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

arXiv:2608.28715 · eess.IV, cs.CV · Submitted 2026-08-28 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: Electrical Engineering. The day in electrical engineering: signals, systems and the hardware that carries them.

Rosa: We're looking at the paper: "SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation".

Dev: Here's the gist of the paper. Ultrasound-guided interventions can require localization of an untracked 2D frame within a 3D anatomical reference.

Rosa: SCoPE-Reg introduces a state-space framework that combines state-space slice–volume interaction, dense 3D coordinate prediction, and parameterfree weighted Kabsch estimation to establish a State-of-the-Art in rigid ultrasound SVR.

Dev: Core Methodology SCoPE-Reg formulates the task of 2D–3D rigid registration between a 2D ultrasound slice and a 3D reference volume as finding a six-degrees-of-freedom (6-DoF) transformation (R, t).

Rosa: Rather than regressing (R, t) directly, SCoPE-Reg predicts dense coordinates and evidence weights on the encoded slice lattice and solves the pose in closed form.

Title and authors: Rosa: So, let's talk about the title and who wrote this thing. It’s "SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation". Rosa, what do you make of that name?

Dev: I think "Efficient" is the key word here because it points directly at solving that scalability issue we just talked about with the dense cross-attention. They aren't trying to be a brute force method anymore.

Taro: And "State-Space Correlation" suggests they’re using some kind of mathematical model for how the 2D slice and three dee volume interact linearly, which sounds much cleaner than relying on every possible pixel match between them <ref:2608.28715#pg1>.

Rosa: Right. And then they have "Closed-Form Pose Estimation." That means instead of having a neural network learn the transformation like it does with EUReg, this new method solves for the pose using a direct mathematical alignment approach once it has those dense coordinates.

Dev: The authors are Niklas Schwarz, Jens Kleesiek, Moritz Rempe, and others from UK Essen. They’re clearly deep into this specific area of slice-to-volume registration research.

Taro: It makes sense that they focus on rigid registration first because that's the foundational problem for localization in ultrasound applications like guiding interventions.

The paper's summary: Rosa: So, moving into what the paper actually does. The core of SCoPE-Reg is formulating the task as finding a six degree of freedom transformation R and t, but instead of regressing them directly, they predict dense coordinates on the slice lattice and some evidence weights.

Dev: They use something called State-Space Slice–Volume Fusion or SSVF to model that 2D to three dee interaction with linear complexity <ref:2608.28715#pg1>. This means they accumulate spatial correspondences through linear statespace scans instead of using those heavy attention matrices we discussed earlier.

Taro: So, the idea is to build these dense three dee coordinates and weights by running two scans, one over the slice tokens and one over the volume tokens, coupling them in a dual-input state-space module <ref:2608.28715#pg1>.

Rosa: That process constructs dense cross-dimensional correspondences which then feeds into a weighted least squares rigid transformation via closed-form Kabsch estimation. That's the flow.

Dev: And the Kabsch solver they use is parameterfree, meaning it learns the alignment purely from supervision signals, and it’s differentiable almost everywhere, so gradients can flow end-to-end through the whole system.

Taro: So what this means for us is that we aren't training a giant regression head for every possible pose; we’re letting the coordinate prediction guide a direct alignment solver.

The paper's improvements: Rosa: Now let’s talk about the specific improvements they claim over existing work. They suggest replacing quadratic cross-attention with linear statespace modeling and explicit regression with closed-form point alignment for scalability.

Dev: They also focus heavily on how they handle the coordinate field construction. They use SSVF with correlation-weighted depth reduction followed by coordinate normalization to create that dense 2D field of three dee coordinates and evidence weights <ref:2608.28715#pg1>.

Taro: The paper mentions a specific constraint in the coordinate scan: it enforces structural constraints ensuring every predicted coordinate is confined to the convex hull of the encoded grid for any network output. That’s a big deal for accuracy.

Rosa: Because they use this constraint, it means that qi prime lies in the convex hull H of the encoded grid for any network output, which stops unconstrained regression from drifting away and keeps things accurate at native acquisition resolution.

Dev: And look at the evidence weighting part. The coordinates are calculated as a scaled convex combination using a probability distribution over volume voxels, meaning qi prime equals ci prime q-tilde i prime, where ci prime equals wi prime because Gv is centered at zero, so it remains within H.

Conclusion: Rosa: So to wrap up on the performance claims. SCoPE-Reg achieves mean target registration errors of zero point seven three millimeters and two point two seven millimeters against the state of the art methods on CAMUS and µ-RegPro benchmarks <ref:2608.28715#pg1,mean target registration errors of 0.73>.

Dev: That means they’re showing a reduction of forty-one percent and fourteen percent relative to EUReg on CAMUS and µ-RegPro, respectively, which is a significant drop in error.

Taro: And they manage to register one hundred point zero percent of CAMUS frames within three millimeters against that EUReg figure of ninety-seven point two percent, while raising the µ-RegPro success rate from sixty-six point two percent up to eighty point four percent for that benchmark, which is a big jump in real-world success.

Rosa: It's also impressive on efficiency: the method holds a parameter count of six point four nine million parameters, independent of resolution, and sustains fifty one frames per second within six hundred seventy eight mebibytes at the highest resolution tested.

Dev: So the final word is that SCoPE-Reg presents this state-space framework for rigid two dimensional to three dimensional ultrasound registration achieving those error metrics while keeping it computationally manageable for intra-procedural use at native acquisition resolution.

Taro: It’s good that they show how this works outside of a perfect lab setting, because real world environments are messy, and this method seems robust enough to handle that complexity.

Rosa: The paper "SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation" gives us a solid framework for tackling the core problem of matching 2D slices to three dee anatomy without hitting those massive computational walls <ref:2608.28715#pg1,SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space>.

Dev: We’re looking at a system that uses linear complexity modeling and closed-form alignment to get accurate results even when the input resolution is high, which is exactly what we need for practical medical imaging applications.

Institute for AI in Medicine, University Hospital Essen · Cancer Research Center Cologne Essen, University Medicine Essen · RACOON Study Group, Site Essen, Germany · Department of Physics, Technical University Dortmund · German Cancer Consortium (DKTK), Partner Site Essen, Germany · Medical Faculty and Faculty of Computer Science, University of Duisburg-Essen · Department of Radiology, Brigham and Women’s Hospital at Harvard Medical School

eess.IV, cs.CV

Submitted: 2026-08-28

Updated: 2026-10-29

Comments: Accepted to Winter Conference for Applications in Computer Vision 2027, Orlando, Florida

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 97/100

The gist: Ultrasound-guided interventions can require localization of an untracked 2D frame within a 3D anatomical reference.

Terminology

Summary

Ultrasound-guided interventions can require localization of an untracked 2D frame within a 3D anatomical reference. SCoPE-Reg introduces a state-space framework that combines state-space slice–volume interaction, dense 3D coordinate prediction, and parameterfree weighted Kabsch estimation to establish a State-of-the-Art in rigid ultrasound SVR.

Core Methodology

SCoPE-Reg formulates the task of 2D–3D rigid registration between a 2D ultrasound slice and a 3D reference volume as finding a six-degrees-of-freedom (6-DoF) transformation (R, t). Rather than regressing (R, t) directly, SCoPE-Reg predicts dense coordinates and evidence weights on the encoded slice lattice and solves the pose in closed form. This involves three main components: feature encoding, coordinate decoding, and WKPS. The Coordinate-Weighted Coordinate Decoder (CWCD) uses State-Space Slice–Volume Fusion (SSVF) to model 2D–3D interaction with linear complexity. This module accumulates spatial correspondences via linear statespace scans, bypassing dense slice–volume attention matrices.

Coordinate Field Construction

The CWCD maps encoded slice and volume features to a dense 2D field of 3D coordinates and evidence weights. It applies SSVF with correlation-weighted depth reduction, followed by coordinate normalization. The SSVF processes D′ axial planes in parallel by replicating F′s across depth; for each plane d, it operates on volume stream (Fv)d, slice stream Fs, and coordinates (Gv)d. The dual-input state-space module (DI-SSM) extends FusionMamba’s dual-input cross-conditioning across the 2D–3D gap by running two scans over xv and xs. This process constructs dense cross-dimensional correspondences to solve a weighted least-squares rigid transformation via closed-form Kabsch estimation.

Pose Estimation and Constraints

The Weighted Kabsch Pose Solver (WKPS) estimates the rigid transformation via closed-form weighted leastsquares alignment. This solver is parameter-free and differentiable almost everywhere, learning correspondence solely from pose supervision while allowing arbitrary input resolution without increasing complexity. The training objective minimizes the mean squared displacement over 14 reference points P (the 8 corners and 6 face centers of [−ρ, ρ]3): Lpose = 1/P X r∈P Rrb + bt − (R⋆r + t⋆)2. Neither predicted coordinates nor evidence weights receive direct supervision; gradients propagate end-to-end through the differentiable pose solver.

Performance and Efficiency Gains

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) on CAMUS and µ-RegPro, respectively. This represents a reduction of 41% and 14% relative to EUReg on CAMUS and µ-RegPro, respectively. SCoPE-Reg registers 100.0% of CAMUS frames within 3 mm against EUReg’s 97.2%, and raises µ-RegPro success from 66.2% to 80.4%. The method holds a parameter count of 6.49 M parameters independent of resolution, sustaining 51 FPS within 678 MiB at the highest resolution tested.

Statistical Validation

Frame-level paired hypothesis testing across the test set T shows that SCoPE-Reg demonstrates statistically significant, largemagnitude error reductions over all direct regression baselines across both benchmarks. On CAMUS, mean reductions reach ∆ = +4.17 mm over FVRNet (r = 0.87) and ∆ = +5.77 mm over DreamReg (r = 0.87). The Kabsch solver bounds failures to plausible rotational errors rather than unconstrained poses, confirming the geometric regularization is effective.

Conclusion

SCoPE-Reg presents a state-space framework for rigid 2D–3D ultrasound registration that achieves 0.73 mm and 2.27 mm mTRE on CAMUS and µ-RegPro, improving on EUReg by 41% and 14%. It reaches this accuracy at 6.49 M parameters independent of input resolution, sustaining frame rate and memory footprint compatible with intra-procedural use at native acquisition resolution.

Acknowledgment

This work received funding from the Bruno & Helene Joster Foundation and KITE (Plattform fur KI-Translation Essen) from the REACT-EU initiative (https://kite.ikim.nrw/) and the Cancer Research Center Cologne Essen (CCCE).

References

[1] Mohamed Said Helmy Alabassy, Martin Christian Hampe, Doreen Erfurt, Horst-Michael Ludwig, and Andrea Osburg. Fourier-Based Non-Rigid Slice-to-Volume Registration of Segmented Petrographic LM and CT Scans of Concrete Specimens. Materials, 19(4):663, 2026.

[2] Zachary M. C. Baum, Shaheer U. Saeed, Ester Bonmati, Dean C. Barratt, and Yipeng Hu. µ-RegPro: MICCAI 2023 Challenge on Prostate MR to Ultrasound Registration — Dataset.

[3] Kathrin Becker, Martin Stauber, Frank Schwarz, and Tim Beißbarth. Automated 3D–2D registration of X-ray microcomputed tomography with histological sections for dental implants in bone using chamfer matching and simulated annealing. Computerized Medical Imaging and Graphics, 44:62–68, 2015.

[4] Stefan Brandstatter, Philipp Seeb ¨ ock, Christoph F ¨ urb ¨ ock, ¨Svitlana Pochepnia, Helmut Prosch, and Georg Langs. Rigid Single-Slice-in-Volume registration via rotation-equivariant 2D/3D feature matching. In Medical Image Computing and Computer Assisted Intervention – MICCAI 2024, pages 280–294, 2024.

[5] Heiko Bulow and Andreas Birk. Scale-Free Registrations in ¨3D: 7 Degrees of Freedom with Fourier Mellin SOFT Transforms. IJCV, 126(7):731–750, 2018.

[6] Junan Chen, Matteo Ronchetti, Verena Stehl, Van Nguyen, Muhannad Al Kallaa, Mahesh Thalwaththe Gedara, Claudia Lolkes, Stefan Moser, Maximilian Seidl, and Matthias ¨Wieczorek. 2D-3D deformable image registration of histology slide and micro-CT with DISA-based initialization. Sci. Rep., 15(1):25972, 2025.

[7] N. Chicherova, S. E. Hieber, A. Khimchenko, C. Bikis, B. Muller, and P. Cattin. Automatic deformable registration ¨of histological slides to µCT volume data.

Improvements for AI systems

  1. State-Space Slice-Volume Fusion (SSVF) allows linear complexity modeling of 2D-3D interaction, which is used to accumulate spatial correspondences via linear statespace scans, bypassing dense slice–volume attention matrices. This enables the system to predict a dense 2D–3D field of 3D coordinates and evidence weights without incurring the O(NsNvC) compute and memory footprint of dense cross-attention.

  2. Parameterfree weighted Kabsch estimation solves the rigid transformation via closed-form weighted leastsquares alignment, which is described as a method that suppress[es] low-confidence regions. This allows the system to recover pose with a parameter count independent of H′, W′, and D′ while maintaining resolution independence.

  3. The coordinate scan enforces structural constraints, ensuring every predicted coordinate is confined to the convex hull of the encoded grid for any network output, which means qi′ lies in the convex hull H of the encoded grid for any network output. This prevents unconstrained regression from leaving direct regression near its initialization and ensures accuracy at native acquisition resolution.

  4. The evidence weighting mechanism, where coordinates are calculated as a scaled convex combination using a probability distribution over volume voxels, yields qi′ = ci′ q˜i′, ci′ = wi′, which remains in H since Gv is centred (0 ∈ H). This makes the predicted coordinate a probabilistic estimate rather than an unconstrained regression.

  5. The system can achieve high throughput at native acquisition resolution, sustaining 51 FPS within 678 MiB at 5122, making it viable for intra-procedural use where prior methods trade accuracy, reliability, or frame rate against one another.

Sources

Related papers