Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-based Segmentation

Horacio Tettamanti; Mattia Zanella; Raffaella Fiamma Cabini

REVIEW 3 major objections 6 minor 58 references

Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-based Segmentation

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The evaluation metric used to optimize a kinetic consensus-based segmentation model changes the MRI tumor masks it produces, and the boundary-aware Surface Dice proves the most suitable loss.

desk verdict The paper's central claim that Surface Dice is more suitable is unsupported by its own mislabeled loss values, and the experiment is too thin to fix that. read the letter →

arxiv 2412.03458 v4 pith:CJZGVINW submitted 2024-12-04 eess.IV

Raffaella Fiamma Cabini , Horacio Tettamanti , Mattia Zanella This is my paper · ORCID

classification eess.IV MSC 35Q8435Q2068U1082C4065C05

keywords consensus-basedsegmentationkineticequationsboundedconfidenceevaluationmetricsSurfaceDiceJaccardindexbraintumorMRIDSMC

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper studies how the evaluation metric chosen as a loss function affects the parameter optimization of a kinetic consensus-based segmentation model for brain-tumor MRI. It shows that optimizing the model against Volumetric Dice, Jaccard, or Surface Dice yields different optimal parameters and different final binary masks, while the scores of the overlap-based metrics remain linked by a known identity. The paper argues that Surface Dice, which compares boundary regions rather than raw pixel overlap, is a better loss for this type of segmentation, and that the Fβ-measure gives misleading results because low β values can reward inaccurate masks. If this is right, the practical lesson is that the choice of evaluation metric is not neutral: researchers calibrating such models need to match the loss to the geometrical property they actually care about.

What carries the argument

The load-bearing object is the bounded-confidence interaction kernel P_Δ₁,Δ₂((x,c),(x*,c*)) = χ(|x − x*| ≤ Δ1)χ(|c − c*| ≤ Δ2), which allows a pixel to influence another pixel only if they are sufficiently close in both space and gray level. Around this kernel the paper constructs a Boltzmann-type kinetic equation and its quasi-invariant Fokker-Planck limit, solved numerically by a Nanbu-Babovsky direct simulation Monte Carlo scheme. The optimization loop minimizes Loss(Sg, St) = 1 − Metric(Sg, St) over the parameters (Δ1, Δ2, σ2), and the identity JAC = DICE/(2 − DICE) ties the two overlap metrics together, while the Surface Dice coefficient replaces pixel intersection with the intersection of tolerance bands around the boundaries.

What would settle it

Run the same 300-iteration optimization procedure on a set of at least twenty brain-tumor MRI slices from different patients, comparing Volumetric Dice, Jaccard, and Surface Dice for both whole-tumor and tumor-core tasks; if Volumetric Dice or Jaccard produces equal or better segmentation masks on a majority of slices, the paper's recommendation of Surface Dice would not generalize.

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Extended reading notes

Core claim

The central claim is that the loss function used in the optimization loop is not a mere evaluation detail but actively determines which model parameters (Δ1, Δ2, σ2) are selected and what binary segmentation mask results. The paper demonstrates this by running the same 300-iteration hyperparameter search on whole-tumor and tumor-core MRI slices, with Volumetric Dice, Jaccard, Surface Dice, and Fβ-measure as the respective losses, and recording the resulting parameters and masks. It confirms the algebraic relationship JAC = DICE/(2 − DICE) between the two volume-based metrics, then shows that Surface Dice with a one-pixel tolerance yields numerically different parameters and visibly improved boundary fidelity, especially for the tumor-core task. The paper concludes that Surface Dice is the more suitable metric for this consensus-based segmentation pipeline, while the Fβ-measure is unreliable because its loss values correlate poorly with actual mask quality.

Load-bearing premise

The conclusion that Surface Dice is the most suitable metric rests on experiments with just one axial MRI slice for the whole-tumor task and one for the tumor-core task, with a fixed random seed and no repeated-run variance, so if those slices are atypical the ranking of metrics could change.

Editorial extensions

If this is right

The optimal model parameters are not intrinsic to an image; they depend on which metric the optimizer is asked to maximize, so reporting parameters without stating the loss is incomplete.
Surface Dice should be preferred as the optimization loss for this consensus-based segmentation model when boundary accuracy matters, which is the case for tumor-core segmentation.
The identity JAC = DICE/(2 − DICE) lets practitioners convert between the two overlap scores without rerunning the experiment, making comparisons across studies that use different metrics straightforward.
The Fβ-measure is unsuitable as a loss for this model, because at low β it can assign a high score to a mask with many false negatives, decoupling the loss from the clinical objective.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension the paper leaves implicit is to repeat the study across many patients and on full 3D volumes; the current evidence rests on a single axial slice per task, so the ranking of metrics could shift on a broader sample.
Boundary-aware losses such as Surface Dice may also be preferable for other particle-based or clustering segmentation methods, since volume-only scores reward any boundary of equal volume regardless of its position.
The observed parameter compensation (lower diffusion offsets by smaller Δ2) suggests the loss landscape contains nearly equivalent parameter manifolds, which would make the metric choice more influential than the exact parameter values for the final mask quality.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The main claim here does not survive a close reading of Table 3. The paper defines Loss = 1 - Metric (Eq. 23), then reports numbers in Table 3 as 'loss' but adds 'loss is equal to 1 for a perfect overlap' — that's a metric, not a loss. The values themselves confirm it: 0.9292 and 0.8672 satisfy JAC = DICE/(2−DICE), so they are Dice and Jaccard scores. The text then says the Surface Dice 'loss' is smaller (0.7447 vs 0.9292) and treats that as better. But a smaller metric means worse; if those numbers were losses, they'd be 1 − metric and the comparison inverts. Either way, Table 3 does not support the conclusion that Surface Dice is more suitable. This is a load-bearing error, not a typo, because the qualitative claim that volumetric metrics ignore boundary proximity is a property, not an empirical demonstration.

What's actually new: very little. The kinetic model, Fokker-Planck derivation, and the DSMC pipeline come from the authors' prior paper [9]. The only genuinely new piece is the comparison of four known metrics on this model and the observation that optimized parameters shift with the metric. That observation is real — the tables show different (Δ1, Δ2, σ2) — and the F-beta analysis, despite the same loss/metric confusion, does show that F-beta is unstable for this task. Proposition 3.1 is a correct but elementary bound on the Jaccard-Dice relation.

The experimental base is also too thin: one axial slice per task, no identification of patient or scan, a fixed random seed, no repeated runs, no error bars. The 'more suitable' recommendation would be hard to support even with correct numbers. The paper reads like a competent write-up of the model and a hasty, underpowered evaluation.

I would not send this to peer review in its current state. The loss/metric labeling is easily fixable, but the deeper issues — single slices, no variance, no external mask-quality check — require a rewrite of the evaluation. If the authors can show that metric choice changes the final mask meaningfully and that Surface Dice consistently tracks boundary quality across a few independent slices, there's a modest paper here. As it stands, it's a desk reject.

Referee Report

3 major / 6 minor

Summary. The paper extends a kinetic consensus-based model for image segmentation, deriving a Fokker-Planck-type PDE via a quasi-invariant limit, and using a Direct Simulation Monte Carlo (DSMC) scheme to approximate its solution. The model interprets image pixels as interacting particles with spatial positions and static gray-level features, and the authors optimize the model parameters (Δ1, Δ2, σ2) by minimizing a loss defined as 1 − evaluation metric. The evaluation metrics considered are Volumetric Dice, Jaccard Index, Surface Dice, and the Fβ-measure. Experiments on synthetic shapes and two brain tumor MRI slices are used to study how the choice of optimization metric affects the resulting parameters and segmentation masks. The paper concludes that the choice of metric does affect the optimized parameters and that Surface Dice is a more suitable metric than Jaccard or Volumetric Dice, while the Fβ-measure is not reliable for this segmentation method.

Significance. The underlying kinetic modeling and DSMC pipeline are of interest to the community working on consensus-based and kinetic approaches to imaging problems, and the idea of linking parameter calibration to clinically used segmentation metrics is commendable and potentially useful. The paper also provides transparent algorithm descriptions and a clear statement of the optimization procedure. However, the central empirical claim that Surface Dice is more suitable than Jaccard or Volumetric Dice is not supported by the reported numbers because the values labeled 'loss' in Table 3 are actually metric values (1 = perfect overlap), yet the text interprets smaller values as better. This internal inconsistency directly affects the paper's headline recommendation. If corrected, and if the empirical evidence is strengthened with repeated runs and more than one slice per task, the manuscript could make a moderate contribution to the field of metric-aware parameter estimation for kinetic segmentation models.

major comments (3)

[Section 4.3, Table 3] The values labeled 'Loss' in Table 3 are, by the paper's own caption and by the relation in Eq. (29), metric values rather than losses. For example, the Whole Tumor row reports Vol. Dice = 0.9292 and JAC = 0.8672, and these numbers satisfy JAC = DICE/(2−DICE), so they are Dice and Jaccard similarity values, not 1−metric losses. The text then states that the 'loss' obtained with Surface Dice is smaller than that for Jaccard and Volumetric Dice, and uses this comparison as evidence that Surface Dice is 'more suitable.' Since a smaller metric value corresponds to worse overlap (for metrics that are 1 for perfect agreement), the reported numbers actually show that Surface Dice gives lower agreement than the other two metrics on both tasks. The quantitative comparison therefore contradicts, rather than supports, the conclusion that Surface Dice is a better representation for this model. The authors must either correct the definition and the reported numbers, or re-evaluate the suitability claim.
[Section 3.2.1, Section 4.3] The generalization claim that the choice of evaluation metric determines the outcome of parameter optimization rests on experiments with a single axial MRI slice for the whole-tumor task and a single slice for the core-tumor task, with no identification of the slice, no repeated optimization runs with different random seeds, and no error bars. Because the optimization uses a fixed random seed (as stated in Section 3.2.1), the differences in optimized parameters across metrics in Tables 3 and 4 could be due to the particular random sampling of hyperparameters rather than to a reproducible property of the metrics. To make the claim load-bearing, the authors should report results over multiple slices and/or multiple seeds, or at least provide variance information from repeated runs.
[Section 4.3, Table 4 and Figure 12] The analysis of the Fβ-measure is internally inconsistent. The caption of Table 4 states that loss is 1 for perfect overlap and 0 for complete deviation, which defines the reported values as metric values, but Eq. (23) defines loss as 1 − metric. The text then says that for β=0.25 the loss is higher, 'meaning that this should be the most accurate result,' while also saying that 'the loss decreases for larger values of β' and that the resulting binary mask is less accurate for lower β. These statements mix the two interpretations: if the reported value is a metric, higher is better; if it is a loss, lower is better. The conclusion that Fβ is not a reliable metric is therefore not supported by the numbers as presented, because the direction of comparison has not been fixed. The authors should clarify which quantity is reported and re-derive the conclusions accordingly.

minor comments (6)

[Abstract and text throughout] There are several typographical errors, including 'mode l' in the abstract, 'Euler-Maryuama' for Euler-Maruyama in Section 2.2, 'Coeﬃcent' in the caption of Figure 10, and 'msethods' in reference [42]. A careful proofreading pass is recommended.
[Section 4.2, Eq. (35)] The variation index T is defined as an integral over the continuous density f, but in the DSMC context the density is a finite particle approximation. It would be helpful to specify how this integral is computed from the discrete particle set, for example via a histogram or kernel density estimate, to make the stopping criterion reproducible.
[Section 3.3, Proposition 3.1] The absolute approximation error bound of 3−2√2 and the relative error of 1 are stated without derivation. Since these bounds are used to argue that Jaccard and Dice are closely related, a brief proof or a reference to the specific derivation would strengthen this part.
[Section 4.1, Table 2] The text says 'the loss is null in both cases' for the square image, but Table 2 shows parameters, not losses. The sentence is understandable, but it would be clearer to explicitly state that the resulting Surface Dice was 1 and hence the loss was 0 for all three metrics.
[Section 3.3.2 and Eq. (29)] The relationship between Jaccard and Dice is correctly stated, but the notation in Eqs. (25) and (28) uses |S1g| for the number of pixels in the foreground; for consistency, the authors should define |·| as the cardinality of the set earlier, before first use.
[Section 4.3, Table 3] The paper does not state the chosen tolerance τ for the Surface Dice metric in the section where it is used for optimization (Section 4.3 mentions τ equal to 1 pixel, but this is only in the caption of Figure 10 and in the surrounding text; the table itself does not note it). Including τ in the table caption would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the parameter fitting and metric comparison are empirical, and the only self-citation is to published prior work; the Table 3 'loss' labeling inconsistency is a correctness issue, not a circular derivation.

full rationale

The paper's central claim is that the choice of evaluation metric changes the optimized parameters (Δ1, Δ2, σ2) and the quality of the resulting segmentation mask. This is an empirical claim: Eq. (23) defines Loss = 1 − Metric, Hyperopt minimizes it over sampled parameter distributions, and Tables 1–3 report the resulting parameters and metric values. No fitted parameter is renamed as a prediction, and no target quantity is defined in terms of the conclusion, so the fitted-input-called-prediction and self-definitional patterns do not apply. The Fokker–Planck limit (18) and the DSMC algorithm are inherited from the authors' prior work [9]; Section 2.2 sketches the quasi-invariant derivation and cites [9] for the convergence of the remainder term. This is self-citation, but it is not circular: [9] is a separate peer-reviewed publication with its own model and experiments, and the present paper's metric-comparison conclusion is evaluated on external tumor images and would stand or fall independently of that derivation. The JAC–DICE relation (29) and the Fβ algebra (31)–(33) are standard identities, not used to force the conclusion. I therefore find no circular step. The main weakness is quantitative: Table 3 labels the column 'loss' but states it is 1 for perfect overlap and 0 for complete deviation, i.e. it reports metric values, whereas Eq. (23) defines loss as 1 − metric. The text then says the Surface Dice 'loss' is smaller than the Jaccard/Volumetric Dice values and uses that to call Surface Dice more suitable. If the numbers are metrics, smaller is worse; if they are losses, they should be complements. Either way, the comparison in Table 3 does not support the Surface Dice recommendation. This is an internal-consistency and evidence-quality problem, not a circularity. Other limitations (a single axial slice per task, fixed random seed, no repeated-run variance) further weaken generalization but do not make the derivation circular.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The metric-comparison conclusions rest primarily on the DSMC simulations and the choice of two test slices, not on the kinetic-theoretic axioms, which are inherited from prior work. The fitted parameters are the main free quantities, and the binarization threshold is an additional hand-chosen constant. No new entities are introduced.

free parameters (4)

Delta_1 (spatial confidence bound) = 0.4972 (Vol. Dice, Whole Tumor); ranges 0.013 to 0.884 across settings
Optimized via Hyperopt to minimize each metric's loss; the value changes with the chosen metric, as shown in Tables 1-4.
Delta_2 (feature confidence bound) = 0.0888 (Vol. Dice, Whole Tumor); ranges 0.054 to 0.407 across settings
Optimized via Hyperopt; differs across metrics and images, demonstrating the paper's central observation.
sigma^2 (diffusion coefficient) = 2.6867 (Vol. Dice, Whole Tumor); ranges 0.0257 to 2.717 across settings
Optimized via Hyperopt; balances the diffusion functions D1-D4 and the interaction terms.
c~ (binarization threshold) = 10th percentile of ROI pixels
Hand-chosen constant in the segmentation pipeline; paper notes it could be treated as an optimizable parameter (Section 3.2).

assumptions (4)

domain assumption Mean-field limit: the empirical density of the particle system converges to the continuous density solving the Fokker-Planck equation (5) as N tends to infinity.
Invoked in Section 2.2 to pass from the agent-based model to the PDE; the convergence is cited to [9, 42] and not proved in this paper.
domain assumption Quasi-invariant limit: for epsilon -> 0 the Boltzmann-type equation (11) converges to the Fokker-Planck equation (18), with the remainder term vanishing.
Stated in Section 2.2; the proof is attributed to [9] and [42], and this paper relies on it without a self-contained derivation.
domain assumption The DSMC algorithm with N/2 random pairs per step and time step epsilon approximates the solution of the Fokker-Planck equation (18).
Adopted in Section 3.1 as a standard Nanbu-Babovsky scheme; no convergence or error bound is given in this paper.
ad hoc to paper A numerical steady state is reached when the variation index T in Eq. (35) falls below delta = 0.005.
Defined in Section 4.2 as the stopping criterion for all experiments; the threshold is chosen without sensitivity analysis.

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Pith. "Pith review of Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-based Segmentation." pith.science (2026). https://pith.science/paper/CJZGVINW

@misc{pith2026241203458,
  author       = {Pith},
  title        = {Pith review of: Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-based Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CJZGVINW}},
  note         = {Machine review of arXiv:2412.03458}
}

read the original abstract

In this article we extend a recently introduced kinetic model for consensus-based segmentation of images. In particular, we will interpret the set of pixels of a 2D image as an interacting particle system which evolves in time in view of a consensus-type process obtained by interactions between pixels and external noise. Thanks to a kinetic formulation of the introduced model we derive the large time solution of the model. We will show that the choice of parameters defining the segmentation task can be chosen from a plurality of loss functions characterising the evaluation metrics.

Figures

Figures reproduced from arXiv: 2412.03458 by the authors.

**Figure 2.** A schematic representation of the proposed model wher [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Representation of the evolution of pixels as they tend to a [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Summary of the segmentation process. The first image sh [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: Representation of the relevant areas between the pred [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: Diffusion functions defined in (34) to assess the variability related to a given feature’s level. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

**Figure 7.** Figure 7: Images used to test different diffusion functions. The firs [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

**Figure 8.** Figure 8: Evolution of T where the kinetic density is the one considered in [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]

**Figure 9.** Figure 9: Segmentation Masks obtained by minimizing the Jaccard Ind [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

**Figure 10.** Figure 10: Segmentation Masks obtained by minimizing the Surface an [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

**Figure 11.** Figure 11: Segmentation masks obtained for the Fβ−Loss metric. (a) Shows the segmentation masks obtained for β = 0.25, 0.5, 0.75, 1.5 for the Core tumor and (b) Shows the segmentation masks obtained using the same values of β for the Whole Tumor. Both images consist of 240 × 240…

**Figure 12.** Figure 12: Relationship between the Fβ− loss value and the β value for both the Core and Whole Tumor Images. As β increases, the Fβ− loss decreases showing that for lower values of β we should obtain a more precise segmentation mask as the loss indicated in this Figure is 1 for …

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Works this paper leans on

58 extracted references · 56 canonical work pages

[9]

& Zanella, M

Cabini, R., Pichiecchio, A., Lascialfari, A., Figini, S. & Zanella, M. A kinetic approach to consensus-based segmentation of biomedical images. Kinet. Relat. Models ,18(2), 286-311 (2025)

work page 2025
[1]

& Others Deep learning for automatic segmentation of thigh and leg muscles

Agosti, A., Shaqiri, E., Paoletti, M., Solazzo, F., Bergsland, N., Colelli, G., Savini, G., Muzic, S., Santini, F., Deligianni, X. & Others Deep learning for automatic segmentation of thigh and leg muscles. Magn. Reson. Mater. Phys. Biol. Med. . 35 pp. 467-483 (2021)

work page 2021
[2]

Recent advances in o pin- ion modeling: control and social inﬂuence

Albi, G., Pareschi, L., Toscani, G., & Zanella, M. Recent advances in o pin- ion modeling: control and social inﬂuence. In Active Particles Volume 1, Advances in Theory, Models, and Applications , Eds. N. Bellomo, P. De- gond, and E. Tadmor, Birkh¨ auser-Springer (2017)

work page 2017
[3]

On the optimal control of opinion dy- namics on evolving networks

Albi, G., Pareschi, L., & Zanella, M. On the optimal control of opinion dy- namics on evolving networks. In System Modeling and Optimization. CSMO

work page
[4]

On the equivalence between Fourier-based and Wasserstein metric s

Auricchio, G., Codegoni, A., Gualandi, S., Toscani, G., Veneroni, M. On the equivalence between Fourier-based and Wasserstein metric s. Rend. Lincei Mat. Appl. . 31: 627–649 (2020)

work page 2020
[5]

& Tanno, R

Barbano, R., Arridge, S., Jin, B. & Tanno, R. Uncertainty quantiﬁ cation in medical image synthesis. Biomedical Image Synthesis And Simulation: Methods And Applications . pp. 601-641 (2022)

work page 2022
[6]

& Cox, D

Bergstra, J., Komer, B., Eliasmith, C., Yamins, D. & Cox, D. Hypero pt: a Python library for model selection and hyperparameter optimizat ion. Comput. Sci. Discov. . 8, 014008 (2015)

work page 2015
[7]

& Blaschko, M

Bertels, J., Eelbode, T., Berman, M., Vandermeulen, D., Maes, F., B is- schops, R. & Blaschko, M. Optimizing the Dice Score and Jaccard Ind ex for Medical Image Segmentation: Theory & Practice. CoRR. abs/1911.01685 (2019)

arXiv 2019

Show all 58 references

[8]

& Lorenzi, T

Borra, D. & Lorenzi, T. Asymptotic analysis of continuous opinion mod- els under bounded conﬁdence. Commun. Pure Appl. Anal. 12, 1487-1499 (2013)

2013
[10]

A., Fornasier, M., Rosado, J

Carrillo, J. A., Fornasier, M., Rosado, J. & Toscani, G. Asymptot ic ﬂocking dynamics for the kinetic Cucker-Smale model. SIAM J. Math. Anal. . 42, 218-236 (2010)

2010
[11]

A., Fornasier, M., Toscani, G., and Vecil, F

Carrillo, J. A., Fornasier, M., Toscani, G., and Vecil, F. Particle, kin etic, and hydrodynamic models of swarming. In In: Naldi, G., Pareschi, L., Toscani, G. (eds) Mathematical Modeling of Collective Behavior in Socio- Economic and Life Sciences , Modeling and Simulation in ...
[12]

& Loreto, V

Castellano, C., Fortunato, S. & Loreto, V. Statistical physics of social dy- namics. Rev. Modern Phys. . 81 pp. 591-646 (2009). 29

2009
[13]

MUC-4 evaluation metrics

Chinchor, N. MUC-4 evaluation metrics. (1992)

1992
[14]

& Ayache, N

Cordier, N., Delingette, H. & Ayache, N. A patch-based approa ch for the segmentation of pathologies: application to glioma labelling. IEEE Trans. Med. Imaging . 35, 1066-1076 (2015)

2015
[15]

& Collins, D

Coup´ e, P., Manj´ on, J., Fonov, V., Pruessner, J., Robles, M. & Collins, D. Patch-based segmentation using expert priors: Application to hipp ocampus and ventricle segmentation. NeuroImage. 54, 940-954 (2011)

2011
[16]

& Weisbuch, G

Deﬀuant, G., Neau, D., Amblard, F. & Weisbuch, G. Mixing beliefs am ong interacting agents. Adv. Complex Syst. . 3, 87-98 (2000)

2000
[17]

Reaching a consensus

DeGroot, M. Reaching a consensus. J. Am. Stat. Assoc. . 69, 118-121 (1974)

1974
[18]

Measures of the Amount of Ecologic Association Betwee n Species

Dice, L. Measures of the Amount of Ecologic Association Betwee n Species. Ecology. 26 pp. 297-302 (1945)

1945
[19]

& Pareschi, L

Dimarco, G. & Pareschi, L. Numerical methods for kinetic equat ions. Acta Numerica. 23 pp. 369-520 (2014)

2014
[20]

Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political se - gregation

D¨ uring, B., & Wolfram, M.-T. Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political se - gregation. Proc. R. Soc. Lond. A . 471 (2015)

2015
[21]

Opinion formation systems via deterministic particles approximation

Fagioli, S., & Radici, E. Opinion formation systems via deterministic particles approximation. Kinet. Relat. Mod. 14, 45–76 (2021)

2021
[22]

A formal theory of social power

French Jr, J. A formal theory of social power. Psychol. Rev. . 63, 181-194 (1956)

1956
[23]

Opinion formation on evolving network: the DP A method applied to a nonlocal cross-diﬀusion PDE-ODE system

Fagioli S, Favre G. Opinion formation on evolving network: the DP A method applied to a nonlocal cross-diﬀusion PDE-ODE system. Euro pean Journal of Applied Mathematics. 35, 748-775 (2024)

2024
[24]

& Krishnapuram, R

Frigui, H. & Krishnapuram, R. A robust competitive clustering alg orithm with applications in computer vision. IEEE Trans. Pattern Anal. Mach. Intell. 21, 450-465 (1999)

1999
[25]

Opinion dynamics and bounded conﬁ dence models, analysis, and simulation

Hegselmann, R., & Krause, U. Opinion dynamics and bounded conﬁ dence models, analysis, and simulation. J. Artif. Soc. Soc. Simul. . 5 Nr.3 (2002)

2002
[26]

& Visconti, G

Herty, M., Pareschi, L. & Visconti, G. Mean ﬁeld models for large data–clustering problems. Netw. Heterog. Media . 15, 463 (2020)

2020
[27]

Deep learning techniqu es for medical image segmentation: achievements and challenges

Hesamian, M., Jia, W., He, X., & Kennedy, P. Deep learning techniqu es for medical image segmentation: achievements and challenges. J. Digit. Imaging. 32, 582-596 (2019)

2019
[28]

nnU-Net: a self-conﬁguring method for deep learning-based biomedical image s egment- ation

Isensee, F., Jaeger, P., Kohl, S., Petersen, J., & Maier-Hein, K. nnU-Net: a self-conﬁguring method for deep learning-based biomedical image s egment- ation. Nat. Methods. 18, 203-211 (2021)

2021
[29]

The distribution of the ﬂora in the alpine zone.1

Jaccard, P. The distribution of the ﬂora in the alpine zone.1. New Phyto- logist. 11, 37-50 (1912). 30

1912
[30]

Data clustering: a review

Jain, A., Murty, M., & Flynn, P. Data clustering: a review. ACM Comput. Surv.. 31, 264-323 (1999)

1999
[31]

Unsupervised image segmentation using the Deﬀuant- Weisbuch model from social dynamics

Kayal, S. Unsupervised image segmentation using the Deﬀuant- Weisbuch model from social dynamics. Signal Image Video Process.. 11 pp. 1405-1410 (2017)

2017
[32]

Uncertainty quantiﬁcation us ing Bayesian neural networks in classiﬁcation: application to biomedical image segmentation

Kwon, Y., Won, J., Kim, B., & Paik, M. Uncertainty quantiﬁcation us ing Bayesian neural networks in classiﬁcation: application to biomedical image segmentation. Comput. Stat. Data Anal. 142 pp. 106816 (2020)

2020
[33]

A review of deep-learning-ba sed medical image segmentation methods

Liu, X., Song, L., Liu, S., & Zhang, Y. A review of deep-learning-ba sed medical image segmentation methods. Sustainability. 13, 1224 (2021)

2021
[34]

Quantiﬁcation of pulmonary involvement in COVID-19 pneumonia by means of a cascade of two U-nets: training and asses sment on multiple datasets using diﬀerent annotation criteria

Lizzi F., Agosti A., Brero F., Cabini R.F., Fantacci M.E., Figini S., La scial- fari A., Laruina F., Oliva P., Piﬀer S., Postuma I., Rinaldi L., Talamonti C., & Retico A. Quantiﬁcation of pulmonary involvement in COVID-19 pneumonia by means of a cascade of two U-nets: training...

2022
[35]

Quantiﬁcation of pulmonary involvement in COVID-19 pneumonia: an upgrade of the LungQuant software fo r lung CT segmentation

Lizzi F., Postuma I., Brero F., Cabini R.F., Fantacci M.E., Lascialfa ri A., Oliva P., Rinaldi L., & Retico A. Quantiﬁcation of pulmonary involvement in COVID-19 pneumonia: an upgrade of the LungQuant software fo r lung CT segmentation. Eur. Phys. J. Plus . 138, 326 (2023)

2023
[36]

Uncertainty quantiﬁcation and control of kinetic models of tumour growth under clinical uncertain ties

Medaglia, A., Colelli, G., Farina, L., Bacila, A., Bini, P., Marchioni, E., Figini, S., Pichiecchio, A., & Zanella, M. Uncertainty quantiﬁcation and control of kinetic models of tumour growth under clinical uncertain ties. Int. J. Non-Linear Mech. . 141 pp. 103933 (2022)

2022
[37]

A comprehensive survey of image segmentation: clustering meth ods, performance parameters, and benchmark datasets

Mittal, H., Pandey, A., Saraswat, M., Kumar, S., Pal, R., & Modwel, G. A comprehensive survey of image segmentation: clustering meth ods, performance parameters, and benchmark datasets. Multimed. Tools. Appl.. pp. 1-26 (2021)

2021
[38]

Heterophilious dynamics enhances con sensus

Motsch, S., & Tadmor, E. Heterophilious dynamics enhances con sensus. SIAM Rev. . 56, 577-621 (2014)

2014
[39]

Deep learning to achieve clinically ap - plicable segmentation of head and neck anatomy for radiotherapy

Nikolov, S., Blackwell, S., Mendes, R., Fauw, J., Meyer, C., Hughes, C., Askham, H., Romera-Paredes, B., Karthikesalingam, A., Chu, C., Car - nell, D., Boon, C., D’Souza, D., Moinuddin, S., Sullivan, K., Consor- tium, D., Montgomery, H., Rees, G., Sharma, R., Suleyman, M., Bac...

2018 arXiv
[40]

N., & Wolfram, M.-T

Nugent, A., Gomes, S. N., & Wolfram, M.-T. Steering opinion dynam ics through control of social networks. Preprint arXiv:2404.09849 (2024)

2024 arXiv
[41]

An Introduction to Monte Carlo Metho ds for the Boltzmann Equation

Pareschi, L., & Russo, G. An Introduction to Monte Carlo Metho ds for the Boltzmann Equation. 10 pp. 35-76 (1999,1). 31

1999
[42]

Interacting multiagent systems: kin etic equa- tions and Monte Carlo msethods

Pareschi, L., & Toscani, G. Interacting multiagent systems: kin etic equa- tions and Monte Carlo msethods. (OUP Oxford,2013)

2013
[43]

Hydrodynamic mo dels of preference formation in multi-agent societies

Pareschi, L., Tosin, A., Toscani, G., & Zanella, M. Hydrodynamic mo dels of preference formation in multi-agent societies. J. Nonlin. Sci. . 29, 2761- 2796 (2019)

2019
[44]

& Zanella, M

Pareschi, L. & Zanella, M. Structure preserving schemes for n onlinear Fokker-Planck equations and applications. J. Sci. Comput. . 74, 1575-1600 (2018)

2018
[45]

Model-based assessment of the impact of driver-assist vehicles using kinetic theory

Piccoli, B., and Tosin, A., & Zanella, M. Model-based assessment of the impact of driver-assist vehicles using kinetic theory. Z. Angew. Math. Phys. , 71:152 (2020)

2020
[46]

A trainable clustering algo rithm based on shortest paths from density peaks

Pizzagalli, D., Gonzalez, S., & Krause, R. A trainable clustering algo rithm based on shortest paths from density peaks. Science Advances. 5, eaax3770 (2019)

2019
[47]

A Bayesian Approach to Cluster ing via the Proper Bayesian Bootstrap: the Bayesian Bagged Clusterin g (BBC) algorithm

Quetti F.M., Figini S., & Ballante E. A Bayesian Approach to Cluster ing via the Proper Bayesian Bootstrap: the Bayesian Bagged Clusterin g (BBC) algorithm. Preprint arXiv:2409.08954, 2024

2024 arXiv
[48]

Opinion Dynamics and Bounded Conﬁdenc e: Models, Analysis and Simulation

Rainer, H., & Krause, U. Opinion Dynamics and Bounded Conﬁdenc e: Models, Analysis and Simulation. Journal Of Artiﬁcial Societies And Social Simulation. 5 (2002)

2002
[49]

U-net: Convolutional networks for biomedical image segmentation

Ronneberger, O., Fischer, P., & Brox, T. U-net: Convolutional networks for biomedical image segmentation. International Conference On Medical Im- age Computing And Computer-Assisted Intervention . pp. 234-241 (2015)

2015
[50]

The truth of the f-measure

Sasaki Y. The truth of the f-measure. Teach Tutor Mater . 1:1–5 (2007)

2007
[51]

& Aggarwal, L

Sharma, N. & Aggarwal, L. Automated medical image segmentat ion tech- niques. J. Med. Phys. . 35, 3 (2010)

2010
[52]

& Sznajd, J

Sznajd-Weron, K. & Sznajd, J. Opinion evolution in closed commu nities. Int. J. Mod. Phys. C . 11, 1157-1165 (2000)

2000
[53]

& Hanbury, A

Taha, A. & Hanbury, A. Metrics for evaluating 3D medical image s egment- ation: analysis, selection, and tool. BMC Medical Imaging. 15, 1-28 (2015)

2015
[54]

Kinetic models of opinion formation

Toscani, G. Kinetic models of opinion formation. Commun. Math. Sci. . 4, 481-496 (2006)

2006
[55]

Van Der Walt, S., Sch¨ onberger, J., Nunez-Iglesias, J., Boulogn e, F., Warner, J., Yager, N., Gouillart, E. & Yu, T. Scikit-image: Image pro- cessing in python. PeerJ. 2:e453 (2014)

2014
[56]

& Tian, J

Yu, Z., Au, O., Zou, R., Yu, W. & Tian, J. An adaptive unsupervised approach toward pixel clustering and color image segmentation. Pattern Recognition. 43, 1889-1906 (2010)

2010
[57]

& Liang, J

Zhou, Z., Rahman Siddiquee, M., Tajbakhsh, N. & Liang, J. Unet+ +: A nested u-net architecture for medical image segmentation. Deep Learning In Medical Image Analysis And Multimodal Learning For Clini cal Decision Support. pp. 3-11 (2018). 32

2018
[2015]

IFIP Advances in Information and Communication Technology. Eds. Bociu L., D´ esid´ eri JA., Habbal A. Eds., vol 494. Springer, Cham

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [9]

& Zanella, M

Cabini, R., Pichiecchio, A., Lascialfari, A., Figini, S. & Zanella, M. A kinetic approach to consensus-based segmentation of biomedical images. Kinet. Relat. Models ,18(2), 286-311 (2025)

work page 2025

[2] [1]

& Others Deep learning for automatic segmentation of thigh and leg muscles

Agosti, A., Shaqiri, E., Paoletti, M., Solazzo, F., Bergsland, N., Colelli, G., Savini, G., Muzic, S., Santini, F., Deligianni, X. & Others Deep learning for automatic segmentation of thigh and leg muscles. Magn. Reson. Mater. Phys. Biol. Med. . 35 pp. 467-483 (2021)

work page 2021

[3] [2]

Recent advances in o pin- ion modeling: control and social inﬂuence

Albi, G., Pareschi, L., Toscani, G., & Zanella, M. Recent advances in o pin- ion modeling: control and social inﬂuence. In Active Particles Volume 1, Advances in Theory, Models, and Applications , Eds. N. Bellomo, P. De- gond, and E. Tadmor, Birkh¨ auser-Springer (2017)

work page 2017

[4] [3]

On the optimal control of opinion dy- namics on evolving networks

Albi, G., Pareschi, L., & Zanella, M. On the optimal control of opinion dy- namics on evolving networks. In System Modeling and Optimization. CSMO

work page

[5] [4]

On the equivalence between Fourier-based and Wasserstein metric s

Auricchio, G., Codegoni, A., Gualandi, S., Toscani, G., Veneroni, M. On the equivalence between Fourier-based and Wasserstein metric s. Rend. Lincei Mat. Appl. . 31: 627–649 (2020)

work page 2020

[6] [5]

& Tanno, R

Barbano, R., Arridge, S., Jin, B. & Tanno, R. Uncertainty quantiﬁ cation in medical image synthesis. Biomedical Image Synthesis And Simulation: Methods And Applications . pp. 601-641 (2022)

work page 2022

[7] [6]

& Cox, D

Bergstra, J., Komer, B., Eliasmith, C., Yamins, D. & Cox, D. Hypero pt: a Python library for model selection and hyperparameter optimizat ion. Comput. Sci. Discov. . 8, 014008 (2015)

work page 2015

[8] [7]

& Blaschko, M

Bertels, J., Eelbode, T., Berman, M., Vandermeulen, D., Maes, F., B is- schops, R. & Blaschko, M. Optimizing the Dice Score and Jaccard Ind ex for Medical Image Segmentation: Theory & Practice. CoRR. abs/1911.01685 (2019)

arXiv 2019