Cell Phantom Video Generation in Elliptical Fourier Descriptor Domain

Francesco Benedetto; Giacomo Boracchi; Luca Magri; Roberto Basla

arxiv: 2605.22563 · v1 · pith:AYF5KJXWnew · submitted 2026-05-21 · 💻 cs.CV

Cell Phantom Video Generation in Elliptical Fourier Descriptor Domain

Francesco Benedetto , Roberto Basla , Luca Magri , Giacomo Boracchi This is my paper

Pith reviewed 2026-05-22 07:15 UTC · model grok-4.3

classification 💻 cs.CV

keywords cell phantom generationelliptical Fourier descriptorsvideo synthesiscell trackingsynthetic databiomedical imagingtime series modelingcontour representation

0 comments

The pith

Representing cell contours with elliptical Fourier descriptors and modeling their time evolution generates biologically plausible phantom videos.

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

The paper develops a method to create synthetic videos of single cell phantoms that maintain consistency over time to simulate real biological processes. Annotated real videos for training cell tracking networks are scarce because labeling them requires significant time and expertise. By converting cell shapes into elliptical Fourier descriptor coefficients and treating their changes as a time series, the approach produces coherent sequences that can be used to generate training data automatically, reducing the annotation burden for medical applications such as cancer research.

Core claim

We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time. Our experimental validation proves that modelling the temporal evolution in EFD space enables the generation of biologically plausible phantom videos that can be used in generative pipelines for synthesizing annotated data for cell tracking.

What carries the argument

Elliptical Fourier Descriptors (EFDs) as a compact representation for 2D closed cell contours, with temporal dynamics modeled via multivariate time series of the EFD coefficients to enforce time consistency.

If this is right

Supports automatic generation of large-scale annotated datasets for training cell tracking algorithms.
Reduces the manual effort required to create new biomedical video datasets for problems like tissue repair and cancer treatment.
Produces phantom videos that replicate biological processes specific to different cell types through coherent temporal evolution.
Facilitates integration into broader generative pipelines for synthetic data creation in medical imaging.

Where Pith is reading between the lines

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

The approach could be extended to model cell division events by incorporating splitting mechanisms into the time series evolution.
Generated phantoms might help evaluate tracking algorithms under controlled variations in cell morphology not easily found in real data.
Adapting the method to other contour-based representations could apply similar ideas to tracking non-cellular objects in video.
Training on these phantoms may improve model robustness to noise or varying imaging conditions in real experiments.

Load-bearing premise

That the elliptical Fourier descriptor coefficients provide a strong enough prior on cell shape to produce sequences whose temporal changes match actual biological behaviors of the cells.

What would settle it

A direct comparison where experts rate the realism of generated phantom videos against real cell videos or where a cell tracker trained only on the synthetic data is tested on real videos and shows no improvement over baselines trained without them.

read the original abstract

Training Deep Neural Networks for tracking individual cells in biomedical videos requires a large amount of annotated data. The annotation of videos for cell tracking is very time consuming and often requires domain expertise; this explains the limited availability of public annotated data to address important medical problems like tissue repair or cancer treatment. Generating synthetic videos along with their Ground Truth annotations is a promising solution that relies, as a foundational first step, on the synthesis of single cell annotations (or phantoms). Phantoms need to be time consistent, as they have to replicate biological processes that are specific to the cell types. In this work, we propose a novel framework for generating videos of cell phantoms in the Elliptical Fourier Descriptors (EFDs) domain, a compact and geometrically interpretable representation for 2D closed contours. We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time. Our experimental validation proves that modelling the temporal evolution in EFD space enables the generation of biologically plausible phantom videos. Our method can be used in generative pipelines for synthesizing annotated data for cell tracking, thus strongly mitigating the annotation effort for creating new datasets. Our code is available for download here: https://github.com/FrancescoBenedetto99/efd-cell-video-gen.

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

The paper frames cell phantom video generation as a multivariate time series on EFD coefficients to enforce temporal consistency, which is a reasonable technical move for synthetic data in cell tracking, though validation details are missing and normalization continuity needs checking.

read the letter

The key point is that this paper shows how to generate videos of cell phantoms that maintain temporal consistency by representing cell shapes with elliptical Fourier descriptors and modeling their coefficients as a multivariate time series. This approach aims to produce biologically plausible sequences for use in training cell tracking networks, helping with the shortage of annotated biomedical video data. What stands out as new is the specific framing of phantom evolution in EFD space as a time series problem. Prior work on EFDs exists for static contours, but applying it dynamically for video generation in this domain seems fresh based on the abstract. They do a good job highlighting the motivation around data scarcity for problems like tissue repair and cancer research, and the method uses a geometrically interpretable representation which is a plus. The soft spots are mainly around the validation. The paper states that experiments prove biological plausibility, yet the abstract provides no numbers, no baselines, no dataset descriptions, or error analysis. Without those, it's difficult to assess how well it actually works. There's also the question of whether per-frame EFD normalization could cause discontinuities in the coefficient time series. If the normalization for rotation, scale, and starting point is independent each frame, smooth cell deformations might still lead to abrupt changes in the descriptors, which would undermine the time series modeling. The paper should clarify how they ensure the series is continuous. Overall, this is aimed at people working on generative models for medical imaging or synthetic data augmentation for tracking tasks. Readers dealing with shape descriptors or time series on contours might find it useful. I think it deserves peer review because the core idea is sound and the problem is relevant, even though the experiments need fleshing out for a full assessment.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a framework for generating time-consistent videos of single-cell phantoms by representing 2D cell contours via Elliptical Fourier Descriptors (EFDs) and modeling the temporal evolution of the EFD coefficient vectors as a multivariate time series. The central claim is that this representation supplies a sufficiently strong morphological prior to produce coherent, biologically plausible sequences that can be used to synthesize annotated data for cell-tracking DNNs.

Significance. If the approach succeeds in producing temporally coherent sequences without introducing artifacts from the representation itself, it would offer a compact, geometrically interpretable alternative to pixel-level or mesh-based phantom generation, directly addressing data scarcity in biomedical video analysis. The availability of code is a positive step toward reproducibility.

major comments (2)

[Abstract] Abstract: the assertion that 'experimental validation proves' biological plausibility is unsupported by any reported quantitative metrics, baselines, dataset descriptions, or error analysis. Without these, it is impossible to determine whether the generated sequences actually replicate cell-type-specific processes or whether post-hoc selections affect the outcome.
[Method] Method section on EFD extraction: the manuscript does not specify whether normalization for rotation, scale, and translation (standard in EFD computation per Kuhl & Giardina 1982) is performed consistently across all frames of a sequence or independently per frame. Independent normalization would risk large jumps in the coefficient time series, directly undermining the claim that the EFD representation itself supplies a strong prior for time-consistent phantoms.

minor comments (2)

[Method] The specific time-series model (e.g., RNN, Gaussian process, or autoregressive) used to evolve the EFD coefficients should be stated explicitly, including any hyperparameters, so that the dynamical prior can be evaluated.
[Figures] Figure captions and axis labels should indicate whether the displayed sequences are real or generated and include the number of EFD harmonics retained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and indicate planned revisions to improve clarity and rigor. Our responses focus on substance and aim to strengthen the presentation of the EFD-based framework without altering its core claims.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that 'experimental validation proves' biological plausibility is unsupported by any reported quantitative metrics, baselines, dataset descriptions, or error analysis. Without these, it is impossible to determine whether the generated sequences actually replicate cell-type-specific processes or whether post-hoc selections affect the outcome.

Authors: We acknowledge that the phrasing 'experimental validation proves' in the abstract is stronger than the supporting details provided in the summary. The full manuscript presents experimental results through visual inspection of generated sequences and qualitative assessment of temporal coherence for different cell types. To address the concern directly, we will revise the abstract to use more measured language ('Our experimental results demonstrate...') and include brief references to the evaluation approach, datasets used, and key consistency measures. These changes will be incorporated in the revised version. revision: yes
Referee: [Method] Method section on EFD extraction: the manuscript does not specify whether normalization for rotation, scale, and translation (standard in EFD computation per Kuhl & Giardina 1982) is performed consistently across all frames of a sequence or independently per frame. Independent normalization would risk large jumps in the coefficient time series, directly undermining the claim that the EFD representation itself supplies a strong prior for time-consistent phantoms.

Authors: We agree this specification is necessary for reproducibility and to support the temporal consistency claim. In our implementation, normalization parameters (rotation, scale, translation) are computed once from the first frame of each sequence and applied uniformly to all subsequent frames, following the standard procedure in Kuhl & Giardina 1982. This choice was made precisely to avoid discontinuities in the EFD coefficient time series. We will add an explicit description of this consistent normalization process, including the rationale, to the Method section in the revision. revision: yes

Circularity Check

0 steps flagged

No circularity: EFD time-series modeling is an independent representational choice

full rationale

The paper introduces EFDs as a compact geometric representation for cell contours (standard in the literature) and then models phantom evolution explicitly as a multivariate time series on the resulting coefficients. This modeling step is presented as a design decision that supplies a prior for coherence; it is not defined in terms of the target output (biologically plausible videos) nor obtained by fitting parameters whose values are then renamed as predictions. No equations, self-citations, or uniqueness theorems are invoked that would reduce the claimed generation capability to the inputs by construction. The derivation chain therefore remains self-contained and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that EFDs supply a compact, geometrically meaningful prior for cell shapes and that time-series modeling of their coefficients will produce biologically plausible temporal evolution; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)

domain assumption EFDs provide a compact and geometrically interpretable representation for 2D closed contours of cells
Invoked in the abstract as the foundational representation that enables efficient generation of time-consistent sequences.
domain assumption Cell phantoms must replicate biological processes specific to cell types and therefore require time-consistent evolution
Stated directly in the abstract as the motivation for modeling temporal evolution in EFD space.

pith-pipeline@v0.9.0 · 5774 in / 1545 out tokens · 65381 ms · 2026-05-22T07:15:14.771809+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/ArithmeticFromLogic.lean LogicNat recovery and embed_strictMono_of_one_lt unclear

?

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

We represent the cell phantom evolution as a multivariate time series of EFD coefficients, introducing a strong prior for cell morphology and enabling the efficient generation of sequences that evolve coherently in time.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking (D=3) unclear

?

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

the truncated Fourier reconstruction is guaranteed to be smooth and yield a closed boundary with a simply connected phantom

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

18 extracted references · 18 canonical work pages · 1 internal anchor

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Cell Phantom Video Generation in Elliptical Fourier Descriptor Domain

models a Markov process over the cell life cycle stages (that go from birth to division, or mitosis) to define more precisely the mor- phology, but it requires phantoms to be additionally annotated with arXiv:2605.22563v1 [cs.CV] 21 May 2026 Contour Extraction Contour Rasterization Training Generation Fig. 2: Our pipeline for phantom video generation. (To...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[2]

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Anirban Chakraborty and Amit Roy-Chowdhury, “A condi- tional random field model for tracking in densely packed cell structures,” in2014 IEEE International Conference on Im- age Processing (ICIP), Paris, France, Oct. 2014, pp. 451–455, IEEE

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Martin Maška, Vladimír Ulman, Pablo Delgado-Rodriguez, Estibaliz Gómez-de Mariscal, Tereza Neˇcasová, Fidel A. Guer- rero Peña, Tsang Ing Ren, Elliot M. Meyerowitz, Tim Scherr, Katharina Löffler, Ralf Mikut, Tianqi Guo, Yin Wang, Jan P. Allebach, Rina Bao, Noor M. Al-Shakarji, Gani Rahmon, Imad Eddine Toubal, Kannappan Palaniappan, Filip Lux, Petr Matula,...

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Cell Phantom Video Generation in Elliptical Fourier Descriptor Domain

models a Markov process over the cell life cycle stages (that go from birth to division, or mitosis) to define more precisely the mor- phology, but it requires phantoms to be additionally annotated with arXiv:2605.22563v1 [cs.CV] 21 May 2026 Contour Extraction Contour Rasterization Training Generation Fig. 2: Our pipeline for phantom video generation. (To...

work page internal anchor Pith review Pith/arXiv arXiv 2026

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A condi- tional random field model for tracking in densely packed cell structures,

Anirban Chakraborty and Amit Roy-Chowdhury, “A condi- tional random field model for tracking in densely packed cell structures,” in2014 IEEE International Conference on Im- age Processing (ICIP), Paris, France, Oct. 2014, pp. 451–455, IEEE

work page 2014

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The Cell Track- ing Challenge: 10 years of objective benchmarking,

Martin Maška, Vladimír Ulman, Pablo Delgado-Rodriguez, Estibaliz Gómez-de Mariscal, Tereza Neˇcasová, Fidel A. Guer- rero Peña, Tsang Ing Ren, Elliot M. Meyerowitz, Tim Scherr, Katharina Löffler, Ralf Mikut, Tianqi Guo, Yin Wang, Jan P. Allebach, Rina Bao, Noor M. Al-Shakarji, Gani Rahmon, Imad Eddine Toubal, Kannappan Palaniappan, Filip Lux, Petr Matula,...

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A survey on automated cell tracking: challenges and solutions,

Reza Yazdi and Hassan Khotanlou, “A survey on automated cell tracking: challenges and solutions,”Multimedia Tools and Applications, vol. 83, no. 34, pp. 81511–81547, Mar. 2024

work page 2024

[5] [5]

ISING-GAN: Annotated Data Augmentation with a Spatially Constrained Generative Adversarial Network,

P. Dimitrakopoulos, G. Sfikas, and C. Nikou, “ISING-GAN: Annotated Data Augmentation with a Spatially Constrained Generative Adversarial Network,” in2020 IEEE 17th Inter- national Symposium on Biomedical Imaging (ISBI), Iowa City, IA, USA, Apr. 2020, pp. 1600–1603, IEEE

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An Expert-Driven Data Generation Pipeline for His- tological Images,

Roberto Basla, Loris Giulivi, Luca Magri, and Giacomo Bo- racchi, “An Expert-Driven Data Generation Pipeline for His- tological Images,” in2024 IEEE International Symposium on Biomedical Imaging (ISBI), Athens, Greece, May 2024, pp. 1– 5, IEEE

work page 2024

[7] [7]

Phe- notypic profiling of the human genome by time-lapse mi- croscopy reveals cell division genes,

Beate Neumann, Thomas Walter, Jean-Karim Hériché, Jutta Bulkescher, Holger Erfle, Christian Conrad, Phill Rogers, Ina Poser, Michael Held, Urban Liebel, Cihan Cetin, Frank Sieckmann, Gregoire Pau, Rolf Kabbe, Annelie Wünsche, Venkata Satagopam, Michael H. A. Schmitz, Catherine Cha- puis, Daniel W. Gerlich, Reinhard Schneider, Roland Eils, Wolfgang Huber, ...

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[8] [8]

Cellcyclegan: Spatiotemporal Microscopy Image Synthesis Of Cell Populations Using Statistical Shape Models And Con- ditional Gans,

Dennis Bahr, Dennis Eschweiler, Anuk Bhattacharyya, Daniel Moreno-Andres, Wolfram Antonin, and Johannes Stegmaier, “Cellcyclegan: Spatiotemporal Microscopy Image Synthesis Of Cell Populations Using Statistical Shape Models And Con- ditional Gans,” in2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), Nice, France, Apr. 2021, pp. 15–19, IEEE

work page 2021

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3D fluorescence mi- croscopy data synthesis for segmentation and benchmarking,

Dennis Eschweiler, Malte Rethwisch, Mareike Jarchow, Si- mon Koppers, and Johannes Stegmaier, “3D fluorescence mi- croscopy data synthesis for segmentation and benchmarking,” PLOS ONE, vol. 16, no. 12, pp. e0260509, 2021

work page 2021

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Annotated Biomedical Video Generation Using Denoising Diffusion Probabilistic Models and Flow Fields,

Rüveyda Yilmaz, Dennis Eschweiler, and Johannes Stegmaier, “Annotated Biomedical Video Generation Using Denoising Diffusion Probabilistic Models and Flow Fields,” inSimula- tion and Synthesis in Medical Imaging, Virginia Fernandez, Jelmer M. Wolterink, David Wiesner, Samuel Remedios, Lian- rui Zuo, and Adrià Casamitjana, Eds., vol. 15187, pp. 197–207. Spr...

work page 2025

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Diffusion-TS: Interpretable Dif- fusion for General Time Series Generation,

Xinyu Yuan and Yan Qiao, “Diffusion-TS: Interpretable Dif- fusion for General Time Series Generation,” inInternational Conference on Learning Representations, 2024, pp. 41582– 41610

work page 2024

[12] [12]

Generic Isolated Cell Image Generator,

Marin Scalbert, Florent Couzinie-Devy, and Riadh Fez- zani, “Generic Isolated Cell Image Generator,”Cytome- try Part A, vol. 95, no. 11, pp. 1198–1206, 2019, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/cyto.a.23899

work page doi:10.1002/cyto.a.23899 2019

[13] [13]

In- ShaDe: Invariant Shape Descriptors for visual 2D and 3D cel- lular and nuclear shape analysis and classification,

Khaled Al-Thelaya, Marco Agus, Nauman Ullah Gilal, Yin Yang, Giovanni Pintore, Enrico Gobbetti, Corrado Calí, Pierre J. Magistretti, William Mifsud, and Jens Schneider, “In- ShaDe: Invariant Shape Descriptors for visual 2D and 3D cel- lular and nuclear shape analysis and classification,”Computers & Graphics, vol. 98, pp. 105–125, Aug. 2021

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Elliptic Fourier fea- tures of a closed contour,

Frank P Kuhl and Charles R Giardina, “Elliptic Fourier fea- tures of a closed contour,”Computer Graphics and Image Pro- cessing, vol. 18, no. 3, pp. 236–258, Mar. 1982

work page 1982

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COMPYDA: An Online Tool for Verifying the Similarity of Image Datasets,

Tereza Ne ˇcasová, Daniel Mú ˇcka, and David Svoboda, “COMPYDA: An Online Tool for Verifying the Similarity of Image Datasets,” in2024 IEEE International Symposium on Biomedical Imaging (ISBI), Athens, Greece, May 2024, pp. 1– 5, IEEE

work page 2024

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Unsuper- vised modeling of cell morphology dynamics for time-lapse microscopy,

Qing Zhong, Alberto Giovanni Busetto, Juan P Fededa, Joachim M Buhmann, and Daniel W Gerlich, “Unsuper- vised modeling of cell morphology dynamics for time-lapse microscopy,”Nature Methods, vol. 9, no. 7, pp. 711–713, July 2012

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A Survey on Time-Series Distance Measures,

John Paparrizos, Haojun Li, Fan Yang, Kaize Wu, Jens E. d’Hondt, and Odysseas Papapetrou, “A Survey on Time-Series Distance Measures,” Dec. 2024, arXiv:2412.20574 [cs]

work page arXiv 2024

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Spherical harmonics decomposition based on Carte- sian level-set field,

Ignacio Roa, Jorge César Brändle de Motta, and Alexandre Poux, “Spherical harmonics decomposition based on Carte- sian level-set field,” Technical Report hal-04004128, CNRS, Normandy Univ., UNIROUEN, INSA Rouen, CORIA, 2023

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