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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