Intelligent Manufacturing: A Fully Annotated Synthetic Dataset for Fiber Orientation Estimation

Abstract

This work introduces a fully annotated synthetic dataset designed to support machine learning-based estimation of fiber orientation in short-fiber reinforced polymers. The dataset comprises 55,092 high-resolution microscopy-like images generated through a physics-informed simulation pipeline that reproduces the morphological characteristics of real microstructures. Each micrograph contains a non-overlapping arrangement of ellipsoidal fiber cross-sections with controlled distributions of aspect ratio, in-plane orientation and areal fraction. These parameters are calibrated using descriptors extracted from X-ray microscopy of ABS-GF20 specimens processed via large-format material extrusion. For every synthetic image, the corresponding second-order orientation tensor is computed analytically from the exact fiber geometry, providing noise-free ground-truth annotations suitable for supervised learning and rigorous benchmarking. The dataset enables reproducible evaluation of deep learning models for orientation prediction and supports the development of automated workflows for composite characterization and intelligent manufacturing. Comprehensive documentation and the accompanying open-source Python code ensure transparency, facilitate reuse and allow users to extend or regenerate the dataset for materials science, computer vision and data-driven manufacturing research.

Background & Summary

Short-fiber reinforced polymers play a central role in modern manufacturing, offering a combination of high stiffness-to-weight ratio, tunable anisotropy and compatibility with high-throughput forming processes. Among these technologies, large-format additive manufacturing (LFAM) has emerged as a transformative platform that enables the production of meter-scale composite components with reduced tooling costs and unprecedented geometric freedom^1,2. The mechanical performance of these materials, however, depends critically on the underlying fiber architecture and, in particular, on the statistical distribution of fiber orientations that develops during processing. Flow-induced alignment governs stiffness, strength, thermal conductivity and residual stress, making fiber orientation a key descriptor for simulation, certification and structural design^3,4. In the context of LFAM, where deposition paths, bead geometry, cooling rates and rheological conditions fluctuate significantly, the resulting microstructure often exhibits a complex mixture of highly aligned regions and locally heterogeneous configurations, amplifying the need for reliable characterization tools^5,6.

Traditional approaches to fiber-orientation characterization rely on microscopy followed by segmentation and ellipse fitting. Scanning electron microscopy (SEM), optical microscopy and X-ray microtomography provide high-resolution images of fiber cross-sections, from which geometric descriptors such as major axis, minor axis and in-plane orientation are extracted⁶. These measurements are then mapped to orientation tensors, a mathematically compact representation of the orientation distribution that is widely used for constitutive modelling and simulation⁷. Although effective, such workflows are labor-intensive, sensitive to operator-dependent thresholding, inherently two-dimensional and difficult to scale to the thousands of samples required for robust statistical analysis. Even when automated image-processing pipelines are used, the reliable annotation of experimental micrographs remains a substantial bottleneck, particularly for data-driven methods that depend on large, diverse and consistently labelled datasets.

In parallel, machine learning (ML) and artificial intelligence (AI) techniques have gained traction in materials science and composite manufacturing. Convolutional neural networks (CNNs), encoder-decoder architectures and hybrid physics-informed models have demonstrated strong potential for predicting fiber orientation, stiffness tensors or morphological descriptors directly from micrographs^8–10. These methods substantially reduce inference time, sometimes by orders of magnitude, making them suitable for digital twins, in-line quality monitoring and real-time process control. More broadly, machine learning is becoming a pervasive tool in composite design, multiscale modelling and topology optimisation^11–13. In additive manufacturing specifically, deep learning has been applied to material-process-property relationships, defect detection and microstructure prediction, highlighting a clear trend towards data-driven optimisation¹⁴. However, the success of these methods depends fundamentally on the quantity and quality of training data, and the scarcity of large annotated datasets remains one of the most significant obstacles to the adoption of ML in composite microstructure analysis.

Synthetic data generation has therefore emerged as a powerful strategy to overcome the limitations of experimental datasets. In computer vision and robotics, physics-based rendering and generative models already play a central role in training perception systems, enabling the development of digital twins and reinforcement-learning agents capable of operating in real-world environments^15,16. In textiles and woven composites, deep learning models have been trained on digital simulations of weaving patterns to infer 3D architectures efficiently¹⁷. Within materials science, synthetic data is increasingly being used to accelerate discovery, quantify uncertainty and augment experimental datasets^18,19. Yet despite these advances, the materials community still lacks large-scale, openly available datasets of fiber microstructures with reliable ground-truth orientation annotations.

Recently, physics-informed synthetic image generation has proven to be a compelling alternative to conventional microscopy-based approaches. By simulating the geometric intersection of cylindrical fibers with a 2D imaging plane, it becomes possible to generate realistic microscopy-like microstructures while preserving exact knowledge of orientation tensors, aspect ratios and areal fractions. This idea has been explored in the context of LFAM, where datasets of synthetic images were used to train CNNs that predict fiber orientation directly from binarised micrographs, achieving high accuracy and demonstrating strong agreement with conventional methods^5,6. The main advantage of synthetic datasets lies in their scalability and the absence of annotation noise: precisely controlled distributions of aspect ratio, density and orientation can be generated at negligible cost, and the ground truth is known analytically. Moreover, synthetic datasets enable balanced sampling across the orientation-tensor space, facilitating the training of machine learning models that generalise well across isotropic, weakly anisotropic and highly aligned regimes.

Orientation tensors provide a compact and physically meaningful descriptor of fiber alignment and are widely used in continuum models and constitutive laws^3,7. Recent research highlights the importance of quantifying uncertainty in orientation reconstruction, since small perturbations in image segmentation or ellipse fitting can propagate into significant variations in predicted mechanical response²⁰. This sensitivity motivates the use of synthetic datasets both for benchmarking and for developing robust estimators. Synthetic microstructures also offer the opportunity to evaluate the effect of sampling density, noise, partial visibility and segmentation artefacts in a controlled manner, allowing researchers to systematically analyse the limits of orientation-reconstruction algorithms^8,9.

At the same time, synthetic datasets must be statistically representative of real microstructures in order to be useful for training predictive models. Advances in LFAM process characterisation have shown that fiber aspect ratios, areal fractions and orientation biases can be extracted from X-ray microscopy (XRM) and SEM, and then used to calibrate physics-based simulation pipelines⁵. Such pipelines incorporate geometric constraints (e.g. non-overlapping ellipses), morphological variability and experimentally derived distributions of orientation and aspect ratio. The resulting images capture the characteristic texture and morphology of microscopy slices, while preserving full analytical access to the underlying fiber geometry. This hybrid approach, experimental calibration combined with physics-based generation, offers a transparent, interpretable and reproducible alternative to GAN- or VAE-based methods, which, despite their generative power, may suffer from mode collapse, limited interpretability or unphysical artefacts^18,19.

The increasing importance of synthetic datasets in engineering disciplines has led to broader efforts to integrate data generation, simulation and AI within digital manufacturing workflows. In the context of composite materials, the potential applications are extensive: process optimisation, predictive simulation, inverse design, uncertainty quantification and adaptive control all benefit from reliable microstructural descriptors. Digital twins for additive manufacturing, for example, require rapid estimation of fiber orientation to assess stiffness evolution and thermal behaviour in real time^14,15. Synthetic datasets make it possible to train such estimators without the overhead of exhaustive microscopy campaigns and provide a platform for testing predictive models under a wide range of controlled scenarios.

Despite this momentum, no open and fully annotated dataset existed prior to this work that simultaneously offered realistic microscopy-like textures, complete ground-truth orientation tensors, calibrated morphological statistics and large sample size. Existing studies typically rely on small datasets curated for specific experiments, limiting the generalisability and reproducibility of machine learning models^6,8. The lack of open benchmarks hampers comparison between methods and slows down progress in automated fiber-orientation analysis. Furthermore, many datasets focus solely on global orientation or average measures, neglecting the rich morphological diversity present in LFAM-processed composites, where local anisotropy can vary significantly across the bead cross-section⁴. A comprehensive dataset must therefore capture microstructural variability across tens of thousands of images, spanning a broad and well-balanced region of the orientation-tensor space.

To address these gaps, the present dataset (Fully Annotated Synthetic dataset (FAS-DS)²¹) introduces a large-scale, physics-informed collection of 2D synthetic microstructures, each annotated with exact fiber geometry and associated second-order orientation tensors. The images reproduce the characteristic features of microscopy slices, including heterogeneous alignment, variable aspect ratios and experimentally derived areal fractions. By generating a statistically balanced set covering isotropic, intermediate and highly aligned configurations, the dataset facilitates the training and benchmarking of machine learning models for fiber-orientation estimation. Its scale enables comprehensive validation across morphological regimes, while its reproducibility ensures that researchers can extend or regenerate subsets under modified assumptions. The dataset is accompanied by open-source Python code for image generation, annotation and tensor computation, thereby ensuring full transparency and reusability²². In this way, it supports ongoing efforts to integrate synthetic data, physics-informed modelling and AI within digital-manufacturing pipelines.

Overall, this dataset provides an essential resource for the composite-materials and manufacturing communities. By bridging the gap between experimental microscopy and data-driven modelling, it establishes a foundation for reproducible benchmarking and accelerates the development of ML-based fiber-orientation estimators. It also opens new opportunities for studying microstructural variability, quantifying uncertainty and designing robust algorithms for orientation prediction. As synthetic data becomes increasingly central to materials informatics, large-scale datasets such as this one will play a vital role in advancing AI-driven composite characterisation and supporting the next generation of digital twins, intelligent manufacturing systems and simulation-informed design frameworks.

Methods

Synthetic microstructure generation

The synthetic microstructures included in this dataset were generated through a fully deterministic, physics-informed pipeline designed to reproduce the morphological characteristics of short-fiber reinforced polymers while ensuring complete control over geometric parameters, spatial constraints and statistical distributions. The objective is to produce microscopy-like binary images with analytically known ground-truth orientation tensors, enabling reproducible benchmarking and large-scale training of machine-learning models. The pipeline comprises three principal stages: (i) parameter sampling, (ii) spatial placement of non-overlapping ellipses within a bounded 2D domain and (iii) analytical computation of orientation tensors and metadata. Each stage is documented to allow full reproducibility and extension by external users.

The microstructural domain is defined as a rectangular image of fixed resolution (typically 512 × 384 px), chosen to approximate the aspect ratio of experimental microscopy frames. All geometrical quantities, ellipse axes, centroid positions, in-plane angles and areas, are expressed in pixel units, which allows the images to be directly used for training convolutional neural networks or for comparison with thresholded SEM/XRM micrographs. The simulation treats each fiber as the intersection of an infinitely long rigid cylinder with the imaging plane. The resulting cross-section is an ellipse characterised by a semi-minor axis a, a semi-major axis b and an in-plane angle ϕ. These parameters are calibrated to match experimentally observed fiber morphologies, as reported in previous LFAM microstructure studies^5,6.

Parameter sampling governs the statistical diversity of fiber geometries and orientations. The semi-minor axis a is sampled from a narrow distribution centred around a base value a_param with a small variation Δa, reproducing the consistent fiber diameter observed in ABS-GF20 composites. The semi-major axis b is drawn from a predefined interval $\left[b_{\min },b_{\max }\right]$, yielding aspect ratios between approximately 5:1 and 15:1, which is consistent with values reported for glass fibers in extrusion-based processes⁴. The in-plane orientation ϕ is sampled using a mixture distribution that reflects both the global alignment imposed by LFAM deposition and local heterogeneity. Specifically, a predominant proportion of fibers (~90%) is drawn from a normal distribution $\varphi ~\mathcal{N}\left(0^{\circ },{\sigma }_{\varphi }^2\right)$, where σ_ϕ is typically 5–10^°, capturing bead-scale alignment. The remaining fibers are sampled uniformly from [−90^°, 90^°], ensuring the presence of misaligned or curved-flow regions that commonly appear in turning segments or near bead boundaries. The sampling process is fully configurable, and the parameters used in each generated image are recorded in the accompanying metadata files, facilitating sensitivity analyses and downstream model explainability.

Fiber placement proceeds through an iterative stochastic algorithm that enforces strict non-overlap among ellipses. A spatial index (STRtree from the Shapely library) is used to efficiently query nearby fibers and detect geometric intersections. For each candidate fiber, a centroid (x, y) is drawn uniformly from the domain, and an ellipse with parameters (a, b, ϕ) is instantiated. Intersection tests are performed between the candidate ellipse and all previously accepted ellipses. If any overlap is detected, defined as positive area intersection computed via polygonal approximation, the candidate is rejected; otherwise, the ellipse is accepted and appended to the spatial index. This procedure continues until the cumulative area of all accepted ellipses reaches a prescribed target area fraction p_target ∈ [0.15, 0.50], consistent with experimentally measured fiber volume fractions in LFAM-deposited beads. The algorithm includes an upper bound on the number of attempts to avoid infinite loops in high-density configurations; the actual number of attempts and successfully placed ellipses are stored as metadata for each image, enabling users to quantify packing difficulty and correlate it with morphological characteristics or ML model performance.

To guarantee that the rendered microstructures are consistent with microscopy segmentation, only the intersection area of each ellipse with the image boundaries is retained. Fibers partially outside the domain contribute only the visible portion of their ellipse, and all geometric descriptors (projected area, centroid and orientation) are computed based on the truncated shape. This step mimics real microscopic fields of view, where fibers are frequently clipped by the image edges, and is important for generating realistic training data for segmentation or orientation-estimation algorithms. The final image is rendered as a binary mask with white ellipses on a black background. This representation intentionally mirrors thresholded SEM/XRM images used in prior LFAM fiber-orientation studies⁶, ensuring compatibility with conventional CNN architectures.

An essential feature of this dataset is the analytical computation of the second-order orientation tensor A for every image. For each fiber i, the apparent aspect ratio b_i/a_i is used to infer an out-of-plane tilt angle β_i via the relation $\sin {\beta }_i=a_i/b_i$, following the geometric interpretation of cylindrical inclusions intersecting a plane⁷. The in-plane orientation ϕ_i is directly obtained from the sampling stage. The direction vector of fiber i is then expressed in three dimensions as

$${\mathbf{p}}_i=\left(\begin{array}{c}\hfill \cos {\varphi }_i\cos {\beta }_i\hfill \\ \hfill \sin {\varphi }_i\cos {\beta }_i\hfill \\ \hfill \sin {\beta }_i\hfill \end{array}\right).$$

The global orientation tensor is computed as the average dyadic product

$$A=\frac{1}{N}\sum _{i=1}^N{\mathbf{p}}_i\otimes {\mathbf{p}}_i,$$

yielding components A_xx, A_yy and A_zz that satisfy $\mathrm{tr}\left(A\right)=1$. These components quantify the degree of anisotropy in the synthetic microstructure and are widely used in continuum-mechanics models for injection-moulding and additive-manufacturing flows³. By construction, the computed orientation tensor represents the exact ground truth of the synthetic image, free from segmentation errors or ellipse-fitting uncertainty. The dataset therefore enables rigorous evaluation of ML estimators, including their sensitivity to noise, morphology and sampling density.

Representative synthetic microscopy-like images from the dataset are shown in Fig. 1. Pictures (a-f) display binary micrographs spanning a broad range of fiber-orientation states, from highly aligned configurations (a,b) to quasi-isotropic patterns (f). Each sample corresponds to a 512 × 384 pixel binary image in which white ellipses depict individual fiber cross-sections against a black background. The tensor components (A_xx, A_yy, A_zz) reported for each panel represent the analytically computed ground-truth orientation tensor stored in the metadata accompanying the full dataset of 55,092 images.

Fig. 1.

Representative synthetic fiber micrographs spanning from highly aligned to quasi-isotropic orientation states.

Alongside the orientation tensor, the full per-fiber geometric dataset is exported in a comma-separated values (CSV) file sharing the same basename as the corresponding image. Each file contains per-ellipse descriptors including centroid coordinates, axis lengths, orientation, individual ellipse area, truncated intersection area and derived quantities such as aspect ratio and inclination angle β_i. The files also record global parameters such as the target and achieved area fraction, image dimensions, sampling bounds and the total number of placement attempts. This rich metadata supports advanced statistical analyses, including parameter-space mapping, fiber-density studies, packing-efficiency characterisation and correlation analyses between morphological properties and orientation anisotropy⁵. The complete dataset thus provides not only training images for machine-learning applications but also a detailed corpus for studying fiber-level interactions and microstructural variability.

Finally, the entire generation procedure is openly available as Python code²², ensuring complete transparency and enabling users to modify sampling distributions, introduce new morphological features (e.g. curved fibers, polydispersity, defects) or extend the framework to three-dimensional simulations. Because all randomness is governed by explicit pseudo-random number generators with user-controlled seeds, the pipeline supports deterministic regeneration of the dataset for validation and reproducibility studies. This makes the present synthetic microstructure generator a robust and extensible tool for the composite-materials, additive-manufacturing and machine-learning communities.

Geometric parameterization

The geometric parameterization defines the fundamental building blocks of the synthetic microstructures and establishes the mathematical assumptions that connect the simulated ellipses to the physical behaviour of short fibers embedded in a polymer matrix. Because each fiber is modelled as the planar intersection of a three-dimensional cylindrical inclusion with the imaging plane, a consistent and physically informed parameterization is essential for reproducing the morphological characteristics of real micrographs, ensuring comparability with experimental datasets and enabling exact analytical computation of orientation tensors⁷. The geometric framework adopted here emphasises reproducibility, control and physical interpretability, allowing users to modify the structural assumptions in a transparent manner.

Each fiber cross-section is represented by a two-dimensional ellipse parameterised by three primary quantities: the semi-minor axis a, the semi-major axis b and the in-plane orientation ϕ. These parameters together dictate the fiber’s projected shape, size and orientation within the 2D imaging domain. The semi-minor axis a corresponds to half of the projected width of the fiber, which in turn reflects the actual fiber diameter under the assumption of uniform cylindrical geometry. Experimental X-ray microscopy (XRM) and SEM imaging of ABS-GF20 composites consistently show narrow distributions of fiber diameters, typically around 12-14 μm, with relatively small variance⁵. To reflect this behaviour, a is sampled from a nearly constant distribution centred around a base parameter a_param with a small variation Δa. This approach captures realistic manufacturing tolerances while maintaining consistency across the dataset. All values are expressed in pixel units, which allows direct comparison between synthetic and binarised experimental micrographs.

The semi-major axis b governs the apparent fiber length in the imaging plane and plays a key role in reproducing the aspect-ratio distribution of real fibers. Since the true three-dimensional fiber length does not directly appear in a 2D section, b represents the effective projected length, which depends on both the real fiber length and the out-of-plane intersection angle. Empirical distributions derived from LFAM micrographs indicate that observed aspect ratios (i.e. b/a) commonly range from 4:1 to 20:1, depending on processing history and measurement orientation^4,6. To capture this variability, b is sampled from a uniform or truncated-normal distribution with bounds $\left[b_{\min },b_{\max }\right]$, where the default limits produce aspect ratios of approximately 5:1 to 15:1. These values were selected to balance physical realism with computational stability during packing. The use of controlled aspect-ratio distributions ensures that the dataset spans the full morphological space encountered in LFAM, including configurations with high anisotropy and regions where fibers appear nearly circular due to steep out-of-plane tilt angles.

The in-plane orientation ϕ defines the rotation of the ellipse with respect to the horizontal axis of the image. This parameter is of central importance for orientation-tensor computation and for training machine-learning models that estimate fiber alignment directly from micrographs. In real LFAM-deposited materials, fiber alignment is strongly influenced by the local bead-deposition direction, producing a predominant alignment axis, but also includes stochastic deviations due to secondary flow, bead curvature, cooling-induced disturbances and local rheological effects^1,2. To model this behaviour realistically, the synthetic microstructure generator employs a mixture distribution: the majority of fibers (typically 90%) are assigned orientations sampled from a zero-centred normal distribution with standard deviation σ_ϕ in the range of 5-10^∘, while a minority (10%) are drawn from a uniform distribution over [ − 90^∘, 90^∘]. This approach captures both the dominant alignment behaviour characteristic of extrusion processes and the presence of misaligned or cross-flow fibers. The relative proportions and statistical parameters are fully configurable and recorded as metadata, supporting rigorous sensitivity studies and domain-shift analyses for machine-learning applications.

In addition to the primary geometric parameters (a, b, ϕ), several derived quantities are computed to support subsequent analysis. The aspect ratio, AR = b/a, provides a convenient scalar measure of elongation and is widely used in statistical characterisation of fiber populations. Its distribution strongly influences the achievable packing density and affects mechanical-anisotropy predictions in modelling frameworks³. The ellipse area, A_ellipse = πab, quantifies the contribution of a given fiber to the overall area fraction and determines its likelihood of interacting with neighbouring fibers during packing. Because some fibers are clipped by the image boundaries, a truncated intersection area is computed for each ellipse through polygonal intersection with the domain limits. This truncated area, rather than the full ellipse area, governs the evaluation of the final achieved area fraction p_achieved and ensures consistency with what would be observed in a real micrograph.

The geometric parameterization also enables inference of out-of-plane fiber inclination, an otherwise unobservable property in a two-dimensional section. Under the cylindrical-fiber model, the inclination angle β is related to the observed ellipse axes by $\sin \beta =a/b$. Although this relation assumes exact cylindrical geometry, it provides a consistent means of estimating a three-dimensional orientation vector from two-dimensional measurements, forming the basis of the analytical orientation tensor used throughout this dataset. This geometric link ensures that the dataset not only provides visually realistic microstructures but also carries physically meaningful three-dimensional orientation information necessary for continuum-scale constitutive modelling and AI-driven property prediction^7,10. The ability to compute β analytically, without segmentation or inference error, distinguishes synthetic datasets from experimental ones, where measurement noise introduces uncertainty into tensor estimation²⁰.

For clarity, the default ellipse-parameter distributions used in this work can be summarised as:

• Semi-minor axis: a = 6 ± 1 px, representing the fiber diameter calibrated from XRM data.

• Semi-major axis: b ∈ [30, 100] px, producing aspect ratios between 5:1 and 15:1.

• In-plane orientation:

  • 90% of fibers sampled from $\varphi ~\mathcal{N}\left(0^{\circ },5^{\circ }\right)$ to emulate LFAM-induced alignment.
  • 10% sampled uniformly from [ − 90^°, 90^°] to model local misalignment and edge effects.

These distributions reproduce the anisotropic microstructure observed in LFAM-processed materials while enabling controlled variability for machine learning. Figure 2 provides an overview of the physics-informed pipeline used to generate the synthetic fiber microstructure dataset. Experimental X-ray microscopy (XRM) and SEM images are first analysed to extract key morphological descriptors (fiber aspect ratio, area fraction and orientation bias). These parameters are then used as inputs for a Python-based simulator that places non-overlapping ellipses, computes the associated second-order orientation tensor and renders microscopy-like binary images. Repeating this process yields the final dataset of 35,893 fully annotated images.

Fig. 2.

Overview of the synthetic fiber-image generation pipeline. Experimental XRM/SEM images are used to calibrate morphological descriptors, which feed a physics-informed simulator that generates non-overlapping ellipses, computes the associated orientation tensor and renders binary micrographs with full metadata.

Ellipse placement uses a spatial index (STRtree from Shapely) to efficiently detect geometric intersections. Candidate ellipses that overlap previously placed ellipses are rejected. The algorithm terminates once the accumulated fiber area fraction reaches the target value (typically around 20%), matching the experimentally observed fiber coverage in XRM virtual slices. Images are rendered as binary micrographs with white ellipses on a black background, emulating thresholded SEM/XRM images and ensuring compatibility with standard computer-vision pipelines.

Orientation tensor computation

Each synthetic micrograph is accompanied by an analytically computed second-order orientation tensor A based on the ground-truth geometry of all fibers in the image. For each ellipse, the out-of-plane angle β is estimated from its aspect ratio through

$$\sin {\beta }_i=\frac{a_i}{b_i}.$$

The in-plane orientation angle ϕ_i is directly known from the generation routine. The diagonal components of the tensor are then computed using the Advani-Tucker formulation⁷:

$$A_{xx}=\frac{1}{N}\sum _{i=1}^N{\sin }^2{\beta }_i,$$

$$A_{yy}=\frac{1}{N}\sum _{i=1}^N{\cos }^2{\beta }_i{\sin }^2{\varphi }_i,$$

$$A_{zz}=\frac{1}{N}\sum _{i=1}^N{\cos }^2{\beta }_i{\cos }^2{\varphi }_i,$$

where N is the total number of fibers in the micrograph. All tensors satisfy $\mathrm{tr}\left(\mathbf{A}\right)=1$ within numerical precision.

Tensor components are included in each image filename for traceability, and a separate metadata file stores the values of (A_xx, A_yy, A_zz), the fiber count, area fraction and additional geometric descriptors.

Calibration using X-ray microscopy

Simulation parameters were calibrated using virtual slices extracted from XRM scans of LFAM-processed ABS-GF20 specimens⁶. The XRM volumes provided reference distributions for:

• fiber area fraction (19–21%),

• apparent aspect ratios,

• in-plane orientation dispersion,

• fiber count per field of view (approximately 750–800).

These descriptors guided the selection of a, b, ϕ and the area-fraction target in the synthetic generator. Although the simulation does not explicitly model flow dynamics or thermal gradients, its statistical calibration ensures morphological fidelity to real microstructures.

The final dataset comprises 55,092 synthetic images, each with its corresponding orientation tensor and metadata. Images are stored in JPG format, while labels are saved in CSV files. Each dataset entry contains:

• the binary micrograph (image.png),

• the tensor components (A_xx, A_yy, A_zz),

• the number of fibers,

• the total fiber area fraction.

The dataset is organised into folders representing different anisotropy levels, enabling balanced sampling and controlled experimental design. The Python code used to generate and annotate the dataset is publicly available in an open-access repository²². The repository enables full reproducibility and supports extensions such as simulating porosity, curved fibers or 3D volumetric data.

Representative XRM images used for the multi-ROI analysis are shown in Fig. 3, where each fiber is treated as an independent region of interest.

Fig. 3.

XRM images used for multi-ROI analysis, in which each fiber is treated as an independent region of interest (ROI) for quantitative calculations. From left to right, the images correspond to consecutive cross-sections of the same field of view, illustrating the evolution of fiber orientation with depth in the 3D-printed part.

To further support the calibration process, Fig. 4 shows a comparison of an experimentally microscopy image and its processed version, which is used for quantitative analysis. The raw micrograph is segmented to identify individual fibres, which are then approximated as ellipses to extract geometric and orientation descriptors. As can be seen, the synthetic images produced by the proposed methodology closely replicate the main morphological and orientational features of the real microstructure, such as fibre shape, spatial distribution and alignment patterns. This strong agreement demonstrates that the synthetic generation approach effectively captures the key characteristics of the material, thereby supporting the realism and reliability of the published dataset.

Fig. 4.

Real fibrous microstructure (top left) and its binary segmentation (right)⁶.

Data Records

The Fully Annotated Synthetic dataset (FAS-DS)²¹ is available at Zenodo repository 10.5281/zenodo.17856003. The released dataset comprises 55,092 synthetic micrographs of short-fiber reinforced polymer microstructures. Each image is accompanied by a metadata file containing per-fiber geometric descriptors and the analytically computed second-order orientation tensor. All data are provided in open, human-readable formats (PNG for images and CSV for metadata) to ensure long-term accessibility, interoperability and straightforward integration into machine-learning workflows.

Each synthetic micrograph is a binary image of resolution 512 × 384 pixels, where white ellipses represent individual fiber cross-sections on a black background, mimicking thresholded SEM/XRM images. The dataset spans a broad range of anisotropy levels, from nearly isotropic configurations to highly aligned orientations, with fractional anisotropy values covering the full admissible range. In total, the collection contains 5,354,445 individual ellipses, corresponding to an average of 97.2 fibers per image. Global statistics (fiber count, area fraction, anisotropy and geometric descriptors) are summarised in accompanying log files and dataset-level tables.

All image files follow a consistent naming convention that embeds the analytically computed orientation-tensor components, for example:

Axx,Ayy,Azz.jpg

0.0003,0.9970,0.0027.jpg

This convention enables rapid indexing of the dataset and facilitates the construction of supervised learning pipelines without requiring a separate label file. Each image corresponds to an independent draw of geometric parameters and spatial configurations, ensuring broad coverage of the orientation-tensor and morphological parameter spaces.

For every micrograph, a corresponding CSV file stores the complete set of analytical labels derived from the ground-truth geometry of all fibers. These metadata files are organised as one CSV per image and include both global image-level quantities and fiber-resolved descriptors. A typical record contains:

• image_name: filename of the corresponding JPG micrograph,

• Axx, Ayy, Azz: second-order orientation-tensor components for the full image,

• fiber_count: total number of ellipses in the image,

• area_fraction: fraction (or percentage) of the image domain covered by fibers,

• per-fiber geometric descriptors such as centroid coordinates (x, y), semi-minor and semi-major axes (a, b, in pixels), in-plane orientation angles phi (degrees), ellipse area and visible intersection area (ellipse_area, intersection_area),

• packing-related quantities, including target and achieved area (target_area, final_area) and corresponding densities (p_target, p_achieved),

• generator diagnostics such as total_attempts and num_ellipses, which document convergence and packing efficiency.

All fields follow consistent units and formats to facilitate automated parsing and integration into data-processing pipelines. These metadata files enable full traceability and allow users to recompute orientation tensors, derive additional morphological descriptors or perform customised filtering and subsampling.

The publicly available repository is organised into distinct directories to separate image data, per-image metadata, global logs and source code:

• /images/: all JPG micrographs (binary masks) representing synthetic fiber microstructures,

• /csv_metadata/: one CSV file per image containing the complete set of fiber-level and image-level descriptors,

• /code/: Python scripts and example Jupyter notebooks for loading, visualising and regenerating the dataset.

All records are distributed under an open licence to promote reuse in materials science, image analysis and machine-learning applications.

Repository contents

The publicly available repository includes:

• the full dataset of synthetic micrographs,

• analytical labels and per-image metadata in CSV format,

• global logs and dataset summary files,

• the Python scripts used to generate and annotate the dataset,

• example notebooks illustrating how to load, visualise and process the data.

All data files are provided under an open licence to facilitate reuse in materials science, machine learning and computational microscopy research.

Technical Validation

All data generated in this work are released as a fully annotated dataset of synthetic fiber microstructures specifically designed for machine-learning-based orientation estimation. Each microscopy-like image is paired with its analytically computed second-order orientation tensor and extensive per-image metadata. To validate the dataset, we assess four key dimensions: internal consistency, morphological realism, spatial statistics and tensor-space coverage—criteria that collectively determine its suitability for reproducible benchmarking and model development.

Figure 5 shows representative examples of microscopy-like images across three anisotropy regimes: (i) isotropic (low fractional anisotropy, FA), (ii) intermediate anisotropy and (iii) highly aligned microstructures. These examples highlight the range of textures, fibre densities and alignment patterns present in the dataset. All images are generated using a physics-informed simulator that enforces strict non-overlap constraints and provides exact analytical orientation-tensor annotations.

Fig. 5.

Representative synthetic microstructures drawn from three anisotropy regimes: isotropic (low FA), intermediate anisotropy and highly aligned (high FA). Each image is generated by the physics-informed simulator and annotated with its analytical second-order orientation tensor.

A quantitative assessment of orientation-tensor coverage is shown in Fig. 6. The joint distribution of (A_xx, A_yy, A_xy) demonstrates that the dataset spans the full continuum between isotropic and strongly aligned configurations. The A_xx-A_yy distribution adheres to the expected constraint A_xx + A_yy ≈ 1, and microstructures populate both sides of the isotropy line A_xx = A_yy without leaving gaps, even in extreme anisotropy regimes. The A_xx-A_xy map shows a symmetric distribution of positive and negative shear components, indicating balanced sampling of clockwise and counterclockwise fibre orientations. Together, these statistics confirm broad and unbiased coverage of the physically admissible tensor space.

Fig. 6.

Coverage of the second-order orientation-tensor space (A_xx, A_yy, A_xy) across the full dataset. The distributions show continuous, balanced sampling from nearly isotropic to highly aligned microstructures and symmetric populations of positive and negative shear components.

Morphological realism is validated in Fig. 7, which reports statistics from 100,000 simulated fibres sampled from the generator. The aspect-ratio distribution (mean 7.59) is positively skewed, reflecting the predominance of elongated fibres characteristic of short-glass-fibre composites such as ABS-GF20. The orientation distribution shows a strong peak near 0^∘ due to the imposed alignment bias, while retaining substantial variability-mimicking local flow-induced misalignment. The joint distribution of semi-axes (a, b) confirms tight control over fibre diameter and a broader spread of projected fibre lengths, consistent with physical intersection patterns. The heavy-tailed ellipse-area distribution further captures the coexistence of short transverse cuts and long oblique intersections. These observations demonstrate that the generated fibre geometries are realistic, diverse and physically interpretable.

Fig. 7.

Morphological statistics for 100,000 simulated fibers, including aspect ratio, in-plane orientation angle, semi-axis distributions and ellipse area. The results confirm realistic geometric variability consistent with short-fiber composite microstructures.

Figure 8 summarises the distribution of fractional anisotropy (FA) across the dataset. The histogram exhibits full coverage of the range [0, 1], capturing isotropic, weakly anisotropic and strongly aligned regimes. The FA-A_xx relationship, coloured by A_yy, displays a monotonic trend consistent with the geometric behaviour of aligned fibre populations. This result provides an internal validation of the analytical tensor computation and confirms that the synthetic microstructures behave in accordance with physical expectations.

Fig. 8.

Global distribution of fractional anisotropy (FA) across the dataset and its relationship with the horizontal tensor component A_xx (coloured by A_yy). The plots confirm full FA coverage and the expected coupling between tensor components and anisotropy level.

The generator’s ability to reproduce prescribed packing densities is validated in Fig. 9. The left panel compares target and achieved area fractions for thousands of simulations, revealing a tight clustering around the identity line, p_target = p_achieved. This indicates that the packing routine successfully reaches the desired densities across the full parameter space. The right panel examines the packing deficit Δp = p_target − p_achieved as a function of mean aspect ratio. As expected, highly elongated fibres exhibit slightly larger deficits due to geometric constraints, but deviations remain modest and do not compromise generator robustness.

Fig. 9.

Performance of the synthetic microstructure generator. (Left) Comparison between target and achieved area fractions across all images, showing strong agreement along the identity line. (Right) Packing deficit as a function of mean aspect ratio, indicating mild decreases in packing efficiency for highly elongated fibres.

At the dataset level, fibre counts vary widely, from fewer than 50 to more than 800 fibres per image, supporting machine-learning models that must generalise across sparse and dense microstructures. Figure 10(a) reports the distribution of fibre counts, while Fig. 10(b) shows the dependence of FA on fibre density. As expected, dense packings restrict alignment and therefore favour lower FA values, whereas highly aligned configurations tend to be sparser. Importantly, examples exist across the full FA range for all densities.

Fig. 10.

Global statistics of fiber count and anisotropy.

Additional statistical relationships are consolidated in Fig. 11. The correlation matrix reveals strong, physically interpretable couplings between FA and the tensor components A_xx and A_yy, while geometric descriptors such as aspect ratio and area fraction show only weak correlations with orientation. This indicates that morphological and orientational parameters are sampled largely independently—an essential property for designing controlled ML experiments and avoiding unintended biases.

Fig. 11.

Correlation structure among geometric and tensorial descriptors, including FA, mean aspect ratio, area fraction and the analytically computed orientation-tensor components. The patterns confirm physically meaningful relationships without unintended couplings between morphology and orientation.

Spatial realism is assessed in Fig. 12. The centroid-density map reveals a uniform spatial distribution with no clustering or voids, confirming unbiased fibre placement. The nearest-neighbour distance distribution is unimodal and consistent with random non-overlapping packings. Quadrant-wise comparisons of nearest-neighbour distances and local orientation distributions show no detectable boundary artefacts or directional biases. This spatial homogeneity is crucial for machine-learning pipelines, as spurious regularities could bias convolutional filters or impair generalisation to experimental data.

Fig. 12.

Spatial statistics of representative high-density microstructures. Top-left: Spatial density of fiber centroids. Top-right: Nearest-neighbour distance distribution. Bottom-left: Quadrant-wise comparison of nearest-neighbour distances. Bottom-right: Local orientation distributions. Together, these analyses confirm spatial realism, homogeneity and the absence of boundary artefacts.

Overall, the synthetic dataset exhibits broad, balanced and physically meaningful coverage of the microstructure-anisotropy landscape. The combination of millions of individually parameterised fibers, wide variability in geometric descriptors and uniform sampling of the orientation-tensor space ensures that the dataset is well suited for training machine-learning models, conducting statistical analyses of fiber networks and benchmarking orientation-estimation algorithms under controlled yet realistic conditions.

Usage Notes

The dataset is intended to support research in machine learning, composite characterisation, microstructure modelling and digital manufacturing. Each synthetic micrograph is accompanied by a CSV file containing per-fiber descriptors and the corresponding second-order orientation tensor. Users may directly load the images for computer-vision applications or operate exclusively on metadata files for statistical analysis, benchmarking, or model validation.

The dataset follows a consistent naming convention, where each image and its associated CSV file share an identical filename encoding the ground-truth orientation tensor. This ensures full traceability between visual content and analytical descriptors. The CSV files include both geometric properties of each ellipse (e.g., semi-axes, orientation angle, centroid position, intersection area) and global parameters such as achieved area fraction, number of fibers, and the analytically computed orientation tensor. A complete description of the columns is provided in the accompanying documentation.

Because the images are synthetic and analytically annotated, they contain no segmentation noise, missing fibers, artefacts, or operator bias. This makes the dataset especially suitable for benchmarking supervised learning methods and for generating controlled experiments in which specific aspects of microstructure variability (e.g., anisotropy, density, aspect-ratio distribution) can be isolated and quantified. When training neural networks, researchers are encouraged to apply data augmentation strategies that mimic real microscopy imperfections (e.g., blur, partial occlusion, contrast variations) to enhance robustness.

Users may also regenerate new datasets by modifying the simulation parameters included in the code repository. This allows exploring custom distributions of fiber orientations, aspect ratios, or packing densities, as well as designing targeted training sets for specialised tasks such as uncertainty quantification, domain adaptation, or sensitivity analysis. No restrictions apply to reuse, modification or redistribution of the dataset beyond attribution requirements of the license.

To ensure both accessibility and reproducibility, the synthetic images can also be directly regenerated by executing the Python code publicly available in²². This guarantees full reproducibility of the dataset and enables users to generate additional samples under identical or modified conditions. While previous work⁶ employed synthetic data primarily as a tool for training a specific deep learning model, the present dataset is explicitly released as a standalone, reusable resource designed for broad applications beyond a single methodological framework. At the same time, the dataset is distributed as a ready-to-use collection of images and metadata files, allowing researchers without programming expertise to directly employ it for training, validation and benchmarking of artificial intelligence models without the need to run the generation code. Advanced users may leverage the open-source implementation to customise the dataset or extend it to new scenarios, thus combining ease of use with full flexibility.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the authors used ChatGPT in order to check grammar and style. After using this tool/service, the authors reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.

Author contributions

All authors contributed to the study conception and design. Data collection and analysis were performed by C.G.G. C.G.G and J.A.G.M collected the samples and performed the experiments. All authors read and approved the final manuscript.

Funding

This research received partial funding from the Government of Spain under the project PID2023-151110OB-I00, and from the Generalitat Valenciana through projects CIPROM/2022/3, CIACIF/2021/286, and CIBEFP/2024. César García-Gascón is supported by a predoctoral contract funded under CIACIF/2021/286 and has also received a mobility grant for a research stay under reference CIBEFP/2024. Javier Bas-Bolufer is funded through the project CIPROM/2022/3. All co-authors are contributors within the framework of the national project PID2023-151110OBI00. Funding for open access charge: CRUE-Universitat Politècnica de València.

Data availability

The dataset described in this study is openly available in the Zenodo repository at 10.5281/zenodo.17856003. The repository contains the complete collection of 55,092 synthetic microstructure images together with their corresponding CSV metadata files. Each image is provided in PNG format, and each CSV file includes per-fiber geometric descriptors as well as the analytically computed second-order orientation tensor. Additional global statistics, summary tables and full documentation are also included to facilitate large-scale analysis and reuse. The dataset is released under an open license to ensure long-term accessibility, interoperability and unrestricted reuse in research, education and industrial applications.

Code availability

All Python scripts used to generate the synthetic microstructures, compute the associated orientation tensors, and export the accompanying metadata are openly available in the project repository: https://github.com/polila6/Fibers. The repository includes the full simulation pipeline—ellipse generation, non-overlap placement algorithms, parameter sampling routines, and analytical tensor computation—as well as utilities for batch dataset creation. Example Jupyter notebooks illustrate data loading, visualisation and parameter customisation, enabling users to reproduce the dataset or generate new variants under modified conditions. The code is released under an open-source license to ensure transparency, reproducibility and ease of reuse.

Competing interests

The authors declare no competing interests.