bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Structural Repetition Detector: multi-scale
quantitative mapping of molecular complexes
through microscopy
Afonso Mendes1 , Bruno M. Saraiva1 , Guillaume Jacquemet2,3,4,5 , João I. Mamede6 , Christophe Leterrier7 , and Ricardo
Henriques1,8,
1
Optical Cell Biology group, Instituto Gulbenkian de Ciência, Oeiras, Portugal
Turku Bioimaging, University of Turku and Åbo Akademi University, Turku, Finland
3
Faculty of Science and Engineering, Cell Biology, Åbo Akademi University, Turku, Finland
4
InFLAMES Research Flagship Center, Åbo Akademi University, Turku, Finland
5
Turku Bioscience Centre, University of Turku and Åbo Akademi University, 20520, Turku, Finland
6
Department of Microbial Pathogens and Immunity, Rush University Medical Center, Chicago, Illinois, USA
7
Aix Marseille Université, CNRS, INP UMR7051, NeuroCyto, Marseille, France
8
UCL Laboratory for Molecular Cell Biology, University College London, London, United Kingdom
2

From molecules to organelles, cells exhibit recurring structural motifs across multiple scales. Understanding these structures provides insights into their functional roles. While superresolution microscopy can visualise such patterns, manual detection in large datasets is challenging and biased. We present
the Structural Repetition Detector (SReD), an unsupervised
computational framework that identifies repetitive biological
structures by exploiting local texture repetition. SReD formulates structure detection as a similarity-matching problem between local image regions. It detects recurring patterns without prior knowledge or constraints on the imaging modality.
We demonstrate SReD’s capabilities on various fluorescence microscopy images. Quantitative analyses of three datasets highlight SReD’s utility: estimating the periodicity of spectrin rings
in neurons, detecting HIV-1 viral assembly, and evaluating microtubule dynamics modulated by EB3. Our open-source ImageJ and Fiji plugin enables unbiased analysis of repetitive
structures across imaging modalities in diverse biological contexts.
structural biology | quantitative image analysis | super-resolution microscopy
Correspondence: (R. Henriques) rjhenriques@igc.gulbenkian.pt

Introduction
Biological systems exhibit structural repetition across multiple scales, from biomolecules to supramolecular assemblies and cellular structures (1). Understanding these patterns is crucial for identifying their functional significance
and underlying biological processes (2). Microscopy techniques offer molecular-level resolution but manually detecting repetitive motifs in large datasets is impractical, biased, and expertise-dependent (3). To address these limitations, machine learning, particularly deep convolutional neural networks (CNNs), has been employed to detect and segment biological structures automatically (4, 5). However,
CNNs require extensive labelled training data, inheriting biases (6). Previous methods enable unbiased registration but
need single-molecule localisation data, limiting their applicability (7, 8). We present the Structural Repetition Detector (SReD), an unsupervised framework to identify repetitive

Fig. 1. Applications of the Structural Repetition Detector (SReD) Algorithm
in Fluorescence Microscopy. a, Detection of Structural Repetition Using Simulated Blocks: Microtubules imaged with STORM analysed for repetitive patterns
using simulated structural blocks. Coloured regions in repetition map correspond
to repetitions of same-coloured blocks above. b, Detection of Structural Repetition Using Empirical Blocks: HeLa cell nuclei stained with DAPI used to detect
repetitive structural patterns using manually extracted empirical blocks. Coloured
regions in repetition map correspond to repetitions of same-coloured blocks in previous subpanel. c, Global Repetition Detection: Jurkat cell expressing inducible
HIV-1 Gag-EGFP fusion protein analysed using global repetition detection. Image
probed for structural repetition using all possible empirical patches. Repetition map
reveals structures not easily detectable in input image and their relative frequency.
d, Multiscale Global Repetition: Xenopus laevis nuclear pores imaged with STORM
analysed using different-sized receptive fields to detect structural repetition at various scales. Repetition map identifies repeated structures from single nucleoporins
(orange) to nucleoporin clusters (blue) and nuclear pore units (magenta). Centre
panel: Simplified SReD algorithm workflow, illustrating key steps from input preprocessing to repetition map generation.

biological structures by exploring local texture redundancy.
SReD formulates structure detection as similarity matching
between local image regions, allowing pattern detection without prior knowledge or microscopy modality constraints. We
demonstrate SReD’s capabilities on fluorescence microscopy
images of diverse cell types and structures, including microMendes et al.

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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

tubule networks, nuclear envelope, pores, and virus particles
(Fig. 1). SReD generates Structural Repetition Scores (SRSs)
highlighting regions with repetitive textures. Users can provide artificial blocks or extract them from the data for repetition analysis. An unbiased sampling scheme maps global
repetition by testing every possible image block as a reference (Note S1). We showcase SReD’s utility through three
datasets: 1) spectrin rings in neuronal axons, accurately estimating ring periodicity and pinpointing periodic patterns, 2)
HIV-1 Gag assembly, mapping viral structures without structural priors, and 3) dynamic EB3 and microtubule structures,
assessing structural displacement and stability over time. Our
open-source ImageJ and Fiji plugin enables versatile, unbiased analysis of redundancy in microscopy images. SReD
advances computational microscopy by providing a generalised framework for detecting repetitive structures without
labelled training data or single-molecule localisation input,
facilitating the quantitative study of structural motifs across
scales in diverse imaging datasets.

Results
General applications of SReD. SReD is an open-source
ImageJ and Fiji plugin that leverages GPU acceleration to
identify repetitive patterns in microscopy images. The algorithm’s workflow, outlined in Fig. 1 (centre panel) and
Note S1, begins with the application of the Generalised
Anscombe Transform (GAT) to stabilise noise variance (9).
This step addresses the noise in microscopy images, which
often exhibit Poisson and Gaussian noise. The GAT nonlinearly remaps pixel values to produce an image with nearGaussian noise and stabilised variance, preserving local contrast and overall image statistics. This stabilisation is essential for robust downstream processing, mitigating violations
of normality, homoscedasticity, and outlier assumptions that
can compromise correlation metrics. Following noise stabilisation, SReD generates a relevance mask to exclude regions
lacking substantive structural information (Note S1; Fig. S1).
The analysis proceeds using reference blocks, either simulated or empirically sampled from the image. These blocks
are matched against the input using correlation metrics to
generate repetition maps, as detailed in the Methods section.
The resulting repetition map highlights regions likely to contain structural repetitions, with nonlinear mapping applied to
visually emphasise salient features. To demonstrate SReD’s
versatility across diverse biological contexts, we conducted
a comprehensive analysis of various microscopy datasets
(Fig. 1; Note S2). We first examined a STORM image reconstruction of a cell with labelled microtubules (10). This
approach effectively mapped microtubules at various orientations and crossings (Fig. 1a; Fig. S2). We further illustrate
SReD’s versatility by detecting nuclear envelopes in DAPIstained cells (11) using empirical reference blocks extracted
directly from the input image, distinguishing different morphological states potentially related to cell division or stress
(Fig. 1b; Fig. S3). SReD also enables characterisation of
structures without user-provided references. We exemplify
this functionality by analysing an image of a Jurkat cell ex2

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pressing an HIV-1 Gag-EGFP construct, which induces the
production of virus-like particles (VLPs) (Fig. 1c; Fig. S4).
In this mode, SReD mapped every structure in the image
and assigned scores based on their relative repetition. As
expected, the top score was given to the most repeated element, the diffuse eGFP signal, with viral structures exhibiting lower frequencies. Localisation of round viral structures
via local extrema calculation revealed that the repetition map
provided a superior platform for extrema detection compared
to direct analysis of the raw images. The algorithm’s multiscale analysis capability is achieved by adjusting the ratio
of block-to-image dimensions. Larger ratios capture larger
structures, while smaller ratios capture finer details. For
computational efficiency, it is preferable to modulate scale
by downscaling the input rather than enlarging blocks, although combining both approaches often preserves structural
detail best. We demonstrate this multiscale analysis by examining nuclear pore complexes in STORM image reconstructions with labelled gp210 proteins (12). SReD successfully
mapped structures across different scales, discerning single
nucleoporins, nucleoporin clusters, and entire nuclear pores
(Fig. 1d; Fig. S5).

Fig. 2. Automated detection and quantification of spectrin ring periodicity
in neuronal axons. a, SReD-based analysis pipeline: the algorithm determines
axon orientations, optimises a reference block for spectrin rings, and maps structural repetitions. Quantitative analysis is performed using autocorrelation and other
methods. b, Control dataset image: STORM localization density (grey) overlaid with
SReD repetition map (magenta). Insets: (i) ’Angles’ - axon skeletons colour-coded
by orientation; (ii) ’High order’ - repetition map with a 9-ring reference block; (iii) ’Low
order’ - repetition map with a 3-ring reference block. Scale bar: 5 µm. c, Repetition
maps comparing control (CTRL) and swinholide A-treated (SWIN) groups. SWINtreated samples show reduced periodic structures. Scale bar: 1 µm. d, Quantification of axon segments with ring patterns. Bar graph shows a significant reduction
in pattern-containing segments in SWIN vs. CTRL (n=6 per group, mean±SEM;
CTRL: 0.694±0.008, SWIN: 0.421±0.007; p<0.001, unpaired t-test).
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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

1-to-all case example: detection of spectrin ring periodicity in axons. We used SReD’s block repetition mode

to map and quantify the membrane-associated periodic scaffold (MPS) architecture in neuronal axons automatically and
without bias (Fig. 2). The MPS, composed of actin, spectrin,
and associated proteins, forms a crucial structural component
of neuronal axons (13, 14). Super-resolution microscopy has
shown that the MPS consists of ring-like structures spaced
180-190 nm apart, with alternating actin/adducin and spectrin rings orthogonal to the axon’s long axis (15). Mapping
this nanoscale organisation across entire neuron samples has
been challenging due to the need for manual region selection, potentially introducing bias. We analysed datasets from
Vassilopoulos et al. (16), comparing neurons treated with
DMSO (control) or swinholide A (SWIN, an actin-disrupting
drug). Using SReD, we developed an automated workflow
to determine axon orientations by probing skeletonised neuron images with simulated lines at varying angles (Note S3;
Fig. S6). This enabled consistent alignment of axon segments for downstream analysis. We optimised parameters
for simulated ring blocks to match observed ring patterns in
control data, yielding an inter-ring spacing of 192 nm, consistent with previous studies (Fig. S7)(15, 16). SReD generated repetition maps highlighting regions of high local similarity across neuron samples, allowing automatic extraction
and quantification of MPS organisation without manual region selection (Fig. 2b; Fig. S8). We measured an average spacing of 178 nm under control conditions (Fig. 2c;
Fig. S9d). In agreement with Vassilopoulos et al. (16), repetition maps showed that swinholide A treatment disrupted
MPS structure, with reduced pattern prominence and frequency compared to controls (Fig. 2b,c). We used correlation metrics that minimise information loss while being
aware of potential imprinting. Nonlinear mapping effectively
distinguishes real patterns from imprinted ones (Fig. S2d,e;
Fig. S9c). Our method accounts for neuron thickness variability and provides the average distance between patterns
for additional biological insights. SReD’s local repetition
scores quantified the fraction of structures with MPS patterns, revealing a 39% reduction in axons with detectable
periodic scaffolds after swinholide A treatment (P<0.001,
Fig. 2d). SReD’s maps identified drug-affected regions with
confidence values, offering a detailed platform for analysing
structural dysregulation (Fig. 2c). SReD also showed higher
statistical sensitivity, detecting a 12% reduction in pattern
prominence post-treatment (P<0.05) previously unreported
(Fig. S9e). To test SReD’s noise robustness, we conducted
a sensitivity analysis with images at varying signal-to-noise
ratios (SNRs) (Fig. S10). SReD consistently detected ring
structures even at low SNRs near 1, where patterns were visually indiscernible. SReD-generated maps outperformed direct STORM reconstructions in autocorrelation analysis, reliably identifying an average inter-ring spacing of 192 nm
across all SNRs, demonstrating the algorithm’s robustness
in detecting structural periodicity despite significant noise.
We assessed SReD’s specificity and robustness to pattern deformations by applying stretch deformations to test images

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(Fig. S11). As the stretch factor increased, the average SRS
decreased, indicating pattern disruption. However, SReD remained specific to the original pattern within the expected
interval. Even at higher stretch factors, non-specific patterns were quantitatively discernible and reflected the intrinsic properties of the test data. This robustness is valuable
for analysing periodic structures in diverse biological contexts, where deviations from ideal patterns are common due
to sample preparation artefacts, imaging noise, or biological
variability.
All-to-all 3D case example: detecting HIV-1 Gag assembly in 3D. The establishment of a viral infection is

the product of complex host-pathogen interactions, comprising an evolutionary "tug-of-war" where cells evolve protective mechanisms whilst viruses evolve to circumvent them.
Viruses typically hijack cellular transcription and translation
machinery to produce viral progeny required for viral replication (17). Therefore, viral assembly represents a critical
platform for host-pathogen interactions that significantly impact infection outcomes. The HIV-1 gag gene encodes the
Gag polypeptide precursor, which is cleaved into several key
structural components. This polypeptide aggregates at the
membrane of infected cells and induces the budding of mem-

Fig. 3. Detecting HIV-1 Virus-Like Particles in 3D. a, Analysis pipeline schematic.
The algorithm uses 3D reference blocks for structural repetition analysis, locating
viral structures via local maxima from the input image and repetition map. b, Zprojections of the input image (left) and repetition map (right), highlighting viral-like
particles ("EGFP") and simulated reference particles ("Reference"). c, Local maxima plots showing detected structures in the input image (left) and repetition map
(right), with increased sensitivity in the repetition map. d, Accuracy plot comparing
artificially added reference particle detection: input image (32%) vs. repetition map
(96%). e, Intensity profile graph of EGFP signal (green) and structural repetition
score (SRS, magenta), with a threshold at SRS 0.8 (dashed red line). Inset shows
pixels below (dark) and above (light) the threshold, indicating high-SRS structures.
Scale bars: 5 µm (main images), 1 µm (insets).
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available under aCC-BY 4.0 International license.

branous viral particles (17). Expression of Gag alone is sufficient to induce the formation of non-infectious virus-like
particles (VLPs)(18, 19). To map viral structures in an unbiased manner, we examined an image of a Jurkat cell expressing an inducible HIV-1 Gag-EGFP construct using SReD
(Fig. 3a,b). To evaluate the algorithm’s accuracy, we generated a population of simulated diffraction-limited particles
with randomly distributed intensities across the image’s dynamic range, which served as a reference for comparison.
Local maxima corresponding to active viral assembly sites
were calculated from both the input image and the repetition
map using identical parameters (Fig. 3c). Remarkably, SReD
enabled the detection of 96% of the simulated particles, compared to only 32% in the input image, demonstrating the algorithm’s superior accuracy over direct analysis of input images
(Fig. 3d). Visual inspection of the detected EGFP intensity
signal vs. the SRS for the same pixel location revealed that
high SRS regions corresponded to input regions with a wide
range of intensity values. We observed that most structures
of interest were allocated to the sample fraction above an arbitrary threshold of SRS 0.8, whilst the fraction below this
threshold contained mostly background signal and some reference particles (Fig. 3e). Given that autofluorescence often
corrupts microscopy analyses, we evaluated the algorithm’s
performance in the presence of synthetic non-specific structures (Note S4). The repetition maps produced by SReD
consistently provided a superior platform for detecting simulated reference particles and viral structures across conditions
(Fig. S12). This analysis demonstrates SReD’s robust capability to map biological structures, such as assembling viral particles. The algorithm’s high sensitivity and specificity,
even in the presence of non-specific structures, highlight its
potential for studying dynamic cellular processes like viral
assembly, where the ability to accurately detect and characterise structures amidst variable backgrounds is showcased.
All-to-all live-cell case example: assessment of microtubule dynamics. The multidimensional capabilities of

SReD can be extended to analyse structural dynamics over
time, providing insights into structural stability. We demonstrate this application using time-lapse imaging of RPE1 cells
stably expressing End-binding Protein 3 (EB3) fused to GFP
(Fig. 4a). EB3 binds to the plus ends of microtubules, appearing as comet-like structures that travel along the cytoplasm when visualised under fluorescence microscopy (20).
We generated a global repetition map by treating time as
the third dimension in our analysis, using a time-lapse sequence of approximately 2 minutes (Fig. 4b). To quantify
structural changes, we calculated the Normalised Root Mean
Squared Error (NRMSE) between the first and last frames of
the time-lapse for both the input images and the repetition
maps. The NRMSE of the input images reflected the spatial
displacement of dynamic structures, yielding a relatively low
value. In contrast, the NRMSE calculated from the repetition maps was substantially higher, indicating greater sensitivity to structural changes over time (Fig. 4c). SReD effectively mapped the spatial distribution of EB3 comet activity
over time. By quantifying the repetitiveness of structures, it
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Fig. 4. Assessment of microtubule dynamics using SReD. a, Analysis pipeline
schematic. Global repetition analysis used time as the third dimension on a timelapse sequence of RPE1 cells expressing EB3-GFP over 105 seconds (35 frames).
The first frame served as the control. Normalised Root Mean Squared Error
(NRMSE) quantified structural differences between time points. b, Input images
(left) and global repetition maps (right). The first frame’s repetition map highlights
EB3 comets, while the entire time-lapse map shows comet trajectories and repetition over time. c, Bar graph of average NRMSE between input images and repetition maps. Higher error in repetition maps (0.08) vs. control images (0.03) indicates
greater sensitivity to structural changes. d, NRMSE maps of input images (left)
and repetition maps (right), showing structural stability over time. High NRMSE values (warmer colours) in EB3 trajectories indicate lower stability, while lower values
(cooler colours) in the Microtubule Organising Centre (MTOC) indicate higher stability. Scale bars: 10 µm (main images), 2 µm (insets).

assigned scores to different regions, highlighting areas with
high EB3 comet presence and their trajectories. The NRMSE
maps further emphasised this distinction, revealing elevated
values along comet paths, indicative of their dynamic nature.
In contrast, the MTOC demonstrated notably lower NRMSE,
suggesting its greater stability compared to the more mobile
EB3 comets (Fig. 4d). The time interval used in the analysis
captures the relatively slower dynamics of EB3 comets in this
context. While individual comet tracking is not the primary
focus of this method, the approach effectively reveals the spatiotemporal stability of structures, where instability often results from displacement, visually manifesting as comet trajectories. To further validate our approach, we performed the
analysis with increased temporal resolution. We compared
SReD’s results with conventional time projections of the input data, revealing advantages of our method. Unlike time
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available under aCC-BY 4.0 International license.

projections, which typically integrate local intensities across
time, SReD calculates local correlations of images across
time, providing relative repetition scores that indicate how
much the texture at each location changes relative to all other
textures. This approach offers two significant benefits: (i) it
provides a more nuanced measure of structural stability over
time, and (ii) it is less susceptible to noise and intensity inconsistencies across time points (Note S5; Fig. S13). In this
type of combined spatial and temporal analysis, instead of
producing a time series, SReD’s output is a single map that
shows the local stability of the timelapse over a specific time
interval. This representation offers a comprehensive view of
the structural dynamics that is not easily achieved using traditional methods such as kymographs. While kymographs
are useful for tracking individual structures over time, SReD
provides a broader perspective on the overall stability and
dynamics of subcellular structures across the entire field of
view.

Discussion and Conclusions
Our results demonstrate SReD’s versatility and analytical
power across diverse biological contexts. In neuronal axons, SReD enabled automated, unbiased mapping of the
membrane-associated periodic scaffold (MPS), revealing nuanced changes in pattern frequency and prominence following pharmacological perturbation. While previous studies
by Vassilopoulos et al. (16) reported a 40% reduction in
overall MPS prominence after treatment with swinholide A,
SReD’s analysis provides a more detailed characterisation of
the phenotype. By first distinguishing between regions with
and without periodic patterns, and then analysing only the
pattern-present areas, SReD detected a 12% reduction in pattern prominence and a 32% reduction in pattern frequency.
This refined analysis not only corroborates the previously reported overall effect but also decomposes it into two distinct
components, offering deeper insights into the nature of the
structural changes. For HIV-1 Gag assembly, SReD achieved
highly sensitive detection without relying on structural priors,
significantly outperforming direct analysis of input images.
This capability is particularly valuable in studying dynamic
cellular processes like viral assembly, where the ability to
accurately detect and characterise structures amidst variable
backgrounds is crucial. In live-cell imaging of microtubule
dynamics, SReD’s multidimensional capabilities allowed for
quantitative assessment of structural stability across space
and time. This analysis provided novel insights into the differential dynamics of EB3 comets and the microtubule organising centre, demonstrating SReD’s potential for studying
complex, time-dependent cellular processes. A key advantage of SReD is its ability to detect and characterise structures without the need for extensive labelled training data
or single-molecule localisation input. This feature is particularly useful for exploratory analysis of complex biological systems where the underlying structural patterns may not
be fully known a priori. The framework’s flexibility in accommodating different reference blocks, from simulated idealised structures to empirically extracted image patches, enMendes et al.

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hances its utility across diverse experimental scenarios. Another crucial feature is SReD’s robustness to noise and pattern deformations, as demonstrated in our sensitivity analyses. This resilience enables reliable structure detection and
quantification even in challenging imaging conditions, expanding the range of biological questions that can be addressed through quantitative image analysis. The algorithm’s
multiscale mapping capabilities provide a unique perspective on hierarchical structural organisation, as exemplified
by our analysis of nuclear pore complexes at different spatial scales. While SReD offers significant advantages, it is
important to acknowledge its limitations. The algorithm’s
performance can be influenced by the choice of reference
blocks, possibly requiring their optimisation. Additionally,
while SReD reduces the need for manual region selection,
some level of results curation may still be necessary, particularly in highly complex or heterogeneous samples. Finally,
the algorithm’s computational complexity warrants attention.
Consider a 2D image with dimensions n1 × n2 pixels and a
block of size k1 × k2 pixels. Each pairwise comparison between the block and an image region requires O(k1 k2 ) operations. The total number of such overlapping image regions
is (n1 − k1 + 1)(n2 − k2 + 1). Consequently, the "1-to-all"
scheme (block repetition) entails a computational complexity of O((n1 − k1 + 1)(n2 − k2 + 1)k1 k2 ). When the image
dimensions significantly exceed the block size (n1 ≫ k1 and
n2 ≫ k2 ), this simplifies to O(n1 n2 k1 k2 ). In the "all-toall" scheme (global repetition), the computational complexity scales quadratically with the image size and linearly with
the block size, resulting in O(n21 n22 k1 k2 ). SReD mitigates
this computational burden by harnessing GPU acceleration
and pre-calculating background regions that do not warrant
analysis. Future developments of SReD could focus on further automating the reference block selection process, potentially incorporating machine learning approaches to optimise
block parameters based on image characteristics. Integration
with other computational tools, such as deep learning-based
segmentation algorithms, could also enhance SReD’s capabilities for more comprehensive structural analysis pipelines.
DATA AVAILABILITY
The data obtained in this study is available at https://doi.org/10.5281/
zenodo.13764726 under CC BY 4.0 license. The STORM data containing cells
with labelled microtubules is available at (10). The data containing DAPI-stained
nuclei is available at (11). The STORM data containing nuclear pores with labelled
gp210 is available at (12).
CODE AVAILABILITY
The SReD algorithm is available at https://github.com/HenriquesLab/
SReD. All source code is under an MIT License.
AUTHOR CONTRIBUTIONS
A.M. and R.H. conceived the study in its initial form; A.M. and R.H. developed the
SReD framework with code contributions from B.M.S.; B.M.S., G.J., J.I.M and C.L.
provided samples, data, critical feedback, testing and guidance; A.M. performed
experiments and analysis; G.J., J.I.M., C.L. and R.H. acquired funding; C.L., R.H.
supervised the work; A.M and R.H. wrote the manuscript with input from all authors.

ACKNOWLEDGEMENTS
A.M. thanks Simão Coelho and Estibaliz Gómez-de-Mariscal for their feedback during the formulation of the algorithm and its demonstration in biological studies.
A.M. and R.H. acknowledge the support of the Gulbenkian Foundation (Fundação
Calouste Gulbenkian), the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement No.
101001332) (to R.H.) and funding from the European Union through the Horizon Eu-

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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

rope program (AI4LIFE project with grant agreement 101057970-AI4LIFE and RTSuperES project with grant agreement 101099654-RTSuperES to R.H.). Funded by
the European Union. Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union. Neither the
European Union nor the granting authority can be held responsible for them. This
work was also supported by a European Molecular Biology Organization (EMBO) installation grant (EMBO-2020-IG-4734 to R.H.), a Chan Zuckerberg Initiative Visual
Proteomics Grant (vpi-0000000044 with https://doi.org/10.37921/743590vtudfp to
R.H.) and a Chan Zuckerberg Initiative Essential Open Source Software for Science
(EOSS6-0000000260). This study was also supported by the Research Council of
Finland (338537 to G.J.), the Sigrid Juselius Foundation (to G.J.), the Cancer Society of Finland (Syöpäjärjestöt; to G.J.), the Solutions for Health strategic funding
to Åbo Akademi University (to G.J.), the InFLAMES Flagship Programme of the
Academy of Finland (decision numbers: 337530, 337531, 357910, and 357911)
and the CNRS ATIP program (AO2016 to C.L.). This research was also supported
by the National Institutes of Health (NIH) with grants K22AI140963, K61DA058348
and subcontract R01AI50998 (to J.I.M).
EXTENDED AUTHOR INFORMATION

•
•
•
•
•
•

A. Mendes:

0000-0001-7324-555X; 7afonsomendes92

B. Saraiva:

0000-0002-5940-2990; 7Bruno_MSaraiva

G. Jacquemet:

0000-0002-9286-920X; 7guijacquemet

J. I. Mamede:

0000-0002-6048-1876; 7Micromede

C. Leterrier:

R. Henriques:

0000-0002-2957-2032; 7christlet

0000-0002-2043-5234; 7HenriquesLab

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Methods
Noise variance stabilisation. The Generalised Anscombe

Transform (GAT) is applied to the input image to stabilise
noise variance, a crucial step in processing microscopy images. These images typically exhibit a combination of Poisson and Gaussian noise, which can obscure the underlying signal. In fluorescence microscopy, noise variance is
signal-dependent, limiting some of the assumptions required
for the proper application of correlation metrics. Namely,
the assumptions of normality, homoscedasticity (equal variance), and absence of outliers. The GAT employs a nonlinear
remapping of pixel values, resulting in an output image with
near-Gaussian noise and stabilised variance, whilst preserving local contrast and overall image statistics (9). This variMendes et al.

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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

ance stabilisation thus improves downstream processing, enabling more accurate analysis of the image’s structural content.
Relevance mask. We use a relevance mask to filter out areas lacking significant structural information. The rationale
is that structural elements present themselves as regional image textures with non-zero variance. Therefore, areas devoid
of structure will exhibit minimal texture. Determining the
threshold for "minimal" texture is challenging due to the presence of ubiquitous image noise. Rather than choosing an arbitrary value close to zero, we estimated the average noise
variance of the input image using a robust estimator (21).
This is obtained by sampling the variance of the input image
using non-overlapping blocks of the same size as those used
for the repetition analysis, and then calculating the average
of percentile 0.03. This sampling approach ensures that the
noise variance is estimated at the same scale as the analysed
structures. The relevance threshold is established by multiplying the estimated average noise variance by an adjustable
constant, with the default set at 0. This produces a binary
mask outlining areas with sufficient structural content.
Sampling scheme and mathematical basis. Our algo-

rithm leverages a custom sampling scheme in which a reference block is compared with all possible test blocks in the
image. The scheme can be "1-to-all" or "all-to-all", depending on the application. The first requires a user-provided
reference block, while the latter provides unbiased structure
detection. The comparisons between blocks consist of calculating correlation metrics. The correlation metrics can be
rotation-variant (e.g., Pearson’s correlation coefficient) or invariant (e.g., modified cosine similarity). In both cases, the
blocks’ dimensions are predefined by the user to match a specific scale. After defining the blocks’ dimensions and the relevance threshold, the algorithm calculates the noise variancestabilised input, the relevance mask, and normalises the input
image to its range. Then, it calculates the local means and
standard deviation maps for the entire universe of blocks that
can be extracted from the image within the previously defined constraints. To minimise blocking artefacts, the square
blocks are transformed into their inbound elliptical counterparts. Using these statistics, a repetition map is calculated for
each "1-vs-all" comparison, where each pixel is assigned a
score (named Structural Repetition Score, or SRS), which reflects the similarity between the local neighbourhood centred
at that position and the reference block. Finally, the repetition
map is normalised to its range. The SRS is given by:
SRS(Xi , Yj ) = Corr(Xi , Yj ) · Rel(Yj )

Xi = {x1 , x2 , ..., xn }

(2)

Yj = {y1 , y2 , ..., yn }

(3)

SReD: Quantitative Mapping of Molecular Complexes

where N is the size of the input image (excluding borders),
and
2
W (Xi , Yj ) = e

−

|σX −σY |
i
j
V ar

(6)

is the exponential weight function, where σXi and σYj are
the standard deviations of the reference and test blocks.
Multiscale analysis. The scale at which structures are anal-

ysed can be adjusted by modulating the ratio between the input image and the block size. For example, larger blocks
contain information about higher-order structures compared
to smaller blocks. Due to the iterative nature of the algorithm, increasing the block size adds an exponential amount
of data points to each comparison, introducing an unwanted
load on the computational resources and drastically slowing
the calculations. Therefore, modulation of the ratio between
the input image and the block size can instead be achieved by
adjusting the input image size (i.e., downscaling). A direct
consequence of this method is the loss of lower-order information, which should not be problematic when the goal is to
increase the sensitivity to higher-order textures.
Non-linear mapping. Non-linear mapping can enhance the

and

|

the binary "relevance" label of the test block, where Var is
the average noise variance of the input image. To analyse local textures and calculate a single value for each, the
reference and test blocks require a defined centre. Therefore, the blocks’ dimensions need to be odd, and as a result,
i = [(rh , H − rh ] and j = [rw , W − rw ], where rw and rh
are the blocks’ width and height radii, and W and H are
the input image’s width and height. In the global repetition
mode, SReD enables unbiased structure analysis by using the
entire universe of image blocks as a reference. Each reference block generates a repetition map that is averaged, and
the average value is plotted at the coordinates corresponding to the centre of the reference block. The average uses an
exponential weight function based on the distance between
the standard deviations of the blocks in each comparison,
which enhances structural details. Therefore, the global repetition scores represent the relative repetition of a local texture
across the image. Mathematically, the global SRS is given
by:
P
j Corr(Xi , Yj ) · W (Xi , Yj ) · Rel(Yj )
P
(5)
S(Xi , Yj ) =
N · j W (Xi , Yj )

(1)

where

Mendes et al.

are the reference and test blocks with size n (in pixels) centred at pixel positions i and j, and

0, if V ar(Yj ) ≤ V ar
(4)
Rel(Yj ) =
1, if V ar(Yj ) > V ar

contrast between different SRSs within the repetition maps,
facilitating visual interpretation and subsequent analysis. In
our experience, we have found that applying a power transformation to the SRSs often yields the most effective enhancement. This transformation involves raising each SRS
value to a specific exponent. The choice of exponent plays
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

a crucial role in determining the degree of contrast enhancement. In this study, we explored a range of exponents between 10 and 10,000. Typically, we initiate the analysis with
an exponent of 10 and iteratively adjust it based on the visual assessment of the resulting repetition map. For datasets
with subtle structural repetitions or low signal-to-noise ratios, higher exponents may be necessary to amplify the differences between SRSs and reveal hidden patterns. Conversely,
for datasets with prominent structural repetitions, lower exponents may suffice to achieve adequate contrast enhancement without introducing excessive noise amplification. The
optimal exponent ultimately depends on the specific characteristics of the data and the desired level of visual clarity. By
carefully selecting the exponent, users can tailor the contrast
enhancement to their needs, facilitating the identification and
interpretation of repetitive patterns in diverse microscopy images.
Optimisation of block parameters for ring pattern detection. A collection of 248 testing blocks incorporating var-

ious combinations of inter-ring spacing and ring height was
generated. This process was automated using a custom ImageJ macro. To create input images, five representative segments from the distal axons within each dataset were randomly selected, comprised of six neurons per treatment.
These regions were then rotated to align with the horizontal axis to guarantee consistency across subsequent calculations. Then, SReD was used to generate repetition maps for
every test block, and their autocorrelation functions were calculated. The relative amplitude of the autocorrelations’ first
harmonic was used to assess how effectively each block captured the underlying periodic pattern. The set of block parameter values that maximised the first harmonics’ relative
amplitude was systematically identified. The optimised set
of parameter values served as a reliable representation of the
periodic pattern within the dataset. The optimisation was performed separately for each dataset analysed in this study.
Detection of reference and virus-like particles using
Global Repetition. An image volume containing 3D sim-

ulated reference particles was generated using a custom
Python script. The reference particles were added to the input
volume by addition. Global Repetition maps were calculated
using a block size of 5x5x5 pixels and a relevance constant of
0. Then, the repetition maps were non-linearly mapped using
a power transformation with an exponent of 10000. 3D maxima were calculated using the ImageJ "3D Maxima Finder"
plugin, with an XY and Z radius of 5 pixels and a minimum
threshold of 0.1. The comparison of coordinates between the
3D maxima calculated and the reference particles was performed using a custom Python script.
Cell culture. Jurkat cells were cultured in RPMI 1640

(Gibco) supplemented with 10% fetal bovine serum (FBS), 2
mM L-glutamine and 50 µg/mL gentamycin. HEK293T and
RPE1-EB3-GFP cells were cultured in DMEM supplemented
with 10% fetal bovine serum (FBS), 2 mM L-glutamine and
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50 µg/mL gentamycin. Cell lines were cultured at 37ºC and
5% CO2.
DNA plasmids and cell lines. The RPE1-EB3-GFP cell

line was kindly provided by Dr. Mónica Bettencourt-Dias.
A plasmid expressing HIV-1 Gag with an internal EGFP
tag was generated using the NEB HiFi Assembly Kit (New
England Biolabs). A lentiviral backbone containing a
tetracycline-inducible promoter and a gene encoding rtTA
was prepared by digesting the pCW57.1 plasmid (Addgene
#41393) with 5 µg/mL restriction enzymes BamHI and NheI
(New England Biolabs) according to the manufacturer’s
instructions for 1 hour at 37ºC. The digestion product was
separated using 1% agarose gel electrophoresis (AGE) and
the 7̃.6 kb band was purified using the GFX PCR & Gel
Band Purification Kit (Sigma-Aldrich) according to the manufacturer’s instructions. Then, three DNA fragments were
generated by polymerase chain-reaction (PCR) using Q5
High-Fidelity DNA Polymerase (New England Biolabs). The
first fragment (445 bp), encoding the HIV-1 Matrix protein
followed by an HIV-1 protease cleavage site (MA-PCS), was
generated using Optigag-mNeonGreen-IN (22) as a template
and primers 5’-tcagatcgcctggagaattgggccaccatgggtgcgcga3’ (Fw) + 5’-ccatacgcgtctggacaatggggtagttttgactgacc-3’
(Rv). The second fragment (751 bp), encoding EGFP,
was generated using HIV-(i)GFP ∆Env (18) as a template
and primers 5’-ccattgtccagacgcgtatggtgagcaag-3’ (Fw)
+ 5’-tagttttgacttctagacttgtacagctcgtc-3’ (Rv). The third
fragment (1.2 kb), encoding a PCS and the HIV-1 Capsid,
Nucleocapsid and p6 proteins (PCS-CA-NC-p6), was generated using Optigag-mNeonGreen-IN (22) as a template
and primers 5’-caagtctagaagtcaaaactaccccattgtc-3’ (Fw)
+
5’-aaaggcgcaaccccaaccccgtcattgtgacgaggggtctgaac-3’
(Rv). The three fragments were purified using DNA purification columns and their molecular size was confirmed by
AGE. The HiFi Assembly reaction was performed using
50 ng of digested vector and equimolar amounts of the
three fragments, and incubated at 50ºC for 1 hour. The
reaction product was diluted 1:4 in dH20, and 2 µL of
the dilution was transformed into chemically competent
STABL4 bacteria (Thermo Fisher). The bacteria were plated
in LB-agar supplemented with 100 µg/mL ampicillin and
incubated overnight at 37ºC. Several colonies were picked
and inoculated into liquid LB containing ampicillin at 100
µg/mL. The plasmid DNA from these colonies was extracted
using the GenElute Plasmid Miniprep Kit (Sigma-Aldrich),
and was confirmed by digestion with restriction enzyme
XbaI followed by AGE (2.3 kb and 7.5 kb fragments). A
positive colony was then sequenced using Sanger sequencing (Genewiz) and primers 5’-cgtcgccgtccagctcgacca3’,
5’-ccattgtccagacgcgtatggtgagcaag-3’
and
5’aaaggcgcaaccccaaccccgtcattgtgacgaggggtctgaac-3’. This
process yielded the lentiviral plasmid TetOn-Optigag(i)EGFP, where a human codon-optimised gag gene contains
a PCS-flanked EGFP-encoding gene. Lentivirus packaging TetOn-Optigag-(i)EGFP were produced to transduce
Jurkat cells. To do this, HEK293T cells were cultured
in 6-well plates until ∼80% of confluence, transfected
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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

using 300 µL/well of transfection mixture (DMEM, 3 µg
of TetOn-Optigag-(i)EGFP, 1.5 µg of psPAX2 (Addgene
#12260), 1.5 µg of CMV-VSV.G (NIAID) and 12 µL of
linear polyethyleneimine MW-25,000 (final concentration
of 5 µg/µL)(Sigma-Aldrich)) and incubated overnight for 8
hours. Then, the culture medium was replaced with complete
DMEM, followed by a 24-hour incubation. The virus-rich
supernatant was collected and filtered with 0.22 µm syringe
filters. Jurkat cells (2 mL at 1x106 cells/mL) were inoculated
with 300 µL of virus-rich supernatant and Polybrene (10
µg/mL), followed by a 3-day incubation. Antibiotic selection
of transduced cells was performed by replacing the culture
medium with complete RPMI containing puromycin at 2
µg/mL and incubating for 3 days, at which point an "empty
virus" control sample had no live cells remaining. The
cells were incubated with doxycycline at 1 µg/mL for 24
hours to induce expression and single cells were isolated
using Fluorescence-assisted Cell Sorting (FACS). The
EGFP-positive population was divided into three subsets
according to their relative signal intensity ("Low", "Medium"
and "High") and single cells were plated into 96-well plates.
The cultures were expanded for 15 days and the resulting
cell lines were validated using fluorescence microscopy and
Western blotting. A clonal line of the "Medium" subset was
used for this study.
Sample preparation and acquisition of microscopy
data.
HILO imaging of HIV-1 virus-like particle assembly in activated Jurkat cells. Activation surfaces were prepared based

on the protocol in (Ashdown et al.). To do this, Lab-Tek
8-well chambers (Thermo Fisher) were cleaned with 100%
isopropanol for 10 min and followed by three washing steps
with dH2 0. Then, 200 µL of a mouse anti-CD3 antibody diluted in PBS at a final concentration of 1 µg/mL was added
to the wells and incubated overnight at 4ºC. The wells were
carefully washed twice with PBS to remove unbound antibodies. Jurkat cells expressing TetOn-Optigag-(i)EGFP were
incubated with 1 µM of doxycycline (Sigma Aldrich) for 24
hours. Then, 50000 cells were added to each well and allowed to adhere and stabilise for 1 hour. Imaging was done
in a Nanoimager (ONI) using the 488 nm laser at 10% and
channel 0 (two-band dichroic: 498-551 nm and 576-620 nm).
The HILO angle was optimised manually and images were
acquired at 100 ms exposure. The anti-CD3 antibody was
produced at the Flow Cytometry & Antibodies Unit of Instituto Gulbenkian de Ciência, Oeiras, Portugal.

by three washing steps with dH2 0. The PLL-coated coverslips were dried, mounted in an Attofluor chamber (Thermo
Fisher) and fixed on the microscope’s stage. The microscope’s enclosure (Okolabs) was heated at 37◦ C and a manual gas mixer (Okolabs) was used to supply 5% CO2 . The
cells were seeded in the pre-treated coverslips and allowed to
settle in the microscope enclosure for 30 minutes. Imaging
was performed on an inverted microscope ECLIPSE Ti2-E
(Nikon Instruments) equipped with a Fusion BT (Hamamatsu
Photonics K.K., C14440-20UP) and a Plan Apo λ 100x (NA
1.45) Oil objective. The sample was illuminated with LED
light at 515 nm (CoolLED pe800) and acquisition was done
at 75 ms exposure with an active Nikon Perfect Focus system and the NIS-Elements AR 5.30.05 software (Nikon Instruments). Volumes were captured by acquiring frames at
different depths (z-step size: 0.5 µm). Image deconvolution
was performed using a custom Python script based on the
Richardson-Lucy method (23, 24) as described in (25, 26).
Imaging of EB3-GFP comets in RPE1 cells. RPE1-EB3-GFP

cells (50000 per well) were seeded into Lab-Tek 8-well glass
chambers (Thermo Fisher) and allowed to adhere for 24
hours. Imaging was performed in a Nanoimager (ONI) using
the 488 nm laser at 10% and channel 0 (two-band dichroic:
498-551 nm and 576-620 nm). Images were acquired at 75
ms exposure for 2 minutes.
Assessment of microtubule dynamics using SReD.

Subsets of the original time lapse were created by keeping
images belonging to the time frames of interest. Global repetition maps were generated from the temporal subsets using an XY block size of 7x7 pixels, a Z block size equal to
the number of images in each subset, and a relevance constant of 0. The repetition maps were non-linearly mapped
using a power transformation with an exponent of 1000.
NRMSE maps were calculated using the "scikit-image" library (v0.22.0).

3D imaging of HIV-1 virus-like particle assembly in activated
Jurkat cells. Jurkat cells expressing TetOn-Optigag-(i)EGFP

were centrifuged at 200 xg for 5 minutes and resuspended in
complete RPMI containing 0.5 µM of doxycycline to induce
Gag expression. Glass coverslips (1.5 mm thick, round, 18
mm diameter) were washed with isopropanol for 10 minutes
followed by three washes with dH2 0. The coverslips were
coated with Poly-L-Lysine (PLL, Sigma Aldrich) at 0.1%
and incubated for 15 minutes at room temperature, followed
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Note S1: Theoretical foundation and core functionality of SReD
The Structural Repetition Detector (SReD) is an unsupervised computational framework designed to identify repetitive biological structures in microscopy images by exploiting local texture repetition. SReD operates by comparing local image regions
(blocks) to detect recurring patterns without prior knowledge or constraints on the imaging modality. The algorithm’s workflow
includes the following preprocessing steps:
1. Application of the Generalized Anscombe Transform (GAT): This step stabilises noise variance, addressing the complex noise characteristics typical in microscopy images. The GAT employs a nonlinear remapping of pixel values to
produce an output image with near-Gaussian noise and stabilised variance, preserving local contrast and overall image
statistics (1). The pixel values of the transformed image are given by:
r
3
2
g0 Zi + g02 + eDC
(S1)
τGA (Zi ) =
g0
8
where g0 is the gain of the electronic system, eDC = σ 2 − g0 m, and m and σ 2 are the mean and variance of the noise.
The goal is to find parameter values such that the transformed image has variance as close as possible to 1. The initial
parameter values can be user-provided or calculated automatically.
2. Generation of a Relevance Mask: This mask excludes regions lacking substantive structural information, based on
local texture prominence quantified by variance or standard deviation. The relevance threshold is defined by multiplying
the estimated average noise variance (2) by an adjustable constant, with the default set at 0 .
SReD’s primary functionality revolves around two main analysis modes:
1. Block Repetition Analysis: The input image is probed for repetitions of a single reference block, which can be either
simulated or empirically extracted from the data. The output is a repetition map reflecting the likelihood of the reference
pattern occurring at each location. The similarity score is computed using a correlation metric, which can be sensitive or
insensitive to rotation.
2. Global Repetition Analysis: Every block in the input image is used as a reference, generating multiple repetition maps.
These maps are integrated using an exponentially weighted average based on block similarity, producing a final map that
reflects the relative frequency of each structural pattern across the entire image.
The algorithm’s output is a Structural Repetition Score (SRS) for each pixel, quantifying the degree of local structural repetition.
This score can be interpreted as the likelihood of a specific pattern occurring at that location.
SReD also offers multiscale analysis capabilities by adjusting the ratio between the input image and block sizes, enabling the
detection of structural patterns at various scales. This approach is particularly valuable for exploratory analysis of complex
biological systems where the underlying structural patterns may not be fully known a priori.


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available under aCC-BY 4.0 International license.

Note S2: Validation and application examples of SReD across diverse biological contexts
Detection of microtubules using simulated reference blocks. We evaluated SReD’s ability to detect structures using sim-

ulated reference blocks. A series of blocks comprising lines and line crossings at different orientations were generated and used
to detect microtubule structures in a STORM image reconstruction of a HeLa cell with labelled microtubules (3) (Fig. S2a). Using the Pearson’s correlation coefficient metric for orientation sensitivity, SReD produced repetition maps highlighting regions
matching the simulated blocks (Fig. S2b). The specificity was assessed by:
1. Detecting repetitions of a vertical line block in images with vertical lines at varying distances
2. Detecting repetitions of an orthogonal line crossing block in images with crossings at different angles
In both cases, the average SRS decreased markedly when the specific structures were absent, demonstrating high specificity
(Fig. S2c,d).
Detection of nuclear envelopes using empirical reference blocks. To demonstrate structure detection using empirical

reference blocks, we extracted blocks containing nuclear envelope regions at various orientations from a DAPI-stained image
of HeLa cell nuclei (4) (Fig. S3a). Applying SReD with the Pearson correlation metric generated repetition maps highlighting
regions matching the reference blocks, effectively mapping the nuclear envelopes and their local orientations (Fig. S3b,c). This
approach also enables the characterisation of morphological variations. We calculated the relative area percentage of each
repetition map in the combined output to quantitatively describe nuclear shape (Fig. S3d). These measurements distinguished
different morphological states potentially related to cell division or stress.
Detection of HIV-1 virus-like particles using Global Repetition. SReD’s global repetition mode enables unbiased structure

detection by quantifying the relative repetition of all structures in an image. We analysed an image of a Jurkat cell expressing an
HIV-1 Gag-EGFP construct that induces virus-like particle (VLP) assembly (Fig. S4a,b). The global repetition map, calculated
using modified cosine similarity, showed:
• The most repetitive structure was the cell background signal (diffusing Gag protein)
• Lower SRS structures corresponded to active VLP assembly sites
• Some structures not discernible in the input image were detected, likely early VLP assembly stages
We identified VLP locations by calculating local maxima. The repetition map provided more detections than the input image
when using the same prominence threshold (Fig. S4c).
Multiscale detection of Nuclear Pore Complex structures. SReD’s multiscale analysis capability was demonstrated by
examining nuclear pore complexes (NPCs) in STORM reconstructions of labelled gp210 proteins. Global repetition maps were
calculated at different scales by modifying block-to-image size ratios (Fig. S5a,b):

1. Original image (400x400 pixels), 5x5 pixel blocks: detected single nucleoporins
2. Original image, 15x15 pixel blocks: detected nucleoporin clusters
3. Downscaled image (200x200 pixels), 25x25 pixel blocks: detected entire NPC units
This demonstrates SReD’s ability to detect structures at multiple scales without requiring structural priors.


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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Note S3: Automated analysis pipeline for spectrin ring detection in neuronal axons
Automatic estimation of axon orientations. A robust analysis of ring periodicity using autocorrelation functions requires

the axon segments to be oriented with their long axis parallel to the horizontal axis. We designed a streamlined approach that
uses SReD’s block repetition to estimate the orientation of the axons along their span (Fig. S6a). This information can be
used for downstream applications, such as estimating the distribution of angles in each sample (Fig. S6b,c) or automatic region
extraction and rotation. Our method is fully implemented in ImageJ macros and works as follows:
1. Calculate the axons’ "skeletons". "Skeletonize" function produces a binary mask of the axons’ skeletons by shrinking
their to a 1-pixel wide line along their centers of mass. To improve the results of this function, the images are preprocessed
by applying a Gaussian blur (15 pixel radius) to retrieve only the high-order structures and discard the single-molecule
low-order information. Then, thresholding is performed using the Otsu method (5) to remove unwanted objects. The
"Skeletonize" function is applied to the thresholded images. A Gaussian blur (2 pixel radius) is applied to the skeletons to
avoid diagonal discontinuities derived from the 1 pixel-wide lines that form the skeletons. Finally, a range normalisation
step is performed to bring all the skeletons to the same intensity interval.
2. Generate synthetic blocks comprising lines at different orientations. This is done by designing a block containing a
vertical 1 pixel-wide line in a 90x90 black canvas. Then, copies of this block are created and rotated in 10º increments,
until all possible orientations are recapitulated at that angular resolution. A Gaussian blur (2 pixel radius) is applied to
the blocks to match the appearance of the blurred axon skeletons. The synthetic blocks are then cropped into 45x45 pixel
blocks to avoid border artefacts, and normalised to their intensity range.
3. Calculate block repetition maps using SReD. SReD’s block repetition is used to generate repetition maps using the
synthetic blocks and axon skeletons generated previously. Each round of block repetition produces a repetition map
where regions containing skeletons at the specific orientations display higher SRS. The repetitions maps are normalised
to their intensity range, multiplied by the Gaussian blurred masks to remove unwanted detections, and normalised once
more.
4. Generate the angle maps. Each coordinate of the 1 pixel-wide skeletons is labelled with the angle corresponding to the
highest SRS in the repetition maps.
Reference block optimisation for ring pattern detection. The detection of specific structures requires the use of a reference. In SReD, the reference is provided as an image block containing a representation of the structure of interest. To minimise
the bias of downstream analyses towards the reference block, we devised a method to optimise the reference block based on the
data characteristics (Fig. S7a). The method is implemented as a combination of ImageJ macros and Python code. It works as
follows:

1. Conceptualisation of the reference block. The reference block used for spectrin ring detection should recapitulate a
periodic ring pattern while using the minimum amount of information to minimise bias towards that pattern’s characteristics. We concluded that the simplest pattern would comprise a black canvas with 3 vertical lines resembling a side-view
of a 2D projection of rings. While using 2 lines instead of 3 seems more parsimonious, doing so would centre the pattern
at the inter-ring spacing and not the ring itself. The 3-ring pattern can be defined by two parameters: (i) inter-ring spacing
and (ii) ring height. The first parameter is the main target of our study, while the latter is less important and is mostly a
function of axon girth.
2. Optimisation of the ring pattern’s parameters. To minimise the bias of our study towards the reference pattern, a
parameter sweep was performed to optimise the pattern’s characteristics according to the input data. To do this, we generated a collection of 248 blocks incorporating various combinations of inter-ring spacing and ring height. Representative
segments of distal axons (6 for each group) were extracted from the data. From these axon segments, a total of 30 test
regions were extracted and rotated to align with the horizontal axis. This rotational adjustment guaranteed consistency
when applying the same set of reference blocks across the datasets, eliminating any potential variations stemming from
block rotation and interpolation. SReD was used to calculate block repetition maps for every reference block and the autocorrelation functions of the repetition maps was calculated. The relative amplitude of the autocorrelations’ first harmonic
was used to assess how effectively each block captured the underlying periodic pattern. We systematically identified the
set of block parameter values that maximised the first harmonic’s relative amplitude (Fig. S7b-d). This optimised set
of parameter values serves as a reliable representation of the periodic pattern within the dataset. The optimisation was
performed separately for each dataset analysed in this study.
Detection of ring patterns in large fields-of-view.. Using the optimised ring pattern and the angle distributions previously
generated, SReD can be used to map ring patterns at all orientations across large fields-of-view.


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available under aCC-BY 4.0 International license.

1. Preparing the input data for analysis An input image comprising a large-field-of-view of axons featuring labelled
spectrin rings is copied and rotated for each angle defined previously (0º to 180º in 10º steps). To avoid cropping at the
borders, the image is zero-padded before this step. A range normalisation is also applied.
2. Detecting spectrin rings at all orientations. Block repetition maps are calculated for each rotated input. Doing this
ensures that each axonal region in the input is probed at least once while oriented parallel to the horizontal axis. Then,
the repetition maps are rotated back to their original orientation.
3. Generation of angular weight maps From the repetition maps calculated previously, we are interested in retrieving
only the information that is relevant for a specific angle. For example, in the repetition map calculated from the input
image rotated by -10º, we want to keep the segments whose orientation relative to the horizontal axis was estimated to be
10º. To do this, we use a weight multiplication approach. An angular weight map is generated for each orientation. The
weight maps are generated using the angle repetition maps calculated previously. The maps are slightly transformed to
accommodate the extent of the axons in the input data by applying a power function (exponent of 8) and a Gaussian blur
(radius 2 pixels), followed by a range normalisation step.
4. Application of the angular weight maps and generation of the final output The angular weight maps are multiplied
by the ring repetition maps that were calculated using inputs rotated to their corresponding angle. For example, the ring
repetition map calculated from the input image rotated 10º is multiplied by the angular weight map comprising regions
that are oriented at 10º from the horizontal axis. This step retains only the ring pattern information that is relevant at
each orientation. After a range normalisation step, the final image reconstruction is generated by averaging the weighted
repetition maps (Fig. 2b).
Automatic extraction and quantitative analysis of ring patterns in axon segments. Previous studies focusing on characterising the periodicity of spectrin rings in axons were limited by the need to manually select regions for analysis. This
method is labour-intensive and the results can vary between experts. Semi-automatic methods also exist, where algorithms
such as NeuronJ (6) produce tracings of the neurons and provide a framework for quantitative analysis. However, these algorithms do not take into account the underlying low-order structures, resulting in axon segments that may or may not contain
periodic ring patterns, which impacts their quantitative descriptions. Our approach leverages SReD’s multiscale capabilities to
ensure that only regions containing patterns are analysed:

1. Detection of high-order ring patterns. Ensuring that the axon segments analysed contain ring patterns is essential to
avoid corrupting the results with unwanted structural patterns. This entails mapping regions of the input data where
high-order patterns exist. This is often achieved by convolving data with Gaussian kernels. However, this method
inherently discards the low-order information and its results are mostly a function of local signal intensity. We approach
this problem by leveraging SReD’s multiscale analysis capabilities. Using the optimised ring reference block, a new
reference block comprising an extension of the original is generated with 9 rings instead of 3 (Fig. S8a). SReD is used to
calculate block repetition maps, in which regions where the high-order patterns are more likely to exist will have higher
SRS (Fig. S8b). A quantitative comparison between our approach and the more common approach using convolutions
with Gaussian kernels demonstrates that SReD produce a more robust analysis by retaining the low-order information
of ring units while providing mapping the presence of high-order patterns (Fig. S8c,d). The high-order repetition map
is thresholded using the Otsu method (5) to generate a binary mask where regions containing high-order patterns are
segmented. These regions can be used for downstream analysis using the optimised low-order reference block, ensuring
that the data analysed contains the structures of interest.
2. Removing axon crossings and bifurcations. This step is essential to the study of axon ring periodicity because (i)
regions containing axon crossings may contain multiple periodic patterns at different phases and orientations, and (ii) the
arrangement of spectrin in regions where axons bifurcate is not well-characterised and is known to not display the periodic
patterns observed in more distal regions (7). These regions are filtered out from the analysis using a custom ImageJ macro
that detects coordinates where a pixel of the skeleton contacts with more than 2 pixels. This creates discontinuities in
the skeletons exactly where the crossings/bifurcations are detected. Then, the extremities of the isolated segments are
iteratively pruned, until each extremity is reduced by an amount of pixels equal to the radius of the regions chosen for
downstream analysis (75 pixels). This completely eliminates unwanted regions.
3. Extraction of regions containing periodic patterns from the input data. The segmented axon skeletons generated in
the previous step are used as a basis to extract structurally relevant regions (Fig. S9a). The characteristics of the segments
already provide a basis to study the stability of spectrin rings, enabling comparisons between control axons and axons
treated with swinholide A. We demonstrate this by calculating their length distribution. No significant differences were
found between the length distributions, indicating that swinholide A treatment did not impact the high-order arrangement
of spectrin rings (Fig. S9b). To automatically extract regions for the analysis of low-order patterns, the axon segments


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are divided into non-overlapping 150x150 pixel blocks centred at their skeletons. The coordinates of each block are used
to crop the corresponding regions from the large field-of-view ring repetition maps generated previously. Then, each
block is rotated to become parallel to the horizontal axis using the angle estimations calculated previously. This process
yields a library of regions containing ring patterns and their ring repetition maps (Fig. S9c).
4. Quantitative analysis of local ring patterns. The rings patterns detected and extracted using SReD can be used for
downstream analysis. This enables the characterisation of the patterns’ characteristics. We calculated the autocorrelation
functions of each region and, from the first harmonics’ position, determined that the average inter-ring spacing in our
datasets was approximately 180 nm. We found no significant differences between the control and the swinholide Atreated samples (Fig. S9d). The first harmonics’ amplitude can be interpreted as the strength or prominence of the
periodic pattern. Here, we found a 12% reduction in prominence in the samples treated with swinholide A (Fig. S9e). This
reduction was smaller compared to previous studies (7). However, when we analysed the fraction of regions containing
periodic patterns, we found a 39% reduction in the samples treated with swinholide A that was not reported previously.
These results demonstrate that our approach enabled discerning the effects of swinholide A in pattern frequency from
pattern prominence.
5. Evaluation of SReD’s performance in noisy data. The image reconstructions used in the previous sections were generated from localisation data obtained using Single-Molecule Localisation Microscopy (SMLM). Due to the synthetic
nature of these reconstructions, the images produced are devoid of noise originated from the electronic acquisition systems. However, the generalisability of our method to other microscopy modalities requires sensitivity to structures in
noisy data. We evaluate SReD’s performance in noisy data using a test image of an axon segment, to which Gaussian
noise with incrementally higher standard deviation is added. SReD is then used to detect repetitions of the optimised
ring block and its performance is evaluated by comparing the block repetition maps with the "noise-free" control sample (Fig. S10a). The repetition maps calculated showed that SReD was able to detect ring patterns in a wide range of
signal-to-noise ratios (SNRs). Notably, it enabled detecting ring patterns in images with very low SNR, where structures are usually not discernible (Fig. S10b). Despite the reduction in confidence, evidenced by the lower SRSs, the
detections remained specific, as shown by their colocalisation with the reference structures (Fig. S10b, bottom row). We
quantified the performance of the algorithm by calculating correlation metrics between the noisy inputs and the control
(Fig. S10c). We used two metrics commonly used to assess image quality and fidelity (the Structural Similarity Index
Measure (SSIM) and the Root Means Squared Error (RMSE)). This analysis showed that the repetition maps were a
more robust representation of the control sample. We also analysed the results using autocorrelation functions. Here,
the autocorrelation harmonics degraded quickly in the noisy input images while remaining well-defined in the repetition
maps (Fig. S10d). The characteristics of the autocorrelations’ harmonics revealed that the expected inter-ring spacing of
approximately 190 nm was discernible in all repetition maps, while in the input data it was only detected in the control
sample. The prominence of the periodic patterns attributes high confidence to these conclusions (Fig. S10e). Together,
our results show that SReD’s repetition maps were a superior platform for the quantitative analysis of periodic patterns
and structure detection in noisy data when compared to the direct analysis of input data.
6. Evaluation of SReD’s specificity.
When detecting repetitions of a reference structure, it is important to evaluate their specificity, since a common caveat
of this approach is the introduction of bias towards the reference. This could result in false-positive detections. We
evaluated SReD’s specificity by analysing an image of axon segment whose width was incrementally stretched, disrupting
the periodic ring pattern’s characteristics (Fig. S11a). SReD was used to calculate repetition maps using the optimised
reference block (Fig. S11b). The average SRS across the repetition maps decreased abruptly upon stretching the input
image, indicating a high specificity for the reference structure (Fig. S11c). Importantly, this decrease in the average SRS
was followed by a slight increase that then faded, suggesting the detection of a secondary pattern when the input image
was stretched to twice the original width. This observation was investigated by analysing the corresponding repetition
maps. We determined that the secondary pattern corresponded to the detection of the second harmonic of the ring periodic
pattern. This was explained by the alignment of the reference block’s centre line with a single spectrin ring or the two
outer lines with two spectrin rings (Fig. S11d,e). The confidence of this detection was highest at a stretch factor of 2
because the patterns period is exactly twice the original at this level. Furthermore, autocorrelation functions showed that,
in these conditions, the peak of the second harmonic colocalised with the input’s intrinsic pattern (Fig. S11f). Analysis
of the first harmonic of the autocorrelations revealed that the period of the pattern in the input image increased with
the stretch factor, whereas in the repetition maps it remained at approximately 180 nm but with incrementally lower
prominence, indicating the high specificity of the algorithm. The second harmonic remained at twice the period of the
first harmonic while the reference pattern was present, and reflected the input’s intrinsic period thereafter (Fig. S11g,h).
Together, these results suggest that SReD is highly specific for the reference structures, with false-positive detections still
reflecting the structural arrangements of the input data and being discernible from true-positives by the magnitude of the
SRS.


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available under aCC-BY 4.0 International license.

Note S4: Evaluation of SReD’s performance in images corrupted with non-specific structures
Generating images containing non-specific structures. Due to non-specific labelling and autofluorescence, microscopy

data often contains unwanted structures, corrupting its integrity. This presents a challenge for structural analysis. Unlike camera
noise, which can be effectively addressed through established denoising algorithms leveraging its predictable characteristics,
non-specific structures add complexity by introducing additional structures into the data. This can obscure specific structures
or alter their appearance, complicating accurate analysis. While an expert might visually distinguish specific from non-specific
structures in certain cases, their presence still impacts the analysis. Given that SReD’s global repetition mode is designed to
detect all structures in an image, it was crucial to evaluate how non-specific structures affect the analysis of specific structures
in a controlled sample. To achieve this, non-specific structures were introduced into images of a Jurkat cell producing viruslike particles (VLPs), along with simulated free particles exhibiting similar characteristics (Fig. S12a). Perlin noise at varying
frequencies was added to simulate non-specific structures with different levels of complexity using the Python (3.9.4) "PerlinNoise" library (v1.13). Different noise frequencies were achieved by modifying the "scale" parameter, which corresponds to
the inverse of the frequency. Higher frequencies generate structures with increased complexity.
Analysis of SReD’s robustness against non-specific structures. Global repetition maps were calculated for each sample

(Fig. S12b). The coordinates of small round objects were identified by calculating 3D local maxima. The number of detections
in the global repetition maps was higher than in the input images for all samples (Fig. S12c). Specifically, the input images had
detection counts of 251, 235, and 223 at noise frequencies 0, 0.02 and 0.04, while the global repetition maps showed detection
counts of 505, 281, and 462 (Fig. S12d). Furthermore, the percentage of ground-truth detections was substantially higher in
the global repetition maps compared to the input images. In the input images, the ground-truth detection percentages were
32%, 30%, and 24%, whereas in the global repetition maps, these percentages increased to 96%, 63%, and 79%, respectively
(Fig. S12e). These results underscore the significant impact of non-specific structures on structural analysis and highlight the
enhanced detection capabilities of SReD’s global repetition mode. By substantially increasing the detection of ground-truth
structures, even in the presence of complex non-specific noise, this method demonstrates its robustness and effectiveness in
accurately identifying specific structures within corrupted microscopy data.


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Note S5: Assessment of microtubule dynamics using SReD
Calculation of spatiotemporal global repetition maps. The versatility of SReD’s global repetition mode is demonstrated

by extending its 3D capabilities to enable spatiotemporal analysis. A 2D time-lapse was analysed by defining time as the third
dimension, resulting in the analysis of texture repetitions within a given time interval. Several time intervals were defined, and
subsets of the input data were created by only keeping images within those intervals. Then, the depth of SReD’s block size was
defined as having the same size as the number of images in each subset. Since SReD’s sampling scheme dictates that blocks
are not allowed to analyse regions beyond the data’s dimensions, this results in a single repetition map for each subset, which
highlights the degree of repetition of local textures across the specified time intervals (Fig. S13a). Here, the global SRSs can be
interpreted as the spatiotemporal stability of structures at each coordinate, with higher SRSs representing more stable structures
and vice versa.
Analysis of microtubule dynamics. Assessment of microtubule dynamics was conducted using spatiotemporal global repetition maps. These maps were generated by comparing the state of structures at each time interval with their initial state,
employing NRMSE metrics (Fig. S13a). Higher NRMSE values indicated less stability of structures over time, and vice versa.
NRMSE maps derived from SReD’s repetition maps were compared to maps derived from (i) final images of each time interval
and (ii) temporal projections. Visual analysis revealed that NRMSE maps from input images highlighted displacements between successive time points. Some regions with high error values in these maps corresponded to local noise patterns because
the block size required to capture structures was unable to capture the average noise distribution. NRMSE maps from temporal
projections, due to their additive nature, were substantially corrupted by local noise differences. Consequently, these maps
poorly distinguished specific structural stability from noise. In contrast, global repetition maps remained highly robust against
local noise variations and effectively emphasised the recurrence of structures over time. The global repetition maps combined
the evaluation of structure displacement over time with measurements of structure repetition, providing a superior platform
for analysis. In these maps, NRMSE values highlighted regions with low NRMSE, indicating that the underlying structures
(MTOCs), were significantly more stable compared to EB3 comets. This superior capability of global repetition maps to detect differences between time intervals is attributed to their resistance to noise corruption and their accurate representation of
spatiotemporal information. While the average NRMSE values from input images and temporal projections remained stable
over time, SReD effectively captured the dynamic nature of microtubules, showcasing its efficacy in tracking and analysing
microtubule dynamics (Fig. S13b).


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Supplementary Bibliography
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1046-2023. doi: 10.1016/j.ymeth.2019.05.008.
4. Olivier Burri and Romain Guiet. DAPI and Phase Contrast Images Dataset, May 2019.
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S1. Generation of the relevance mask. a, Representative input image with local variance calculated using non-overlapping
blocks, illustrating spatial distribution of image texture. Scale bar: 10 µm. b, Histogram of calculated block variances, highlighting
the lower tail (magenta, percentile 0.03) and upper tail (green) of the distribution. c, Example blocks extracted from the distribution
tails: upper tail (green border) showing regions with significant structural information, and lower tail (magenta border) representing
predominantly noise. The variance of each block is shown in white text. d, Series of relevance masks generated using different filter
constants (C). Each mask is created by multiplying C with the previously calculated average noise variance to determine the final
threshold for structural relevance. This demonstrates how adjusting C impacts the discrimination between structurally relevant and
irrelevant image regions.


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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S2. Structure detection using simulated blocks. a, Workflow diagram illustrating the use of simulated reference blocks for
structure detection. Simulated blocks containing lines and line crossings at various orientations were generated and used by SReD to
analyze a STORM image of microtubules in a HeLa cell. SReD produces a repetition map for each reference block, highlighting regions
of structural similarity. b, Composite images showing the original STORM reconstruction (grey) overlaid with repetition maps (colour)
for each simulated reference block. Scale bar: 2 µm. c, Analysis of SReD’s specificity for linear structures at varying proximities.
(i-iv) Repetition maps generated using a vertical line reference block (yellow box in i) on test images with vertical lines at increasing
distances. Graph shows the average Structural Repetition Score (SRS) versus line displacement, with dashed lines corresponding to
examples i-iv. d, Evaluation of SReD’s specificity for complex structures. (i-iv) Repetition maps generated using an orthogonal line
crossing reference block (yellow box in i) on test images with line crossings at increasing angles. Graph displays the average SRS
versus angle increment, with dashed lines corresponding to examples i-iv.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S3. Structure detection using empirical blocks. a, Workflow diagram illustrating the use of empirically extracted reference
blocks for structure detection. Reference blocks containing nuclear envelope regions at various orientations were extracted from a
DAPI-stained image of HeLa cell nuclei. SReD generates a repetition map for each reference block, highlighting regions of structural
similarity. b, Top panel: Input image of DAPI-stained HeLa cell nuclei with locations of extracted empirical blocks highlighted. Bottom
panel: Composite image showing the overlay of colour-coded repetition maps, each corresponding to a different empirical reference
block. Scale bar: 30 µm. c, Expanded view of individual repetition maps for each empirical reference block, demonstrating SReD’s
ability to detect nuclear envelope structures at different orientations. Scale bar: 30 µm. d, Top panels: Composite images showing
the overlay of colour-coded repetition maps of nuclei i-iv. Scale bar: 30 µm. Bottom panels: Polar plots depicting the relative area
percentages of each repetition map in the nuclei composites.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S4. Detection of HIV-1 virus-like particles using Global Repetition. a, Workflow diagram illustrating the "all-to-all" sampling
scheme in Global Repetition. The global repetition map is a platform for quantitative analysis such as local extrema calculation. b,
Top panel: Image reconstruction of an acivated Jurkat cell expressing an HIV-1 Gag-EGFP construct, which induces the assembly of
virus-like particles (VLPs). Scale bar: 5 µm. Bottom panel: Global repetition map calculated from the input image in the top panel,
using a block size of 7x7 pixels and the modified cosine similarity metric. The insets in both panels highlight a region where assembling
viral structures can be discerned in the global repetition map but not in the input image. c, Local maxima calculated from the input
image and the (inverted) global repetition map, showing a higher number of detections in the global repetition map using the same
prominence threshold.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S5. Multiscale detection of Nuclear Pore Complex structures using Global Repetition. a, Workflow diagram illustrating the
modulation of block-to-image size ratio modulation for multiscale global repetition analysis. b, Image reconstructions of the input image
and the block sizes used for global repetition analysis. A low- and intermediate- order analysis used the original image dimensions
(400x400 pixels) and 5x5 and 15x15 pixel block sizes to detect single nucleoporins (orange) and nucleoporin clusters (blue). A highorder analysis used a downscaled input image (200x200 pixels) and a block size of 25x25 pixels to detect entire NPC units.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S6. Automated estimation of axon orientations. a, Workflow diagram illustrating the estimation of axon orientations. Synthetic
blocks comprising lines at different orientations are used to calculate repetitions in skeletonised axons. Each skeleton coordinate is
labelled with the angle corresponding to the highest SRS. b, Polar plots depicting the distribution of axon angles in the control (top
panel) and swinholide A (bottom panel) samples. c, Overlay of representative input images and their angle-labelled skeletons, using
the same colour code used in panel b). Scale bar: 5 µm.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S7. Optimisation of block parameters for ring pattern detection. a, Schematic representation of the tasks performed. A set of
248 synthetic blocks with different spacing and height combinations were generated. Test images (30 for each group) were randomly
extracted from each dataset and SReD was used to calculate the repetition maps of each reference block. The repetition maps were
analysed using autocorrelation functions and the patterns’ prominence (given by the autocorrelations’ first harmonic amplitude) was
used to assess how well each reference block fitted the data. For each test image, this information is depicted in a heatmap. The
combination of parameters with the highest pattern prominence value is chosen in from each heatmap and averaged within each
dataset to calculate the optimised block. b, Representative examples of the optimisation process. The heatmaps where the highest
pattern prominences were found are shown. Scale bar: 0.4 µm. c-e, Plots of the optimised parameters calculated by comparing the
distributions of each parameter between groups (n=248, n.s. p>0.05, * p<0.05, Mann-Whitney U test).


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S8. Detection of high-order ring patterns. a, Schematic representation of the samples generated. Top panel: Reference
block containing a high-order ring pattern with 9 rings. Center panel: Reference block containing a low-order ring pattern with 3 rings.
Bottom panel: Convolution with a Gaussian kernel (15 px radius). b, Overlay of a representative example of the input data and the
corresponding block repetition maps. c, Error maps demonstrating that SReD enables detecting high-order patterns without discarding
low-order information. The high-order repetition maps are a more robust representation of the low-order structures compared to the
method using convolutions with Gaussian kernels. Scale bars: 5 µm.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S9. Quantitative analysis of ring patterns in axon segments. a, Image reconstructions illustrating the approach used to
automatically extract non-overlapping regions along the axons’ skeletons. Scale bar: 1 µm. b, Length distributions of the skeletonised
axon segments analysed. c, Representative examples of the non-overlapping regions extracted along the axons’ skeleton segments
(STORM in gray, SReD repetition maps in magenta). Scale bar: 1 µm. d, Average spacing of the regions analysed (N=6, mean ± SEM
- CTRL: 177 nm ± 1 nm, SWIN: 179 nm ± 2 nm, n.s. p>0.05, t-test). e, Pattern prominence of the regions analysed (N=6, mean ± SEM
- CTRL: 0.253 ± 0.008, SWIN: 0.223 ± 0.007, * p<0.05, t-test).


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S10. Evaluation of SReD’s performance in images containing random noise. a, Schematic of the tasks performed. A control
image containing a periodic pattern is corrupted with random noise. The periodic pattern is mapped using an optimised reference
block. The repetition maps are quantitatively analysed using autocorrelation functions. b, Visual comparison of image reconstructions
at different signal-to-noise ratios (SNRs). Top row: Input images with SNRs decreasing from left to right. Middle row: Repetition maps
calculated using an optimised reference block. Bottom row: Merge of the input images and the repetition maps. Scale bar: 1 µm c,
Evaluation of noise robustness by comparing the distributions of control vs. noisy images (black) and the corresponding repetition maps
(magenta) at different SNRs using different metrics. The repetition maps provided a superior representation of the control conditions
in all cases. Top panel: Distributions calculated using the Structural Similarity Index (SSIM) metric (p<0.0001, t-test). Bottom panel:
Distributions calculated using the Root Mean Squared Error (RMSE) metric (p<0.01, t-test). d, Autocorrelation plots demonstrating the
sensitivity to the periodic patterns in the input images (black) and the SReD repetition maps (magenta). e, Distribution of the inter-ring
spacing (top panel) and pattern prominence (bottom panel) calculated from the autocorrelation functions of the input data (black) and
the SReD repetition maps (magenta) at different SNRs.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S11. Evaluation of SReD’s specificity. a, Schematic of the tasks performed. A control image containing a periodic pattern is
stretched along its width to disrupt the pattern’s characteristics. The periodic pattern is mapped using an optimised reference block.
The repetition maps are quantitatively analysed using autocorrelation functions. b, Visual comparison of image reconstructions at
different stretch factors. Top row: Input images with stretch factors increasing from left to right. Middle row: Repetition maps calculated
using an optimised reference block. Bottom row: Merge of the input images and the repetition maps. Scale bar: 1 µm. c, Average
Structural Repetition Factor (SRS) in the repetition maps plotted against the stretch factor. A primary pattern (blue) and a secondary
pattern (orange) are detected. d, Image reconstructions of the primary and secondary patterns detected in c). e, 2D intensity profiles
(i.e., integrated density) of the images in d). f, Autocorrelation plots of the input images (black) and repetition maps (magenta) at stretch
factors 0 (top) and 2.0 (bottom). g, Inter-ring spacings calculated from the autocorrelation analysis plotted against the stretch factor. h,
Pattern prominences calculated from the autocorrelation analysis plotted against the stretch factor. The dashed gray lines indicate the
samples shown in panel b).


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S12. Evaluation of SReD’s performance in images corrupted with non-specific structures. a, Schematic of the tasks
performed. Perlin noise is added to a 3D image containing a Jurkat cell expressing an HIV-1 Gag-EGFP construct (green) and synthetic
bead structures resembling free viral particles (magenta). A Global Repetition map is calculated and 3D local maxima are calculated. b,
Input images with Perlin noise of different frequencies and their corresponding Global Repetition maps. c, Plots of the spot detections
obtained by calculating local maxima in the input images and their Global Repetition maps. d, Plot showing the number of detections
obtained in each sample. e, Plot showing the percentage of reference detections obtained in each sample.


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bioRxiv preprint doi: https://doi.org/10.1101/2024.09.16.613204; this version posted September 16, 2024. The copyright holder for this preprint
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under aCC-BY 4.0 International license.

Fig. S13. Assessment of microtubule dynamics using Global Repetition. a, Analysis of structural stability by comparing different
time frames with the initial state (0 sec) using the Normalised Root Mean Squared Error (NRMSE) metric. Top row: Input images
showing the final state in each time frame. Middle row: Time projections of all time points within each time frame. Bottom row: SReD
global repetition maps calculated using time as the third dimension of the analysis. b, Plot showing the NRMSE distributions of each
dataset.