A geometry-first tutorial for time-resolved morphological analysis with PyPETANA

Benjamin Evert Himberg; Sanghita Sengupta

arxiv: 2605.18578 · v1 · pith:HQUXIE7Znew · submitted 2026-05-18 · ❄️ cond-mat.soft

A geometry-first tutorial for time-resolved morphological analysis with PyPETANA

Benjamin Evert Himberg , Sanghita Sengupta This is my paper

Pith reviewed 2026-05-20 07:49 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords time-resolved morphologygeometric analysisbinary masksfractal dimensionsevolving shapesimage processingnon-equilibrium systems

0 comments

The pith

A tutorial workflow extracts time-resolved geometric measures like area and fractal dimensions directly from image sequences of evolving shapes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper provides a step-by-step guide to turning time-lapse videos into sequences of binary masks and then computing geometric properties at each time step. These properties include area, perimeter, circularity, and effective fractal dimensions, plus multiscale boundary details from box-counting methods. The emphasis is on reconstructing morphology straight from the images rather than starting from any assumed rules of how the shape grows. This matters for studying complex forms that arise in non-equilibrium settings, such as tumor invasion, because it supplies concrete numbers for how shape changes without needing a full microscopic model first.

Core claim

The tutorial establishes a workflow that starts from time-lapse video input, extracts binary masks, and computes time-resolved geometric observables including area, perimeter, circularity, and effective fractal dimensions, together with multiscale boundary analysis via supersampled box-counting on filled morphologies and finite-width boundary bands, all without assuming microscopic growth mechanisms, as demonstrated on invasive tumor morphologies.

What carries the argument

The central mechanism is the geometry-first pipeline that converts image sequences into binary representations and then derives temporal series of shape descriptors through direct computation.

If this is right

Researchers can track how the area and perimeter of a structure change over time directly from video recordings.
Measures of circularity provide insight into how compact or irregular the morphology becomes during evolution.
Effective fractal dimensions quantify the complexity of boundaries at different scales in growing interfaces.
Multiscale analysis applies to benchmark cases like cancer-growth boundaries in time-resolved data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the masks are reliable, the same geometric tracking could apply to other dynamic systems such as crystal growth or fluid interfaces.
Integrating these observables with simulation data might allow validation of models against experimental morphology evolution.
The box-counting methods for boundaries could be tested on synthetic images with known fractal properties to calibrate accuracy.

Load-bearing premise

The workflow depends on the extracted binary masks faithfully capturing the morphological features without major segmentation errors or loss of boundary information.

What would settle it

Running the analysis on a set of images where the true boundaries are known from high-resolution ground truth and checking if the computed metrics match within expected error bounds would test the claim.

read the original abstract

We present a step-by-step, reproducible tutorial for PyPETANA, an open-source Python framework for geometry-first, time-resolved quantification of evolving morphology from image data. Starting from time-lapse video input, the tutorial demonstrates how to extract binary masks, compute time-resolved geometric observables including area, perimeter, circularity, and effective fractal dimensions, and analyze their temporal evolution. The workflow emphasizes direct reconstruction of morphology from images without assuming microscopic growth mechanisms. In addition to compactness-sensitive geometric descriptors, the framework supports multiscale boundary analysis through supersampled box-counting methods applied to filled morphologies and finite-width boundary bands. The benchmark suite further demonstrates applicability to invasive tumor morphologies and multiscale boundary evolution in time-resolved cancer-growth interfaces. This tutorial accompanies the computational workflow underlying arXiv:2602.05958 and provides a reproducible foundation for geometry-based analysis of evolving non-equilibrium morphologies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a practical tutorial that ships working code and benchmarks for pulling geometric observables from time-lapse images, but it mainly documents standard methods rather than adding new science.

read the letter

The main takeaway is that this paper is a step-by-step tutorial for PyPETANA, an open Python framework that computes time series of shape descriptors like area, perimeter, circularity, and effective fractal dimension straight from image sequences. It targets evolving morphologies such as tumor interfaces and sticks to direct reconstruction from the data without embedding any growth model assumptions. The workflow includes mask extraction followed by multiscale boundary analysis via supersampled box-counting on both filled shapes and finite-width bands. The benchmark examples on invasive cancer-growth interfaces make the steps concrete and testable. What the paper does well is emphasize reproducibility through explicit code paths, parameter settings, and a supplied benchmark suite that ties back to their earlier arXiv:2602.05958 work. This packaging can genuinely help labs standardize measurements in cond-mat.soft without reinventing the image-processing pipeline each time. The focus on geometry-first analysis is a reasonable choice for non-equilibrium systems where microscopic rules are uncertain. The soft spots are modest and expected for a tutorial format. The core techniques are drawn from established literature, so the advance is mostly implementation and documentation rather than new descriptors or theory. There is little discussion of how sensitive the outputs are to mask-generation choices or to typical video artifacts like noise and resolution limits. No statistical validation or error propagation for the fractal-dimension estimates appears in the available description. These gaps do not break the workflow, but they mean users will still need to check robustness on their own data. This paper is for experimentalists and modelers in soft matter or biophysics who work with time-lapse microscopy of dynamic interfaces and want a ready, open-source starting point. A reader who needs consistent geometric tracking will get practical value from the code and examples. I would send it for peer review as a methods contribution that can support the field even without major conceptual novelty.

Referee Report

1 major / 2 minor

Summary. The manuscript is a step-by-step tutorial for the open-source PyPETANA Python framework that extracts time-resolved geometric observables (area, perimeter, circularity, effective fractal dimensions via supersampled box-counting) directly from time-lapse image sequences. The workflow begins with binary-mask generation from video input and proceeds to temporal analysis of evolving morphologies such as invasive tumor interfaces, without invoking microscopic growth rules.

Significance. If the documented code paths, parameter settings, and benchmark examples are correct and fully reproducible, the tutorial supplies a practical, geometry-first pipeline for quantifying non-equilibrium interface evolution in soft-matter and biophysical systems. The emphasis on multiscale boundary analysis and the accompanying code for tumor-growth examples could standardize direct morphological measurements across laboratories.

major comments (1)

[Opening workflow description] Opening workflow description: the central claim that binary masks faithfully preserve morphological features of interest is load-bearing for every subsequent observable, yet the tutorial provides no sensitivity analysis, ground-truth validation, or discussion of segmentation artifacts that could distort perimeter or fractal-dimension measurements.

minor comments (2)

[Abstract] Abstract: the term 'effective fractal dimensions' is introduced without a one-sentence definition or pointer to the exact supersampled box-counting implementation used on filled morphologies versus boundary bands.
[Benchmark suite] Benchmark suite section: explicit numerical parameter values (thresholds, supersampling factors, box-counting scales) employed for the tumor-interface examples should be tabulated to guarantee exact reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and positive recommendation for minor revision. We address the single major comment below.

read point-by-point responses

Referee: Opening workflow description: the central claim that binary masks faithfully preserve morphological features of interest is load-bearing for every subsequent observable, yet the tutorial provides no sensitivity analysis, ground-truth validation, or discussion of segmentation artifacts that could distort perimeter or fractal-dimension measurements.

Authors: We agree that the fidelity of the binary-mask step is foundational. The tutorial already includes explicit code for mask generation from video frames using standard thresholding and morphological operations, but we acknowledge that it does not yet contain a dedicated sensitivity or artifact analysis. In the revised version we will insert a short subsection immediately after the mask-generation workflow that (i) enumerates common segmentation artifacts (boundary smoothing, isolated-pixel noise, and partial-volume effects) and their quantitative impact on perimeter and supersampled box-counting fractal dimension, (ii) provides a compact sensitivity test on synthetic ground-truth shapes with controlled noise levels, and (iii) adds practical recommendations and references for users who wish to validate their own segmentation pipelines. These additions remain within the tutorial’s scope while directly responding to the referee’s concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity: methods tutorial with explicit pipeline

full rationale

The paper presents a reproducible computational workflow and tutorial for PyPETANA to extract geometric observables (area, perimeter, circularity, effective fractal dimension via box-counting) from time-lapse images. No mathematical derivations, predictions, or first-principles claims are made that could reduce to inputs by construction. The workflow is described with code paths, parameter settings, and benchmarks; the central claim of direct geometry-first analysis without growth-mechanism assumptions is supported by the supplied implementation details rather than any self-referential loop or fitted renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The described workflow rests on standard image-processing assumptions for mask extraction and on conventional geometric formulas for area, perimeter, and box-counting; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)

domain assumption Binary masks can be extracted from time-lapse video input such that morphological features remain quantitatively faithful.
Workflow begins from this extraction step without discussing segmentation error or validation against ground truth.

pith-pipeline@v0.9.0 · 5677 in / 1290 out tokens · 46485 ms · 2026-05-20T07:49:18.050570+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The workflow emphasizes direct reconstruction of morphology from images without assuming microscopic growth mechanisms... geometric observables including area, perimeter, circularity, and effective fractal dimensions
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

supersampled box-counting methods applied to filled morphologies and finite-width boundary bands

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

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Julian Bär, Mathilde Boumasmoud, Roger D. Kouyos, Annelies S. Zinkernagel, and Clé- ment Vulin. Efficient microbial colony growth dynamics quantification with coltapp, an automated image analysis application.Scientific Reports, 10:16084, 2020. doi:10.1038/ s41598-020-72979-4

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Rooney , Paul A

Beatrice Bottura, Liam M. Rooney , Paul A. Hoskisson, and Gail McConnell. Intra-colony channel morphology in Escherichia coli biofilms is governed by nutrient availability and substrate stiffness.Biofilm, 4:100084, 2022.doi:10.1016/j.bioflm.2022.100084

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Christoph Spahn, Estibaliz Gómez-de Mariscal, Romain F . Laine, Pedro M. Pereira, Lucas von Chamier, Mia Conduit, Mariana G. Pinho, Guillaume Jacquemet, Séamus Holden, Mike Heilemann, and Ricardo Henriques. Deepbacs for multi-task bacterial image analysis using open-source deep learning approaches.Communications Biology, 5:688, 2022. doi:10.1038/ s42003-0...

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R. Hartmann, H. Jeckel, E. Jelli, et al. Quantitative image analysis of microbial communities with biofilmq.Nature Microbiology, 6:151–156, 2021. doi:10.1038/s41564-020-00817-4

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A. Ducret, E. M. Quardokus, and Y. V . Brun. Microbej, a tool for high throughput bacterial cell detection and quantitative analysis.Nature Microbiology, 1:16077, 2016. doi:10.1038/ nmicrobiol.2016.77

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McConnell Rooney, M

L. McConnell Rooney, M. Bottura, P . A. Hoskisson, and O. Hallatschek. Analysis of biofilm complexity in 3d (abc3d): an open-source framework.bioRxiv, 2026. doi:10.64898/2026. 02.27.708470

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Stringer, T

C. Stringer, T . Wang, M. Michaelos, and M. Pachitariu. Cellpose: a generalist algorithm for cellu- lar segmentation.Nature Methods, 18:100–106, 2021. doi:10.1038/s41592-020-01018-x

work page doi:10.1038/s41592-020-01018-x 2021
[20]

sanghita211/pypetana: Pypetana, February 2026

Sanghita Sengupta and Benjamin Himberg. sanghita211/pypetana: Pypetana, February 2026. doi:10.5281/zenodo.18454785

work page doi:10.5281/zenodo.18454785 2026
[21]

A novel time-lapse imaging method for studying developing bacterial biofilms.Scientific Reports, 12:21120, 2022.doi:10.1038/s41598-022-24431-y

Momir Futo, Tin Široki, Sara Koska, Nina ˇCorak, Anja Tušar, Mirjana Domazet-Lošo, and Tomislav Domazet-Lošo. A novel time-lapse imaging method for studying developing bacterial biofilms.Scientific Reports, 12:21120, 2022.doi:10.1038/s41598-022-24431-y. 28 29

work page doi:10.1038/s41598-022-24431-y 2022
[22]

Geometry and dynamical morphology of growing bacterial colonies, 2026

Benjamin Evert Himberg and Sanghita Sengupta. Geometry and dynamical morphology of growing bacterial colonies, 2026. URL: https://arxiv.org/abs/2602.05958, arXiv:2602. 05958

work page arXiv 2026
[23]

O’Reilly Media, Inc

Gary Bradski and Adrian Kaehler.Learning OpenCV: Computer vision with the OpenCV library. " O’Reilly Media, Inc.", 2008

work page 2008
[24]

Barabási and H

A.-L. Barabási and H. E. Stanley.Fractal Concepts in Surface Growth. Cambridge University Press, 1995. 29

work page 1995

[1] [1]

The formation of patterns in non-equilibrium growth.Nature, 343:523–530, 1990.doi:10.1038/343523a0

Eshel Ben-Jacob and Peter Garik. The formation of patterns in non-equilibrium growth.Nature, 343:523–530, 1990.doi:10.1038/343523a0

work page doi:10.1038/343523a0 1990

[2] [2]

J. S. Langer. Instabilities and pattern formation in crystal growth.Rev. Mod. Phys., 52:1– 28, Jan 1980. URL: https://link.aps.org/doi/10.1103/RevModPhys.52.1, doi:10.1103/ RevModPhys.52.1

work page doi:10.1103/revmodphys.52.1 1980

[3] [3]

The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid.Proceedings of the Royal Society of London

Philip Geoffrey Saffman and Geoffrey Ingram Taylor. The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid.Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 245(1242):312–329, 06 1958. URL: https:// royalsocietypublishing.org/rspa/article-pdf/245/1242/312/998143/rspa.1958.0085.pd...

work page doi:10.1098/rspa.1958.0085 1958

[4] [4]

T . A. Witten and L. M. Sander. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett., 47:1400–1403, Nov 1981. URL: https://link.aps.org/doi/10.1103/PhysRevLett. 47.1400,doi:10.1103/PhysRevLett.47.1400

work page doi:10.1103/physrevlett 1981

[5] [5]

M. C. Marchetti, J. F . Joanny , S. Ramaswamy , T . B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha. Hydrodynamics of soft active matter.Rev. Mod. Phys., 85:1143–1189, Jul 2013. URL: https://link.aps.org/doi/10.1103/RevModPhys.85.1143, doi:10.1103/RevModPhys. 85.1143

work page doi:10.1103/revmodphys.85.1143 2013

[6] [6]

Proliferating active matter.Nature Reviews Physics, 5, 05 2023

Oskar Hallatschek, Sujit Datta, Knut Drescher, Jörn Dunkel, Jens Elgeti, Bartek Waclaw, and Ned Wingreen. Proliferating active matter.Nature Reviews Physics, 5, 05 2023. doi:10.1038/ s42254-023-00593-0

work page 2023

[7] [7]

M. C. Cross and P . C. Hohenberg. Pattern formation outside of equilibrium.Rev. Mod. Phys., 65:851–1112, Jul 1993. URL: https://link.aps.org/doi/10.1103/RevModPhys.65.851, doi: 10.1103/RevModPhys.65.851. 27 28

work page doi:10.1103/revmodphys.65.851 1993

[8] [8]

& Knops, H

Mitsugu Matsushita and Hiroshi Fujikawa. Diffusion-limited growth in bacterial colony formation.Physica A: Statistical Mechanics and its Applications, 168(1):498–506, 1990. URL: https://www.sciencedirect.com/science/article/pii/037843719090402E,doi:10.1016/ 0378-4371(90)90402-E

work page arXiv 1990

[9] [9]

Matsushita, J

M. Matsushita, J. Wakita, H. Itoh, I. Rafols, T . Matsuyama, H. Sakaguchi, and M. Mimura. Formation of colony patterns by a bacterial cell population.Physica A, 274(1–2):190–199, 1999

work page 1999

[10] [10]

Nelleke P . M. Brouwer, Amjad Khan, John-Melle Bokhorst, Fazael Ayatollahi, Jennifer Hay, Francesco Ciompi, Femke Simmer, Niek Hugen, Johannes H. W . de Wilt, Martin D. Berger, Alessandro Lugli, Inti Zlobec, Joanne Edwards, and Iris D. Nagtegaal. The complexity of shapes: How the circularity of tumor nodules affects prognosis in colorectal cancer.Modern P...

work page doi:10.1016/j.modpat.2023.100376 2026

[11] [11]

The anomalous diffusion of a tumor invading with different surrounding tissues.PLOS ONE, 9(10):1–16, 10 2014

Chongming Jiang, Chunyan Cui, Li Li, and Yuanzhi Shao. The anomalous diffusion of a tumor invading with different surrounding tissues.PLOS ONE, 9(10):1–16, 10 2014. doi: 10.1371/journal.pone.0109784

work page doi:10.1371/journal.pone.0109784 2014

[12] [12]

From snowflake formation to growth of bacterial colonies

Eshel Ben-Jacob. From snowflake formation to growth of bacterial colonies. ii. cooperative formation of complex colonial patterns.Contemporary Physics, 38(3):205–241, 1997

work page 1997

[13] [13]

Kouyos, Annelies S

Julian Bär, Mathilde Boumasmoud, Roger D. Kouyos, Annelies S. Zinkernagel, and Clé- ment Vulin. Efficient microbial colony growth dynamics quantification with coltapp, an automated image analysis application.Scientific Reports, 10:16084, 2020. doi:10.1038/ s41598-020-72979-4

work page 2020

[14] [14]

Rooney , Paul A

Beatrice Bottura, Liam M. Rooney , Paul A. Hoskisson, and Gail McConnell. Intra-colony channel morphology in Escherichia coli biofilms is governed by nutrient availability and substrate stiffness.Biofilm, 4:100084, 2022.doi:10.1016/j.bioflm.2022.100084

work page doi:10.1016/j.bioflm.2022.100084 2022

[15] [15]

Laine, Pedro M

Christoph Spahn, Estibaliz Gómez-de Mariscal, Romain F . Laine, Pedro M. Pereira, Lucas von Chamier, Mia Conduit, Mariana G. Pinho, Guillaume Jacquemet, Séamus Holden, Mike Heilemann, and Ricardo Henriques. Deepbacs for multi-task bacterial image analysis using open-source deep learning approaches.Communications Biology, 5:688, 2022. doi:10.1038/ s42003-0...

work page 2022

[16] [16]

Hartmann, H

R. Hartmann, H. Jeckel, E. Jelli, et al. Quantitative image analysis of microbial communities with biofilmq.Nature Microbiology, 6:151–156, 2021. doi:10.1038/s41564-020-00817-4

work page doi:10.1038/s41564-020-00817-4 2021

[17] [17]

Ducret, E

A. Ducret, E. M. Quardokus, and Y. V . Brun. Microbej, a tool for high throughput bacterial cell detection and quantitative analysis.Nature Microbiology, 1:16077, 2016. doi:10.1038/ nmicrobiol.2016.77

work page 2016

[18] [18]

McConnell Rooney, M

L. McConnell Rooney, M. Bottura, P . A. Hoskisson, and O. Hallatschek. Analysis of biofilm complexity in 3d (abc3d): an open-source framework.bioRxiv, 2026. doi:10.64898/2026. 02.27.708470

work page doi:10.64898/2026 2026

[19] [19]

Stringer, T

C. Stringer, T . Wang, M. Michaelos, and M. Pachitariu. Cellpose: a generalist algorithm for cellu- lar segmentation.Nature Methods, 18:100–106, 2021. doi:10.1038/s41592-020-01018-x

work page doi:10.1038/s41592-020-01018-x 2021

[20] [20]

sanghita211/pypetana: Pypetana, February 2026

Sanghita Sengupta and Benjamin Himberg. sanghita211/pypetana: Pypetana, February 2026. doi:10.5281/zenodo.18454785

work page doi:10.5281/zenodo.18454785 2026

[21] [21]

A novel time-lapse imaging method for studying developing bacterial biofilms.Scientific Reports, 12:21120, 2022.doi:10.1038/s41598-022-24431-y

Momir Futo, Tin Široki, Sara Koska, Nina ˇCorak, Anja Tušar, Mirjana Domazet-Lošo, and Tomislav Domazet-Lošo. A novel time-lapse imaging method for studying developing bacterial biofilms.Scientific Reports, 12:21120, 2022.doi:10.1038/s41598-022-24431-y. 28 29

work page doi:10.1038/s41598-022-24431-y 2022

[22] [22]

Geometry and dynamical morphology of growing bacterial colonies, 2026

Benjamin Evert Himberg and Sanghita Sengupta. Geometry and dynamical morphology of growing bacterial colonies, 2026. URL: https://arxiv.org/abs/2602.05958, arXiv:2602. 05958

work page arXiv 2026

[23] [23]

O’Reilly Media, Inc

Gary Bradski and Adrian Kaehler.Learning OpenCV: Computer vision with the OpenCV library. " O’Reilly Media, Inc.", 2008

work page 2008

[24] [24]

Barabási and H

A.-L. Barabási and H. E. Stanley.Fractal Concepts in Surface Growth. Cambridge University Press, 1995. 29

work page 1995