\times 0.8$ /5 ep)	constant	–	$16$	$150$	$1500$
CU-Reg [ 31 ]	Adam	$5{\times}10^{-5}$	$5{\times}10^{-5}$	$0$	one-shot $\times 0.3^{\ddagger}$	constant	–	$24$	$500$	$1500$
EUReg [ 44 ]	Adam	$10^{-4}$	$10^{-4}$	$0$	poly ( $p=0.9$ )	poly ( $p=0.9$ )	–	$6$	$1000$	$30000$
DreamReg [ 28 ]	AdamW	$10^{-4}$	$10^{-5}$	$0.01$	plateau ( $\times 0.5$ , pat. 1)	plateau ( $\times 0.2$ , pat. 2)	$6$ ep	$64$	$100$	$100$
Ours	AdamW	$5{\times}10^{-5}$	$5{\times}10^{-5}$	$0.01$	poly ( $p=0.9$ )	poly ( $p=0.9$ )	–	$6$	$500$	$1500$

Appendix

Table S1 : Training hyperparameter configurations across experimental benchmarks. Optimization protocols, learning-rate schedules, weight decay ( WD ), batch sizes, and epoch budgets for each model.

	Baseline	$\Delta$ (mm)	$95\%$ CI	$\|z\|$	$p_{\mathrm{adj}}$	$r$	Magnitude
CAMUS [ 30 ] ( $\mathcal{T}=4000$ paired frames)
	FVR-Net [ 19 ]	$+4.17$	$[+4.09,+4.25]$	$54.8$	$<10^{-4}$	$0.87$	Large
	CU-Reg [ 31 ]	$+1.73$	$[+1.67,+1.80]$	$47.2$	$<10^{-4}$	$0.75$	Large
	EUReg [ 44 ]	$+0.51$	$[+0.49,+0.53]$	$33.8$	$<10^{-4}$	$0.53$	Large
	DreamReg [ 28 ]	$+5.77$	$[+5.73,+5.82]$	$54.8$	$<10^{-4}$	$0.87$	Large
$\mu$ -RegPro [ 2 ] ( $\mathcal{T}=584$ paired frames)

Appendix

Table S2 : Paired significance and effect size, SCoPE-Reg vs. each baseline (mTRE). Frames are paired by identity.

\Delta

denotes mean frame-level error reduction (positive favors ours) with a bootstrap

95\%

CI (

1000

resamples);

p_{\mathrm{adj}}

reflects two-sided Wilcoxon signed-rank testing with Holm–Bonferroni correction.

Panel of Figure 10 — Figure S1 : Frame-level mTRE distributions (log scale). Boxes show median and IQR ( $1.5\times\mathrm{IQR}$ whiskers); points represent outliers beyond whiskers (max 40 shown, including absolute peak error). Statistics are pooled across all 5-fold test frames.

Panel of Figure 11 — Figure S2 : Qualitative registration performance across error percentiles on CAMUS (top) and $\mu$ -RegPro (bottom). Rows depict Best, Median, $\mathrm{p95}$ , and Worst test cases ranked by SCoPE-Reg frame-level error. Each method presents the resampled slice at predicted pose (left) and absolute intensity difference $|\mathrm{GT}-\text{pred}|$ on a normalized red scale (right; black denotes exact structural alignment).

Variant	mean	p95	max	(MiB)	FPS
	mTRE (mm) $\downarrow$			Mem
CWCD + WKPS (Ours)	$\mathbf{0.73\pm 0.04}$	$\mathbf{1.37}$	$\mathbf{5.49}$	$\mathbf{79}$	$\mathbf{150}$
Tri-plane CWCD + WKPS	$0.87\pm 0.03$	$1.83$	$8.13$	$98$	$110$
CWCD + WKPS + $\mathcal{L}_{\mathrm{phy}}$	$0.82\pm 0.06$	$1.64$	$7.31$	$\mathbf{79}$	$\mathbf{150}$
CWCD + WKPS + $\mathcal{L}_{\mathrm{flow}}$	$0.79\pm 0.05$	$1.52$	$6.75$	$\mathbf{79}$	$\mathbf{150}$
CWCD + WKPS + $\mathcal{L}_{\mathrm{phy}}$ + $\mathcal{L}_{\mathrm{flow}}$	$0.76\pm 0.05$	$1.45$	$6.18$	$\mathbf{79}$	$\mathbf{150}$

Appendix

Table S3 : Ablation of flow regularization (

\mathcal{L}_{\mathrm{flow}}

), physics loss, and advanced scan mechanism on CAMUS (

128^{2}

). mTRE in mm (mean

\pm

std over 5 folds; p95 and max pooled). Memory and FPS measured at batch size 1. Best results in bold .

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Ultrasound (US) is widely used for surgical navigation, yet real-time registration between intraoperative 2D slices and preoperative 3D volumes remains challenging due to partial observability, speckle noise, and the action-dependent US acquisition. Existing methods are one-shot or short-horizon, making it hard for them to gather evidence over time or capture how surgeons adjust probe motion based on on-screen feedback. We propose DreamReg, a belief-driven world-model framework that formulates 2D-3D registration as belief updating over rigid transformations. DreamReg maintains a latent belief state that summarizes past observations and poses information, and continuously refines the transformation through learned dynamics as new slices arrive. During training, DreamReg is exposed to probe-motion trajectories that mimic clinical scanning behavior and learns to update its belief by conditioning pose refinement on the current US observation. During inference, DreamReg refines registration via internal imagination: it rolls out the learned world model to simulate candidate probe motions and their predicted observations, and integrates these imagined outcomes to converge to an accurate rigid transformation. Experiments on CAMUS and u-RegPro datasets demonstrate improved robustness and competitive registration accuracy for real-time guidance compared with state-of-the-art methods.

Abstract

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