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UBone3D: Physics-Rectified Conditional Flow Matching for Anatomical 3D Shape Completion from Ultrasound

Weiying Chen, Yuchong Gao, Siyuan Li, Marek Reformat, Rui Zheng, Edmond Lou

arXiv:2609.11506v1cs.CVeess.IV

TL;DR

Recovering complete 3D bone geometry from artifact-laden partial ultrasound is difficult because discretization and physics-induced dropouts obscure true anatomy. UBone3D combines an anatomical generative prior with test-time physics rectification, achieving anatomically plausible reconstructions on simulated and zero-shot in-vivo data.

  • Problem

    Artifact-induced dropouts, reverberation, and lossy voxel stacking obscure bone geometry, making accurate 3D reconstruction from ultrasound an unsolved challenge.

  • Method

    UBone3D uses physics-rectified conditional flow matching, combining BoneFM’s anatomical prior with USimNet’s differentiable physics proxy during test-time completion.

  • Results

    UBone3D preserves global anatomical consistency and local structural sharpness on simulated data, while producing anatomically plausible vertebrae and more accurate laminae distances on zero-shot in-vivo data.

  • Takeaways & Limitations

    The framework provides a new approach for completing vertebral anatomy from artifact-laden partial ultrasound observations, although real-world results still need improvement.

Abstract

from arXiv · show

Three-dimensional ultrasound (US) is a safe, radiation-free complementary modality to CT and X-rays for longitudinal monitoring, yet its segmentation-derived partial point clouds are extremely artifact-laden. Consequently, it is challenging to recover a clean and complete anatomical structure from such US point clouds. In this paper, we present UBone3D, a novel framework based on physics-rectified conditional flow matching (CFM) that performs point cloud completion directly from partial US observations. UBone3D models deterministic physics artifacts (e.g., surface thickening, streaking, dropouts) via a simulated physics proxy, and introduces test-time physics rectification to steer the shape completion. At inference, the completion is jointly steered by two decoupled forces: (1) anatomical plausibility enforced by a CT-trained generative shape prior, BoneFM, and (2) physics consistency enforced by USimNet in the ultrasound formation space. Extensive experiments on simulated and in-vivo data demonstrate significant improvements in reconstruction accuracy and anatomical fidelity over existing baselines.

1 Introduction

UBone3D addresses artifact-laden, partial ultrasound point clouds by combining conditional flow matching with anatomical and physics-based guidance. The framework is designed to recover complete, anatomically consistent bone structures from imperfect observations and shows robustness on simulated and zero-shot in-vivo data.

  • 1 Introduction: VNN voxel stacking blurs thin cortical surfaces and propagates ultrasound dropouts and reverberation into empty or spurious regions.These artifacts further obscure the underlying bone geometry.
  • 1 Introduction: Existing ultrasound reconstruction and general completion methods commonly assume clean geometric or intensity data and lack ultrasound acoustic-physics knowledge.This mismatch limits their suitability for artifact-dominated in-vivo observations.
  • 1 Introduction: UBone3D combines a generative anatomy prior with test-time physical rectification to recover complete structures from artifact-laden, partial ultrasound observations.BoneFM supplies anatomical plausibility, while USimNet models acoustic artifacts and provides gradient-based physical guidance during inference.
  • 1 Introduction: UBone3D is reported to perform well on simulated data and remain robust on zero-shot in-vivo data where pure geometric baselines fail.The framework targets both global anatomical integrity and local fidelity to observed ultrasound signals.

2 Literature Review

Prior 3D completion and medical reconstruction methods generally rely on clean observations, while clinical ultrasound introduces alignment difficulties and deterministic physics-driven artifacts. Physics-guided generation offers a relevant direction for enforcing physical consistency during model inference or training.

  • 2 Literature Review: Earlier point-cloud completion methods progressed from encoder–decoder coarse-to-fine generation to transformer, hierarchical, view-disentangled, and guidance-based designs.These methods primarily address geometric completion rather than ultrasound-specific acoustic distortion.
  • 2 Literature Review: Clinical ultrasound bone completion is challenged by deterministic, physics-driven artifacts that systematically distort observations.Perfectly aligned scans are also impractical because of tissue deformation, probe pressure, and respiratory motion.
  • 2 Literature Review: Physics-guided frameworks enforce consistency either through training-time governing-law regularization or inference-time simulation guidance.Examples include PIDM and PhysDiff, with related strategies extending to geometry and animation.
  • 2 Literature Review: Medical shape reconstruction methods using statistical models, implicit representations, and volumetric approaches typically depend on clean and relatively complete observations.That assumption is poorly matched to artifact-laden ultrasound bone inputs.

3 Methodology

The methodology builds BoneFM with optimal-transport flow matching to map Gaussian noise toward clean anatomical bone geometries, then conditions the transport on ultrasound observations. A linear transport path and learned velocity field support efficient inference while incorporating observation-consistent completion.

  • 3.1 Preliminary: Optimal Transport Flow Matching: BoneFM uses optimal-transport flow matching to transport a standard Gaussian distribution toward clean, anatomically consistent bone geometries.The target distribution p_AC represents clean anatomical shapes, while the Gaussian provides the base distribution.
  • 3.1 Preliminary: Optimal Transport Flow Matching: A neural velocity field v_θ(x, t) is trained by regression to approximate the optimal transport velocity, enabling efficient ODE integration during inference.Straight trajectories are desirable because they accelerate numerical integration.
  • 3.1 Preliminary: Optimal Transport Flow Matching: UBone3D extends OT-FM to a conditional velocity field in which ultrasound observations reshape the transport trajectory toward an observation-consistent posterior manifold.The target anatomy x denotes the completed point cloud, while y denotes the ultrasound observation point cloud.

3.2 Framework Overview

UBone3D formulates completion as inferring a complete anatomy from artifact-laden partial ultrasound observations. Its inference combines BoneFM’s anatomical prior with USimNet’s differentiable physics proxy to steer reconstructions toward observation-consistent shapes.

  • 3.2 Framework Overview: UBone3D infers a complete vertebral geometry x* from an artifact-laden, partial in-vivo ultrasound observation y.The formulation treats completion as a posterior proportional to p(y|x)p(x).
  • 3.2 Framework Overview: BoneFM transports Gaussian samples toward the clean anatomical manifold pAC using an observation-conditioned velocity field.The field is optimized through the OT-FM objective and conditions transport on y.
  • 3.2 Framework Overview: USimNet models p(y|x) by mapping candidate clean anatomy into the ultrasound domain through a learned differentiable forward model.Its output is ˆxphys=fϕ(x), learned to replicate in-vivo observation geometry from physics-based simulation.
  • 3.2 Framework Overview: During test-time inference, BoneFM supplies the shape basis while USimNet provides observation-consistency gradients that steer the flow toward the posterior manifold.This joint process is termed physics-rectified conditional flow matching.

Conditional Velocity Parameterization.

BoneFM parameterizes a conditional velocity field that incorporates partial ultrasound context and integration time through FiLM-modulated point features. It is trained to predict the constant transport velocity from a Gaussian base state to clean anatomy.

  • Conditional Velocity Parameterization.: BoneFM fuses an encoded partial ultrasound observation with a sinusoidal time embedding through FiLM transformations in its velocity network.FiLM applies affine scale-and-shift transformations to intermediate point features, adapting the spatial receptive field to the observation.
  • Conditional Velocity Parameterization.: The training target is the constant velocity u(t)=x1−x0 along the optimal transport path, predicted from x(t), t, and y.The objective minimizes the squared Euclidean error between vθ(x(t),t,y) and x1−x0.
  • Conditional Velocity Parameterization.: BoneFM maps a standard Gaussian base distribution to clean anatomical shapes conditioned on the partial ultrasound observation y.Here x1 is the clean anatomical point cloud and y is the simulated partial ultrasound point cloud.
  • Conditional Velocity Parameterization.: Classifier-free guidance is enabled by randomly replacing the conditioning signal y with a null token during training.The replacement occurs with probability pdrop.

Physics Simulation.

The physics simulator generates ultrasound-style point clouds from clean anatomical meshes using ray-based imaging and artifact-specific transformations. These simulated outputs supervise the differentiable USimNet proxy.

  • Physics Simulation.: A customized ray-based simulator operates on clean anatomical meshes to generate physically grounded ultrasound supervision.It constructs an orthonormal probe basis, casts rays along the probe direction, and enforces a sector-shaped field of view.
  • Physics Simulation.: The simulator models angle gating and shadowing, depth windowing and attenuation, thick surfaces, axial streaks, and anti-grid sampling.These operations suppress or modify returns, add inward surface samples, duplicate ray hits, and introduce stochastic sampling variability.
  • Physics Simulation.: After the physically motivated filters, the simulator produces the ultrasound-style point cloud Pphys-full used to supervise USimNet training.The simulated point cloud is generated from anatomically clean geometry.

USimNet Architecture and Training.

USimNet is a lightweight differentiable surrogate for the non-differentiable, computationally expensive ray simulator. It learns to transform clean anatomy into simulated ultrasound geometry and supplies gradients for test-time rectification.

  • USimNet Architecture and Training.: USimNet uses a PointNet++ encoder-decoder to approximate complex ultrasound artifacts and the simulator’s output.The surrogate addresses the simulator’s lack of differentiability and prohibitive test-time gradient cost.
  • USimNet Architecture and Training.: Given a complete anatomical point cloud PAC, USimNet learns a nonlinear spatial transformation into the simulated ultrasound point cloud ˆPphys-full.The input is represented as x∈R3N, while the output may contain N′ points.
  • USimNet Architecture and Training.: USimNet is trained by minimizing the symmetric Chamfer Distance between its predicted and simulated ultrasound point clouds.The objective is LUSim=CD(fϕ(x),xphys).
  • USimNet Architecture and Training.: USimNet provides a differentiable mapping PAC→ˆPphys-full that supplies explicit observation-consistency gradients during test-time flow inference.It therefore acts as a structural physics proxy within UBone3D.

3.5 Inference: Physics-Rectified Conditional Flow Matching

At inference, UBone3D integrates a conditional flow from noise while rectifying it with ultrasound physics and anatomical geometry constraints. Observation anchoring and delayed, clipped guidance preserve observed points and stabilize completion.

  • AC via physics-rectified conditional flow matching: The flow starts from Gaussian noise and uses Heun integration to generate a complete anatomy conditioned on the partial ultrasound observation.At each step, the method combines generative velocity with a physics-based correction.
  • Physics rectification: The guided vector field adds a clipped gradient of directed Chamfer discrepancy between the physics-proxy prediction and observation.The clean target is predicted before evaluating the physics proxy because intermediate states are off the clean data manifold.
  • Physics rectification: Directed Chamfer Distance avoids penalizing generated regions that are not covered by the partial observation.
  • Observation Anchoring: Observation anchoring holds visible points on their exact transport paths, allowing rectification to complete only the unobserved region.
  • Time-dependent Guidance Schedule: Physics guidance is disabled early and activated only during the late generative phase through a truncated polynomial schedule.The activation threshold and scaling factor control when and how strongly USimNet intervenes.

4 Experimental Setup

The experiments evaluate UBone3D on simulated vertebral point clouds and an in-vivo sim-to-real test, using geometric, distributional, and clinical fidelity measures. The setup compares against transformer, diffusion, VAE, and statistical completion baselines.

  • Simulation Data: The simulated Spine1K-PC dataset derives vertebral meshes from volumetric scans and samples 8,192 points per anatomical reference.
  • Simulation Data: Training conditions progress from artifact-free partial observations to simple and full physics simulations, including ray casting and spinous-process removal.
  • In-Vivo Data: The in-vivo test contains 24 vertebrae from five healthy adult volunteers, spanning thoracic and lumbar regions.
  • Completion Baselines: Completion baselines include PoinTr, SVDFormer, PCDreamer, Gafencu et al.’s method, and the clinical statistical model SSM-Net.
  • Completion Metrics (Simulation Data): Simulation experiments use Pphys-full inputs and compare completed point clouds with anatomical references using L1 CD, EMD, and F-score@1%.Metrics are computed after normalizing predicted and reference clouds to a unit sphere.
  • Clinical Metrics (In-Vivo Data): Clinical evaluation measures laminae distance error against raw observations and VNN-reconstructed references, comparing UBone3D with SVDFormer and SSM-Net.

5 Results and Discussions

UBone3D’s full-physics simulation better matches in-vivo ultrasound artifacts, while physics-rectified completion preserves anatomical structure across simulated and zero-shot in-vivo data. Ablations show that full physics guidance, BoneFM, balanced rectification, and sufficient sampling improve performance.

  • 5.1 Efficacy of the Physics Proxy: Pphys-full showed the tightest statistical alignment with in-vivo point-cloud distributions, supporting its use as a proxy for real-world ultrasound physics.The full simulation adds shadowing, attenuation, thick-surface responses, streaks, and anti-grid perturbations beyond simpler variants.
  • 5.2 Completion Results of Simulation Data: UBone3D preserved global anatomical consistency and local structural sharpness, whereas baselines produced noise, distorted structures, sparse outputs, or unreasonable completions on simulation data.Gafencu et al.’s method and SVDFormer achieved low Chamfer Distance under different training settings but substantially higher Earth Mover’s Distance.
  • 5.3 Completion Results of Zero-Shot In-Vivo Data: UBone3D consistently preserved anatomically plausible vertebrae and produced more accurate laminae distances on zero-shot in-vivo data, although real-world results still require improvement.The method outperformed or compared favorably with baselines in qualitative and clinical evaluations on in-vivo data.
  • 5.4 Ablation Studies: Full physics rectification enforced the best physical plausibility, while simplified rectification stabilized the flow trajectory relative to BoneFM alone.The comparison is reported in the ablation on USimNet variants.
  • 5.4 Ablation Studies: BoneFM achieved better overall performance than BoneDiff while requiring significantly fewer sampling steps.BoneDiff required twice as many steps as BoneFM to reach comparable convergence.
  • 5.4 Ablation Studies: A rectification strength of λ = 0.6 best balanced the anatomy prior and physics guidance, while 35 integration steps provided a fidelity–efficiency trade-off.Chamfer Distance followed a U-shaped response with guidance strength, and performance improved markedly as sampling steps increased, especially from 25 to 35.

6 Conclusion

UBone3D completes anatomically consistent vertebral reconstructions from artifact-laden, partial ultrasound observations using an anatomical prior and differentiable physics proxy. Evaluations on simulated and in-vivo datasets support the framework’s effectiveness, while further improvements remain needed.

  • UBone3D completes anatomically consistent vertebral reconstructions from artifact-laden and partial ultrasound observations at inference time.It leverages BoneFM as an anatomical generative prior and USimNet as a differentiable physics proxy.
  • Evaluations across simulation and in-vivo datasets confirm the effectiveness of the proposed framework.
  • Further improvements are still needed, although UBone3D offers a new perspective on clinical bone anatomy completion from ultrasound.
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