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Periodicity and image registration for yarn path extraction in large 3D textiles

Hafsa El Herichi, Arturo Mendoza, Yanneck Wielhorski, Hugues Talbot, Stéphane Roux

arXiv:2609.36991v1eess.SP

TL;DR

Dense, low-contrast woven regions make yarn identification in CT difficult, although accurate segmentation is needed for faithful composite models. The method annotates a representative periodic cell and registers its replicated architecture to the real volume to transfer the yarn paths. It reconstructs thousands of warp and weft trajectories with minimal input, with unit-cell segmentation and full registration taking less than 1 minute and under 30 minutes, respectively.

  • Problem

    Dense woven regions make yarn identification difficult, while accurate CT segmentation is needed to build geometrically faithful models for simulation and analysis.

    Source: §1 · p. 2

  • Method

    The framework uses intrinsic weave periodicity to propagate annotations from a representative cell and register the idealized architecture to the real volume.

    Source: §7 · p. 19, §8 · p. 21

  • Results

    The framework reconstructs thousands of warp and weft trajectories with minimal input, with unit-cell segmentation taking less than 1 minute and full registration under 30 minutes.

    Source: §9 · pp. 22–23

  • Takeaways & Limitations

    The method supports robust yarn tracking in dense regions without manual annotations or lengthy training and provides intrinsic validation of tracking quality.

    Source: §9 · p. 23

    Because the studied region lacks annotations, direct ground-truth comparison and rigorous quantitative estimates of reconstruction uncertainty or tracking error across the full volume cannot presently be established.

    Source: §8 · pp. 20–21

Abstract

from arXiv · show

Accurate identification of yarns in X-ray computed tomography volumes remains a critical and complex step in generating high-fidelity numerical models of woven composites. This work introduces a tracking framework that leverages the intrinsic periodicity of woven architectures to transform a complex, large-scale segmentation problem into the annotation of a single representative unit cell. The approach first exploits the periodic nature of the weave to extract a representative unit cell from the volumetric data and segment it to provide a reference description of the yarn geometry. Digital Volume Correlation (DVC) is then performed between an idealised periodic volume obtained by replication of the unit cell and the real composite volume, yielding a three-dimensional displacement field that captures geometric deviations from ideal periodicity. The unit-cell yarn segmentation is propagated to the full volume by exploiting the periodicity of the reference volume, and the annotations are transported to the actual volume using the DVC-derived displacement field. Results obtained on real composite datasets demonstrate the ability of the method to accurately recover warp and weft yarn architectures with minimal input, opening new perspectives for efficient and scalable textile composite characterisation.

1. Introduction

Dense woven regions make individual yarn identification in X-ray CT difficult, yet accurate segmentation supports geometrically faithful models and periodic simulations. This work reduces the task to annotating a representative unit cell, then uses registration to transfer yarn annotations to the real architecture.

1. Introduction

  • Dense, tightly packed yarns with reduced image contrast make reliable warp and weft identification particularly challenging in component-scale regions.Existing studies largely focus on high-resolution coupons with separated yarns and favorable contrast; dense industrial regions remain largely unexplored.Source: §1 · p. 2
  • Accurate CT yarn segmentation supports geometrically faithful mesoscopic models and periodic representative-volume simulations.Such models support multiscale simulations and predictive mechanical analyses of structural integrity.Source: §1 · p. 2
  • Unlike a related study of less densely packed regions, this work targets compacted regions where yarn-wise tracking is impractical.The authors therefore motivate a global description at the periodic-unit-cell scale.Source: §1 · p. 3
  • The framework extracts and segments one representative cell, replicates it into an ideal periodic volume, then uses DVC to transfer annotations to the real volume.Here DVC serves as a geometrically consistent mapping operator rather than a strain-measurement tool.Source: §1 · p. 3
  • The approach reduces large-scale segmentation to annotating a single representative cell, supporting scalable, structurally consistent reconstruction of dense 3D woven architectures.Source: §1 · p. 3

2. Dataset

The study examines the as-woven reinforcement of a LEAP fan blade using X-ray CT, focusing its analysis on the blade root.

2. Dataset

  • The specimen is an as-woven LEAP fan-blade reinforcement before forming and matrix impregnation.Source: §2 · p. 3
  • X-ray CT imaging used 140 µm voxels, and the large part was scanned in four distinct lengthwise sections.Source: §2 · p. 3
  • The analysis uses the first scan of the root, a structurally important region with curved yarn paths and tightly packed architecture.The scanned volume measures 796 × 1848 × 2383 voxels, or 111 × 259 × 335 mm3.Source: §2 · pp. 3–4

3. Studying the weave periodicity

The weave’s periodic structure is identified from a challenging root-region ROI, then used to define and replicate a representative cell. The central cell is selected with boundary degradation and imaging artefacts in mind.

3. Studying the weave periodicity

  • The root-region ROI contains large, tightly packed weft yarns with unclear boundaries and limited contrast, making manual cross-section annotation difficult.Source: §3 · p. 4

3.1. Characterisation of the periodic structure

  • The three nearest-origin peaks of the 3D normalized autocorrelation identify translation vectors that preserve structural similarity and reveal weave periodicity; the three dominant linearly independent vectors define its periodic lattice.Figure 2 shows the autocorrelation along the u = 0, v = 0, and w = 0 planes.Source: Figure 2 · p. 5, §3.1 · p. 5

3.2. Constructing a periodic cell and ideal volume

  • The non-orthogonal basis defines a transformation between image coordinates and an orthonormal periodic coordinate system, where the unit cell is [0, 1]^3.The ROI is transformed and interpolated, and a central cell is extracted to minimize boundary effects.Source: §3.2 · p. 6
  • A central cell is preferred because periodicity deteriorates near component boundaries and textile-transition regions, where imaging artefacts may also affect reconstruction and registration.Source: §3.2 · p. 6
  • Tiling the cell along the periodic directions creates an exactly translationally periodic volume, which can be transformed back into the image reference frame.The extracted cell’s orthogonal views reveal the warp and weft organization and the difficulty of segmenting especially the weft cross-sections.Source: §3.2 · pp. 6–7

4. Segmentation of the unit cell

Warp yarns are grouped across periodic cell boundaries and fitted as smooth periodic paths. Weft yarns are detected after masking the warp yarns and extending the cell to expose boundary-crossing trajectories.

4.1. Warp yarns

  • Periodic boundary continuity lets physically separate warp segments be grouped as one yarn when they meet across opposite cell faces.The illustrated segment continues from A to B to C and wraps back to A in an adjacent cell.Source: §4.1 · p. 8, Figure 4 · p. 8
  • Warp positions are tracked slice by slice using cross-correlation between a fundamental cross-sectional mode and the tomographic slices.Tracking searches for the local correlation maximum within a restricted neighborhood, assuming limited displacement between consecutive planes.Source: §4.1 · p. 8
  • Fitting each tracked warp curve with a periodic 3D sinusoid gives a smooth, explicitly periodic path for propagation, while ignoring small local variations.Raw tracked paths could also be used if periodic continuity is maintained.Source: §4.1 · pp. 8–9, Figure 5 · p. 9

4.2. Weft yarns

  • Approximate elliptical masks centered on annotated warp positions remove warp regions while preserving cell periodicity, making remaining weft patterns more distinguishable.The ellipses approximate average warp cross-sections and are wrapped across opposite cell boundaries when they extend beyond the cell.Source: §4.2 · p. 10, Figure 6 · p. 10
  • Replicating the cell twice in each periodic direction exposes boundary-crossing weft yarns for detection using a 3D cross-correlation heatmap and Dijkstra paths.Paths are fitted by least squares with a periodic sine function and a few harmonics; the figures show the heatmap detection and fitted trajectories.Source: §4.2 · p. 11, Figure 7 · p. 11, Figure 8 · p. 12

5. Registration with a periodic textile

DVC registers the ideal periodic textile against the real volume by minimizing residuals while allowing displacement and grey-level corrections. A progressively refined, mechanically regularized finite-element solution balances image matching with plausible, periodicity-resolving kinematics.

5.1. Theoretical Framework

  • Registration minimizes the residual between the ideal reference and corrected real volume while jointly estimating displacement and spatially variable grey-level corrections.The corrections accommodate slight tomographic artefacts such as beam-hardening cupping.Source: §5.1 · p. 12
  • Finite-element fields are optimized with Gauss–Newton iterations and equilibrium-gap mechanical regularization to balance registration accuracy with mechanically admissible displacements.The regularization length controls the elastic constraints.Source: §5.1 · p. 13

5.2. Implementation and Convergence Strategy

  • Registration progressively reduces regularization length from 1600 to 50 voxels, retaining the lowest-residual solution at each stage as the next initial guess.Each stage stops when the displacement update falls below 0.01 or reaches 100 iterations.Source: §5.2 · p. 13
  • The final displacement field is described as balancing matching accuracy and mechanical plausibility, with residual minimized across the volume.The mesh discretization and regularization are used to maintain a physically meaningful field.Source: §5.2 · p. 13, §5.1 · p. 13
  • The 100×20×25-voxel tetrahedral mesh resolves the warp direction more finely than the unit-cell period while using coarser kinematics along the regular weft direction.The resulting kinematic resolution remains below the textile periodicity in relevant directions.Source: §5.2 · pp. 13–14, Figure 9 · p. 14

6. Registration results

Registration produces small, localized residuals and substantially fainter, nearly stationary slice residuals, supporting the conclusion that the global textile deformation was captured without systematic discretization bias. The largest deformations occur near the textile transition at the lower volume boundary.

6. Registration results

  • The squared residual norm decreases across iterations and regularization lengths, reflecting displacement-field refinement and smooth convergence.Figure 10 displays the residual-norm evolution by regularization length.Source: §6 · p. 14, Figure 10 · p. 15
  • Small, localized residuals mainly at yarn boundaries show no ill-behaviour and support reliable registration of the global textile deformation.The residual image is the difference between the reference and corrected deformed images.Source: §6 · p. 14, Figure 11 · p. 15
  • Final slice residuals are much fainter and almost stationary than the initial difference, with no systematic bias attributed to discretization or displacement-field freedom.The comparison spans three orthogonal slices of the reference, real, and corrected volumes.Source: §6 · p. 15, Figure 12 · p. 16, Figure 13 · p. 16
  • The converged analysis presents the displacement field and grey-level correction fields, with displacement magnitude shown in voxel units.The deformed mesh visualization magnifies deformation by a factor of two.Source: §6 · p. 17, Figure 15 · p. 18, Figure 17 · p. 19
  • The largest deformations localize near w ≈ 0, where the reference’s straight yarn columns correspond to curved yarns in the real volume during the dense-to-less-dense textile transition.The deformation is visible in the mid-plane along the weft direction.Source: §6 · p. 17, Figure 16 · p. 18

7. Mapping yarn paths onto the original volume

The annotated periodic yarn trajectories are propagated in the periodic volume, then mapped into the real CT volume using the inverse DVC transformation. The displayed paths include warp and weft yarns across a small region of the volume.

7. Mapping yarn paths onto the original volume

  • The periodic paths are propagated throughout the volume after the back transformation returns them to the original (u, v, w) coordinate system.The resulting periodic volume can be extended without limit.Source: §7 · p. 19
  • The inverse DVC transformation maps tracked periodic trajectories from the ideal configuration into the actual volume, accounting for large-scale geometric variations and distortions.The trajectories are propagated through the periodic volume before transport to the real state.Source: §7 · p. 19
  • Figure 19 visualizes warp and weft paths overlaid on a small region of the deformed CT volume, with the four original unit-cell yarns distinguished by color.The visualization includes a 3D view and mid-planes showing intersecting yarn paths.Source: §7 · pp. 19–20, Figure 19 · p. 20

8. Discussion

The discussion treats residuals as an intrinsic consistency check while noting that full-volume tracking error cannot yet be quantified against ground truth. It identifies compaction variation, deformable weft paths, and omitted local cross-sectional variation as boundaries or targets for further development.

8. Discussion

  • Without annotations for the studied region, direct ground-truth comparison and rigorous full-volume estimates of reconstruction uncertainty or tracking error are unavailable.Controlled geometric perturbations or synthetic architectures are proposed as possible quantitative validation routes.Source: §8 · pp. 20–21
  • Incorrect yarn paths or correspondences would produce large, weave-correlated residual structures, making residuals an intrinsic consistency indicator for the reconstruction.The paper reports that substantial identification errors would appear as topological differences in the residual field.Source: §8 · p. 21
  • Remaining residuals mainly reflect slight unit-cell compaction modulation, which the current uniform grey-level interpolation does not represent; explicitly modelling it is proposed.The proposed extension would treat compaction alterations similarly to the brightness and contrast fields.Source: §8 · p. 21
  • In the dense root, weft yarns are too deformable for the rigid elliptical model used effectively for warp yarns and require a more elaborate deformation description.Combining the framework with finer local tracking is suggested as a possible extension.Source: §8 · p. 21
  • The propagated paths induce idealized yarn cross-sections rather than representing local cross-sectional variation explicitly.The trajectories could feed deformable-yarn reconstruction such as the hollow shell method, where yarns are expanded and mechanically adjusted.Source: §8 · p. 22
  • Observed local non-orthogonality is treated as an expected draping or manufacturing distortion that the registration is intended to capture, not as a framework limitation.The periodic reference is aligned to local periodic directions rather than an imposed orthogonal frame.Source: §8 · p. 22

9. Conclusion

The conclusion presents periodicity as a structural prior for segmenting dense woven regions where yarn-by-yarn tracking is difficult. The framework supports large-scale reconstruction, intrinsic tracking validation, and modest computation.

9. Conclusion

  • High yarn density and interlacing make individual tracking from 2D images extremely challenging in the blade-root region.The conclusion describes the blade root as a complex, previously unexplored region of woven reinforcements.Source: §9 · p. 22
  • Annotating a minimal representative periodic cell propagates the weave structure across the volume, reconstructing thousands of warp and weft yarn trajectories with minimal input.The authors expect applicability to other woven composites with comparable near-periodic organisation.Source: §9 · p. 22
  • The framework enables robust yarn tracking in densely packed areas and efficient generation of large, coherent annotation datasets.The authors state that this improves segmentation performance and model scalability.Source: §9 · pp. 22–23
  • The approach provides intrinsic validation of tracking quality and does not require manual annotations or lengthy training.The authors note that manual labelling in the fan blade root is challenging and error-prone.Source: §9 · p. 23
  • Unit-cell segmentation takes less than 1 minute on a standard PC, and full registration analysis takes under 30 minutes.The authors contrast these times with the many hours manual segmentation would require for the studied region.Source: §9 · p. 23
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