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Deformable CT-US Registration via Anatomy-Aware Implicit Neural Representations
Agnieszka Lach, Magdalena Wysocki, Feng Li, Mohammad Farid Azampour, Benjamin D. Killeen, Felix Ginzinger, Mathias Braun, Philipp Steininger, Heinz Deutschmann, Nassir Navab
TL;DR
Probe contact deforms soft tissue during ultrasound acquisition, causing misalignment with CT even after rigid registration and hindering precise anatomical alignment. A per-frame SIREN estimates a CT–US displacement field, combining CT-derived stiffness regularization and probe-contact and fan-geometry constraints with an NGF-based objective. Across all four sweeps (478 landmarks), our method achieved the lowest TRE (3.97 mm; p < 10−10 vs. rigid), beating FFD-NGF (4.43 mm) with 0.03% folding.
Problem
Probe contact deforms soft tissue during ultrasound acquisition, causing misalignment with CT even after rigid registration and hindering precise anatomical alignment.
Source: §1 · pp. 1–2Method
A per-frame SIREN estimates a CT–US displacement field, combining CT-derived stiffness regularization and probe-contact and fan-geometry constraints with an NGF-based objective.
Source: §1 · pp. 2–3, §2.4 · p. 5Results
Across all four sweeps (478 landmarks), our method achieved the lowest TRE (3.97 mm; p < 10−10 vs. rigid), beating FFD-NGF (4.43 mm) with 0.03% folding.
Source: §3.1 · pp. 6–7Takeaways & Limitations
The constraints address non-physical deformation of rigid structures and unconstrained behavior outside the imaging field of view in CT–US registration.
Source: §4 · p. 7The CT-intensity-to-stiffness mapping was calibrated for phantoms and may generalize less well to pathological tissue or implants; the fan-geometry assumptions are specific to convex transducers.
Source: §4 · p. 8
Abstract
from arXiv · showhide
Slice-to-volume registration between ultrasound (US) and preoperative computed tomography (CT) imaging would enhance many minimally invasive interventions, for example by locating soft tissue structures intra-operatively that are discernible in CT. While optical tracking enables initial rigid registration, contact from the probe induces soft tissue deformations that inhibit accurate alignment. In this work, we introduce a deformable CT-ultrasound registration framework that incorporates anatomical priors derived from CT to improve registration under deformation. Rigid registration is first established using a robot-assisted optical tracking system, after which a deformable transformation is estimated using a sinusoidal implicit neural representation (SIREN) optimized per frame. Tissue stiffness is approximated from CT-based HU values and used as spatially varying regularization, suppressing deformation in rigid structures such as bone while allowing more flexibility in soft tissue. Two additional constraints capture the physics of probe contact: a contact-zone displacement prior that drives the displacement field to compress tissue below the probe face, and a fan-geometry regularization term based on beam direction and convex transducer field of view. Model parameters are optimized with a normalized gradient field (NGF). The proposed approach improves alignment over rigid initialisation by 17% and outperforms classical deformable baselines while maintaining near-zero topological folding.
1 Introduction
Tracked ultrasound and CT can provide complementary anatomical information, but probe-induced tissue deformation disrupts alignment even after rigid registration. The paper proposes deformable registration that combines CT-derived anatomical priors with physical constraints.
1 Introduction
- Tracked ultrasound and CT offer real-time soft-tissue information alongside three-dimensional anatomical context, addressing limitations such as acoustic shadowing and shallow penetration.The paper frames this combination as useful for minimally invasive interventions.Source: §1 · p. 1
- Figure 1 contrasts probe-induced misalignment and unconstrained deformations with the proposed anatomy- and physics-constrained registration.The caption notes that the non-physical deformations in panel (c) are exaggerated for visual clarity.Source: Figure 1 · p. 2
- Probe pressure needed for ultrasound image quality introduces spatial inconsistencies that hinder precise CT–US alignment for interventions such as liver tumor ablation or biopsy.Existing approaches may require contact-force sensors unavailable in CT–US workflows, while anatomy-unconstrained methods risk non-physical deformations.Source: §1 · p. 2
- The framework combines CT-derived tissue stiffness, a probe-contact displacement prior, and fan-shaped field-of-view regularization in an implicit neural representation.The contact prior penalizes residual tissue in the crescent between the probe face and ultrasound fan arc; fan regularization is tailored to a convex transducer.Source: §1 · pp. 2–3, Figure 2 · p. 3
2 Methods
The method estimates a per-frame displacement field for tracked ultrasound and CT, with the warp constrained to the ultrasound imaging plane. It combines CT-derived stiffness, probe-contact and fan-geometry priors with an NGF similarity objective and Jacobian regularization.
2 Methods
- A per-frame SIREN estimates the displacement field, using NGF similarity and Jacobian regularization while constraining the warp to the ultrasound imaging plane.The resulting registration is a 2.5-D warp because out-of-plane motion is unobservable from a single ultrasound slice.Source: §2 · pp. 3–4
2.1 CT-Derived Stiffness Regularization
- CT-derived stiffness weights each point’s deviation from a rigid consensus, strongly restraining bone while leaving soft tissue more flexible.The stiffness scalar spans approximately 0.01 in air, 1 in soft tissue, and 100 in bone; the Jacobian folding penalty is also stiffness-weighted.Source: §2.1 · p. 4
2.2 Contact-Zone Displacement Prior
- The contact prior samples displaced CT coordinates in the crescent between the probe face and fan arc, penalizing tissue-level intensity where the region should be air.Minimizing the loss drives downward tissue compression without ground-truth annotation.Source: §2.2 · pp. 4–5
2.3 Fan-Geometry-Aware Optimization
- Fan-aware optimization samples patches inside the fan, penalizes retrograde motion more than forward compression, and tapers displacements toward the lateral fan horns.The boundary weight attenuates displacement where beam quality is weakest.Source: §2.3 · p. 5
2.4 Implementation Details
- Implementation normalizes both modalities, denoises ultrasound with Speckle2Self, and optimizes the combined objective with Adam and early stopping.Optimization runs for up to 200 iterations and restores the best-seen weights when validation NGF ceases to improve.Source: §2.4 · pp. 5–6
3 Experiments and Results
Across four phantom sweeps, the deformable method achieved the lowest landmark error with near-zero folding. Ablations show distinct roles for the material, contact, fan, and similarity terms.
3 Experiments and Results
- Evaluation used four robot-assisted phantom sweeps, 478 landmark pairs, and measures of landmark accuracy, image agreement, deformation plausibility, and structure overlap.Baselines included rigid initialization, Demons, B-spline FFD variants, Farnebäck flow, and network variants driven by MIND or LC2.Source: §3 · p. 6
3.1 Quantitative Results
- TRE was 3.97 mm (p < 10−10 vs. rigid), lowest against FFD-NGF (4.43 mm), with 0.03% folding versus 1.4–5.6% for FFD/Demons/optical-flow.FFD-NGF had higher phase-congruency similarity (0.053 vs. 0.048) but 1.41% folding.Source: §3.1 · pp. 6–7, Table 1 · p. 7
3.2 Ablation Study
- Removing Lmat left TRE essentially unchanged (3.95 vs. 3.97 mm) but raised the bone/soft strain ratio from 0.58 to 1.10; removing Lcon worsened TRE by 0.21 mm.Lfan was TRE-neutral; it constrains a near-field region without landmarks.Source: §3.2 · p. 7
- Replacing NGF with MIND or LC2 yielded no significant improvement over rigid, with TREs of 4.63 and 4.80 mm, respectively.The evaluation pooled 478 manually annotated landmark pairs across four sweeps; all methods shared rigid pre-alignment and ran per frame.Source: §3 · p. 6, §3.2 · p. 7
4 Conclusion
The framework combines an implicit displacement representation with anatomy-aware constraints to address non-physical deformation and unconstrained behavior outside the imaging field of view. Phantom results show improved alignment over rigid initialization and classical deformable baselines, with near-zero folding.
Conclusion
- The framework augments an implicit displacement field with three anatomy-aware constraints targeting rigid-structure deformation and unconstrained behavior outside the imaging field of view.The conclusion reports improved alignment over rigid initialization and classical deformable baselines on soft-tissue and bone-containing phantoms, with near-zero folding.Source: §4 · pp. 7–8
- Fig. 3 qualitatively shows stiffness-map registration correcting transducer-induced deformation while bone remains stable relative to compliant soft tissue.The caption describes sub-millimeter structural alignment.Source: Figure 3 · p. 8
- The stiffness map uses a phantom-calibrated CT-intensity mapping that may generalize less well to pathological tissue or implants; fan-geometry assumptions are specific to convex transducers.The authors also note that greater anatomical variability may arise in vivo.Source: §4 · p. 8
- The material-term ablation shows that removing Lmat returns the bone/soft strain ratio to approximately 1, meaning bone deforms like soft tissue.The ablation caption says the material term lowers this ratio without TRE cost.Source: Table 2 · p. 8
- The authors call for a modality-independent registration metric and future volumetric ground-truth deformations for comprehensive validation.Manual landmark selection may introduce inter-observer bias, and simultaneous CT-US capture is challenging because of probe placement.Source: §4 · p. 9