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Deformable Slice-to-Volume Registration for Motion Correction in Fetal Body MRI

Alena Uus, Tong Zhang, Laurence H. Jackson, Thomas A. Roberts, Mary A. Rutherford, Joseph V. Hajnal, Maria Deprez

arXiv:1906.08827v2physics.med-pheess.IV

TL;DR

Rigid SVR cannot resolve local non-rigid deformation in fetal body and placenta, limiting reconstruction quality. DSVR combines hierarchical deformable registration with structure-based outlier rejection. It outperforms SVR and PVR in the reported evaluations, with a stated limitation for large-amplitude motion.

  • Problem

    Rigid SVR is suited to fetal brain motion but cannot resolve local non-rigid deformation of fetal body and placenta, degrading reconstructed features.

    Source: §I · p. 1

  • Method

    DSVR extends SVR with hierarchical deformable registration and structure-based outlier rejection for fetal MRI motion correction.

    Source: B. Contributions · p. 2

  • Results

    DSVR surpassed SVR and PVR on minor- and severe-motion datasets, with the finding also confirmed in simulated non-rigid motion experiments.

    Source: §VI · p. 9

  • Takeaways & Limitations

    The method extends slice-to-volume reconstruction to fetal body and placenta with high-resolution 3D volumes from stacks affected by non-rigid motion.

    Source: §VI · p. 9

    The current implementation is not designed for large-amplitude motion, including large rotations and bending, because of the limited capture range of its gradient-descent optimisation.

    Source: §VI · p. 9

Abstract

from arXiv · show

In in-utero MRI, motion correction for fetal body and placenta poses a particular challenge due to the presence of local non-rigid transformations of organs caused by bending and stretching. The existing slice-to-volume registration (SVR) reconstruction methods are widely employed for motion correction of fetal brain that undergoes only rigid transformation. However, for reconstruction of fetal body and placenta, rigid registration cannot resolve the issue of misregistrations due to deformable motion, resulting in degradation of features in the reconstructed volume. We propose a Deformable SVR (DSVR), a novel approach for non-rigid motion correction of fetal MRI based on a hierarchical deformable SVR scheme to allow high resolution reconstruction of the fetal body and placenta. Additionally, a robust scheme for structure-based rejection of outliers minimises the impact of registration errors. The improved performance of DSVR in comparison to SVR and patch-to-volume registration (PVR) methods is quantitatively demonstrated in simulated experiments and 20 fetal MRI datasets from 28-31 weeks gestational age (GA) range with varying degree of motion corruption. In addition, we present qualitative evaluation of 100 fetal body cases from 20-34 weeks GA range.

I. INTRODUCTION

Inter-slice motion can leave fetal MRI stacks misaligned or remove volumetric information, while local deformation of the fetal body and placenta limits rigid SVR. Prior work includes rigid SVR and piecewise-rigid PVR, but existing deformable SVR approaches have limitations for this setting.

I. INTRODUCTION

  • Inter-slice motion in 3D stacks ranges from minor misalignment to complete loss of volumetric information.The examples compare stacks from the same exam and orientation acquired at different times.Source: §I · p. 1, Figure 1 · p. 1
  • SVR with super-resolution is used to resolve out-of-plane motion, and its validation for fetal brain reconstruction showed strong correlation between 2D and 3D biometry.The brain focus reflects the assumption of rigid motion.Source: §I · p. 1
  • Local non-rigid deformation of the fetal body and placenta makes rigid registration inadequate, degrading reconstructed image quality and blurring local features.Bending and maternal breathing are examples of deformation; inconsistent slices may be rejected or contribute errors to reconstruction.Source: §I · pp. 1–2

A. Related work

  • Rigid SVR has also been applied to fetal thorax and placenta, while PVR addresses deformable organs through piecewise-rigid motion compensation.The thorax application assumes approximately rigid motion; placenta reconstruction relies on excluding slices deformed from its common shape.Source: A. Related work · p. 2
  • Earlier deformable SVR work includes methods limited to in-plane deformation and model-based approaches using biomechanical regularisation.Other monomodal methods combine rigid global alignment with free-form deformation.Source: A. Related work · p. 2

B. Contributions

The paper introduces DSVR as an extension of rigid SVR for non-rigid fetal MRI motion correction, combining hierarchical deformable registration with structure-based outlier rejection. The background describes iterative registration and super-resolution reconstruction.

B. Contributions

  • DSVR extends rigid SVR with hierarchical deformable registration and structure-based outlier rejection to correct in-plane and out-of-plane local deformations in fetal body and placenta.The rejection step is intended to prevent residual registration errors from propagating into the reconstructed volume.Source: B. Contributions · p. 2

II. BACKGROUND

  • SVR iteratively recovers a high-resolution isotropic volume from motion-corrupted slices acquired in multiple stack orientations.The framework interleaves slice-to-volume registration and super-resolution reconstruction for a fixed number of iterations.Source: §II · p. 2
  • The super-resolution reconstruction minimizes squared differences between original and simulated slices with edge-preserving regularisation.The background also describes expectation-maximization robust statistics for outlier rejection and estimating slice bias fields and scaling factors.Source: §II · p. 3

III. METHOD

DSVR extends the rigid SVR reconstruction framework with additional modules. Its deformable transformations also deform the point-spread functions used to model acquired slices during super-resolution reconstruction.

A. Overview of the algorithm

  • DSVR extends rigid SVR reconstruction with a pipeline that registers stacks, uses a template to initialise the target, and interleaves slice registration with reconstruction and structure-based rejection.The pipeline runs for predefined numbers of DSVR and super-resolution iterations.Source: A. Overview of the algorithm · p. 3

B. Incorporating deformations into SR reconstruction

  • Deformable transformations make the acquisition point-spread functions non-Gaussian, allowing them to model fetal-body and placenta deformation in the forward reconstruction problem.The underlying acquired-space PSF is modeled as a 3D Gaussian before transformation.Source: B. Incorporating deformations into SR… · p. 3

C. Hierarchical motion correction

Because continuously deforming fetal body and placenta make deformable SVR under-constrained, DSVR refines transformations hierarchically. It initializes from a selected template stack and progressively increases deformation resolution during slice-to-volume registration.

C. Hierarchical motion correction

  • The hierarchical scheme addresses the under-constrained registration of continuously deforming fetal body and placenta by gradually refining transformations.Unlike rigid-motion brain SVR, the target shape is not assumed to remain fixed across stacks.Source: C. Hierarchical motion correction · p. 3

1) Volumetric registration:

  • A selected template stack initializes the target, with global rigid registration followed by global deformable registration of the other stacks.The template cropped to the mask bounding box initializes the reconstructed volume.Source: 1) Volumetric registration · p. 3

2) Slice-to-volume registration:

  • Each DSVR iteration registers the current reconstructed volume to individual slices, resolving both in-plane and out-of-plane deformable motion.The first iteration deformably registers a smoothed template stack to each slice using low-resolution transformations.Source: 2) Slice-to-volume registration · p. 4
  • Decreasing B-spline control-point spacing refines transformation resolution across iterations, while reducing super-resolution regularisation progressively permits more localised deformations.The regularisation schedule is intended to prevent overfitting residual motion early in the process.Source: 2) Slice-to-volume registration · p. 4

D. Structure-based outlier rejection

DSVR rejects misregistered data at both slice and regional scales: global NCC screens slices before Gaussian reconstruction, while local SSIM excludes low-similarity regions during super-resolution reconstruction.

1) Global structure-based outlier rejection:

  • Slices with global NCC below a threshold are excluded before Gaussian reconstruction.NCC compares the original slice with the current estimated volume transformed into the masked slice ROI.Source: 1) Global structure-based outlier… · p. 4

2) Local structure-based outlier rejection:

  • At each super-resolution iteration, low-structural-similarity regions of simulated slices are excluded from the reconstructed volume.The regional rejection uses local SSIM maps between simulated and original slices.Source: 2) Local structure-based outlier… · p. 4
  • Local SSIM is computed over (n) slices centered on voxel j using a circular window and corresponding intensity means, variances, and covariance; voxels with similarity < T_SSIM are set to zero.Source: 2) Local structure-based outlier… · p. 4

3) Incorporating structure-based outlier rejection into SR reconstruction:

Structure-based outlier rejection weights reconstruction-error contributions during super-resolution reconstruction. Combining global and local criteria outperforms either scheme alone.

3) Incorporating structure-based outlier rejection into SR reconstruction:

IV. IMPLEMENTATION

The implementation specifies input-stack requirements, a hierarchical B-spline deformable-registration schedule, outlier-rejection settings, and software and runtime characteristics.

A. Input data requirements

  • At least two sufficiently different stack orientations are needed; 5–8 stacks were experimentally sufficient, while large rotations or excessive bending exceed gradient-descent registration capability.The template must preserve global target structure, and minor to average template motion corruption is acceptable after Gaussian blurring.Source: A. Input data requirements · p. 5

B. Deformable registration

  • B-spline FFD with NMI was selected for lower computational requirements; 15 mm → 10 mm → 5 mm control-point refinement gave optimal reconstruction quality.The corresponding regularisation schedule is 0.1 → 0.05 → 0.02; stationary-velocity FFD did not produce indicative improvement and increased processing time.Source: B. Deformable registration · p. 5

C. Structure based outlier rejection parameters

  • The selected rejection thresholds are T_NCC = 0.75 globally and T_SSIM = 0.6 locally, with a 20 mm SSIM kernel for subjects at 28–31 weeks GA.Lower thresholds may admit erroneously overfitted regions; the kernel size was selected for feature sizes in this GA range.Source: C. Structure based outlier rejection… · p. 5

D. Software packages and hardware requirements

  • MIRTK2 uses multi-CPU parallelisation, and reconstruction typically takes 15–60 minutes depending on ROI size, stack count, output resolution, and system configuration.Core reconstruction steps follow the IRTK-based SVR implementation, and the code is available in SVRTK.Source: D. Software packages and hardware… · p. 5

V. EXPERIMENTS AND RESULTS

The evaluation compares DSVR with rigid SVR and PVR using 20 fetal MRI datasets and simulated non-rigid motion. In simulation, DSVR volumes correlate strongly with the reference, while SVR and PVR show lower similarity and more local-feature blurring.

A. Fetal MRI data

  • The study evaluated 20 datasets from fetuses at 28–31 weeks GA, split into minor- and severe-motion groups; severe-motion datasets had lower average sequential-slice NCC.Motion severity was visually assessed from volumetric consistency and changes in fetal position between stacks.Source: A. Fetal MRI data · pp. 5–6, Table I · p. 6

B. Simulated experiment

  • Five simulated datasets were generated from a reference volume using transformations containing local non-rigid and global rigid and non-rigid components, then reconstructed with DSVR, SVR, and PVR.Each simulated dataset contained six differently oriented stacks.Source: B. Simulated experiment · p. 6
  • SVR and PVR reconstructions had lower similarity to the reference than DSVR, with non-rigid misregistrations blurring local texture and increasing errors.All three methods reconstructed major anatomy, including kidney topology and the spine.Source: B. Simulated experiment · p. 6, Table II · p. 6
  • DSVR produced significantly lower target registration error than SVR in simulated experiments (p < 0.001).TRE measured average displacement error against the transformations used to generate the motion-corrupted stacks.Source: B. Simulated experiment · p. 6, Table III · p. 6

C. Reconstruction of fetal body

Leave-one-out evaluation found that DSVR outperformed SVR and PVR on intensity and structural characteristics for both minor- and severe-motion fetal-body datasets. Structural outlier rejection further improved severe-motion results, while examples show how deformable registration addresses local anatomy misalignment that rigid SVR leaves unresolved.

C. Reconstruction of fetal body

  • DSVR surpassed SVR and PVR on intensity and structural characteristics in both minor- and severe-motion datasets.The comparison used leave-one-out analysis on the same masked ROI of an excluded stack; all results except DSVR versus DSVR+S for minor motion were significant at p < 0.005.Source: Table IV · p. 7, C. Reconstruction of fetal body · p. 7
  • In a minor-motion example, DSVR retained local anatomy definition, while PVR improved spine definition but smoothed texture and small features.SVR recovered global trunk topology but lost spine structure and texture; the methods also converged to different trunk positions because they used different registration-target initializations.Source: C. Reconstruction of fetal body · p. 7
  • With spine bending, rigid SVR left the kidney displaced, whereas FFD registration improved the slice-to-volume mapping.Deformed ROI boundaries in the DSVR output indicated substantial non-rigid deformation.Source: C. Reconstruction of fetal body · p. 7
  • For severe motion, PVR clarified trunk structure but smoothed abdominal-organ texture, while DSVR improved on SVR yet retained misregistration artefacts.The passage describes a severe-motion example in the coronal plane.Source: C. Reconstruction of fetal body · p. 7, Figure 8 · p. 8
  • The gradient-descent FFD method could not resolve large bending and rotations, leading to misregistrations.This limitation qualifies the severe-motion examples and motivates reliance on outlier rejection in such cases.Source: C. Reconstruction of fetal body · p. 8
  • Structural outlier rejection significantly improved severe-motion results, but rejected 20–50% of slices versus 10–15% with EM robust statistics.The authors report the larger rejection proportion for severe-motion datasets and describe the original EM rejection rate as insufficient in major-motion cases.Source: C. Reconstruction of fetal body · p. 8

D. Parametric study

The parametric study selected a multiresolution control-point spacing that balanced global shape correction against local-feature recovery and overfitting, and found that combining three outlier-rejection approaches performed best in severe-motion cases. In placenta reconstruction, DSVR outperformed SVR and PVR.

D. Parametric study

  • A 15 mm → 10 mm → 5 mm control-point spacing over three iterations was optimal; finer initial spacing did not improve results because of overfitting.Large spacing corrected global body shape but not local features, whereas spacing that was too small risked overfitting and unrealistic deformations.Source: D. Parametric study · p. 8, Figure 9 · p. 8
  • Combining EM-based, global NCC-based, and local SSIM-based outlier rejection produced the best performance in severe-motion cases.The assessment covered five severe-motion datasets and reported NCC alongside the average proportion of excluded slices.Source: Table V · p. 8, D. Parametric study · p. 8

E. Reconstruction of placenta

F. Qualitative analysis

Clinicians rated DSVR reconstructions from 100 fetal-body cases spanning 20–34 weeks’ gestational age, with average weekly grades between 2.5 and 3.5. The authors report that DSVR outperformed SVR and PVR for fetal-body and placenta reconstruction, while noting limitations for large-amplitude motion and unresolved volume preservation.

F. Qualitative analysis

  • Across 100 cases from 20–34 weeks’ gestational age, mean weekly quality grades ranged from 2.5 to 3.5, averaging 3.09 ± 0.78.Grades were assigned by trained clinicians on a 0–4 scale; grades of at least 2 indicated sufficient quality for further analysis and interpretation.Source: F. Qualitative analysis · p. 9, Figure 11 · p. 9
  • Only 6% of cases failed the quality threshold because of severe motion unresolved by gradient-descent FFD registration.Lower grades were primarily associated with motion in younger subjects and low SNR in older subjects.Source: F. Qualitative analysis · p. 9

VI. DISCUSSION AND CONCLUSIONS

  • DSVR outperformed SVR and PVR for fetal-body reconstruction on 20 datasets from 28–31 weeks’ gestational age, with well-defined spine, heart, and abdominal-organ features and texture.The comparison included minor- and severe-motion datasets and was further supported by an experiment with simulated non-rigid motion.Source: §VI · p. 9
  • The implementation is not designed to correct large-amplitude motion, including large rotations and bending, because gradient-descent optimization has limited capture range.In such cases, the method relies on outlier rejection; large-amplitude motion primarily affected datasets from subjects under 25 weeks’ gestational age.Source: §VI · p. 9
  • DSVR also outperformed SVR and PVR for 3D placenta reconstruction.The authors identify respiratory motion, stretching, and bending as relevant placental deformations.Source: §VI · pp. 9–10
  • Whether DSVR preserves volume remains unresolved, and quantitative measurements may depend on template shape and position, stack count, and control-point spacing.The authors identify further deformation-field constraints and automation of template selection and masking as future work.Source: §VI · p. 10
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