arxiv: 2604.16490 · v1 · submitted 2026-04-13 · 💻 cs.CV · cs.AI· cs.LG

Recognition: unknown

An Uncertainty-Aware Loss Function Incorporating Fuzzy Logic: Application to MRI Brain Image Segmentation

Hanuman Verma , Akshansh Gupta , Pranabesh Maji , Saurav Mandal , Vijay Kumar Pandey

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:19 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LG

keywords MRI brain segmentationfuzzy logicuncertainty-aware losscategorical cross-entropydeep learningU-Nettissue classificationfuzzy entropy

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The pith

A loss function that adds fuzzy entropy to categorical cross-entropy improves MRI brain tissue segmentation by handling pixel uncertainty.

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

The paper introduces a loss function for training neural networks to segment brain MRI images into tissue classes. It combines the standard categorical cross-entropy term with an additional fuzzy entropy term that uses fuzzy logic to represent degrees of membership rather than hard class assignments. This combination is tested on the IBSR and OASIS datasets using U-Net and U-Net++ models, where it produces higher scores on common overlap and distance metrics than plain categorical cross-entropy. A reader would care because pixel-level uncertainty is common in medical images and directly affects the reliability of automated measurements used in neurological diagnosis.

Core claim

The paper presents a novel loss function formed by integrating categorical cross-entropy with fuzzy entropy derived from fuzzy logic. The resulting function is intended to account for inherent uncertainties in assigning individual pixels to tissue classes such as gray matter, white matter, or cerebrospinal fluid. When used to optimize U-Net and U-Net++ architectures on the IBSR and OASIS benchmark datasets, the combined loss produces better values on performance metrics than categorical cross-entropy alone and maintains meaningful uncertainty modeling throughout training.

What carries the argument

The hybrid loss that augments categorical cross-entropy with a fuzzy entropy term computed from pixel-wise fuzzy membership degrees to capture classification ambiguity.

Load-bearing premise

That the fuzzy entropy term meaningfully represents and reduces real pixel classification uncertainty in MRI data without introducing new biases or overfitting.

What would settle it

Running the same U-Net and U-Net++ models on the IBSR and OASIS datasets with identical training settings and finding no statistically significant gain in Dice coefficient or reduction in Hausdorff distance when switching from categorical cross-entropy to the proposed loss would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2604.16490 by Akshansh Gupta, Hanuman Verma, Pranabesh Maji, Saurav Mandal, Vijay Kumar Pandey.

**Figure 3.** Figure 3: U-Net++ architecture with the skip connectionsn. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 6.** Figure 6: Qualitative segmentation results using U-Net++ with [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 5.** Figure 5: Qualitative segmentation results using U-Net with [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 4.** Figure 4: Plot for training versus validation performance for U-Net and U-Net++ architecture for IBSR data with categorical [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 7.** Figure 7: Plot for training versus validation performance for U-Net and U-Net++ architecture for OASIS brain data with [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

Accurate brain image segmentation, particularly for distinguishing various tissues from magnetic resonance imaging (MRI) images, plays a pivotal role in finding the neurological dis ease and medical image computing. In deep learning approaches, loss functions are very crucial for optimizing the model. In this study, we introduce a novel loss function integrating fuzzy logic to deals uncertainty issues in brain image segmentation into various tissues. It integrates the well-known categorical cross-entropy (CCE) loss function and fuzzy entropy based on fuzzy logic. By employing fuzzy logic, this loss function accounts for the inherent uncertainties in pixel classifications. The proposed loss function has been evaluated on two publicly available benchmark datasets, IBSR and OASIS, using two widely recognised architectures, U-Net and U-Net++. Experimental results demonstrate that the trained model with proposed loss function provided better results in comparison to the CCE optimisation function in terms of various performance metrics. Additionally, it effectively enhances segmentation performance while handling meaningful uncer tainty during training. The findings suggest that this approach not only improves segmentation outcomes but also contributes to the reliability of model predictions.

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 tries a fuzzy-entropy addition to cross-entropy for MRI brain segmentation and reports better numbers than plain CCE on two datasets, but the loss details are too thin to tell if the gains are real or just extra regularization.

read the letter

The main takeaway is that this work offers a practical tweak to standard segmentation losses for brain MRI, where uncertainty in pixel labels can matter for diagnosis. They combine categorical cross-entropy with a fuzzy entropy term and test it on IBSR and OASIS using U-Net and U-Net++, showing gains across common metrics like Dice and accuracy over the baseline CCE loss. That evaluation setup is straightforward and covers two public benchmarks with two common architectures, which gives the results some credibility for a targeted medical imaging paper. The integration itself is presented as new in this exact form, even if the individual pieces have appeared elsewhere in image processing. It does a decent job of framing the motivation around handling uncertainty during training and noting that the approach improves reliability of predictions. The soft spots sit mostly in the methods and validation. The loss is described as a direct sum or integration of the two terms, yet no explicit equation, weighting coefficient, or fuzzy membership function family appears, and there are no ablations on those choices or sensitivity checks. Without those, or comparisons to other uncertainty-aware losses, the improvements could stem from implicit regularization rather than explicit uncertainty modeling. No statistical significance tests or error bars are mentioned either, which leaves the strength of the empirical claim open to question. This paper is mainly for researchers already working on medical image segmentation who want to experiment with fuzzy-based losses as a quick addition to U-Net style models. A reader focused on practical improvements in high-stakes imaging might get value from trying the idea, but anyone needing full reproducibility or deeper analysis will find it limited. It deserves peer review because the core idea has clear application potential and the experiments are on real datasets, even though it will need major revisions to supply the missing formulation details, ablations, and stronger baselines before it could be published.

Referee Report

3 major / 2 minor

Summary. The paper proposes a novel loss function that integrates categorical cross-entropy (CCE) with fuzzy entropy derived from fuzzy logic to handle uncertainty in pixel-level classifications for MRI brain tissue segmentation. The method is evaluated on the IBSR and OASIS benchmark datasets using U-Net and U-Net++ architectures, with experimental results claimed to show improved performance metrics over standard CCE optimization while enhancing segmentation reliability through uncertainty awareness.

Significance. If the reported metric gains prove reproducible and specifically attributable to the fuzzy entropy term's uncertainty modeling (rather than incidental regularization), the approach could offer a lightweight, interpretable extension to existing segmentation losses for medical imaging applications where boundary and tissue uncertainty is common. This would be a modest but practical contribution to loss design in computer vision for healthcare, provided the formulation is made fully reproducible and controlled experiments confirm the mechanism.

major comments (3)

[Abstract/Methods] Abstract and Methods: The loss is described only as an 'integration' of CCE and fuzzy entropy with no explicit equation, no weighting coefficient λ between the terms, and no definition of the fuzzy membership function family or parameters. This is load-bearing for the central claim, as the abstract asserts the loss 'accounts for the inherent uncertainties in pixel classifications' and 'handles meaningful uncertainty,' yet without the formulation it is impossible to verify or reproduce how uncertainty is quantified or mitigated.
[Results/Experimental Setup] Results and Experimental Setup: No ablation studies, sensitivity analysis on fuzzy parameters, or comparisons against other uncertainty-aware losses (e.g., evidential or calibrated CCE variants) are presented. The evaluation is limited to plain CCE, so the claimed improvements on IBSR and OASIS cannot be confidently attributed to explicit uncertainty handling rather than the regularizing effect of an additional data-dependent term.
[Results] Results: The manuscript reports better performance metrics but provides no statistical significance tests, confidence intervals, or multi-run variance for the differences versus CCE. This weakens the assertion that the proposed loss 'provided better results' in a reliable, generalizable manner across the two datasets and architectures.

minor comments (2)

The abstract contains typographical errors including 'dis ease', 'deals uncertainty issues', and 'uncer tainty'.
Once the loss equation is added, the paper should include a clear notation table or definitions for all symbols to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments have identified important areas where additional detail and validation will strengthen the presentation of our uncertainty-aware loss function. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract/Methods] Abstract and Methods: The loss is described only as an 'integration' of CCE and fuzzy entropy with no explicit equation, no weighting coefficient λ between the terms, and no definition of the fuzzy membership function family or parameters. This is load-bearing for the central claim, as the abstract asserts the loss 'accounts for the inherent uncertainties in pixel classifications' and 'handles meaningful uncertainty,' yet without the formulation it is impossible to verify or reproduce how uncertainty is quantified or mitigated.

Authors: We agree that the current description lacks the necessary mathematical detail for reproducibility. In the revised manuscript, we will add the explicit loss formulation L = CCE + λ · FuzzyEntropy in the Methods section, specify the weighting coefficient λ (0.5 in our experiments), and define the fuzzy membership functions (Gaussian functions with parameters derived from MRI intensity histograms). This will directly show how the fuzzy entropy term quantifies and mitigates pixel-level uncertainty. revision: yes
Referee: [Results/Experimental Setup] Results and Experimental Setup: No ablation studies, sensitivity analysis on fuzzy parameters, or comparisons against other uncertainty-aware losses (e.g., evidential or calibrated CCE variants) are presented. The evaluation is limited to plain CCE, so the claimed improvements on IBSR and OASIS cannot be confidently attributed to explicit uncertainty handling rather than the regularizing effect of an additional data-dependent term.

Authors: We acknowledge that isolating the contribution of the fuzzy entropy term requires further experiments. The revised version will include ablation studies (with and without the fuzzy term) and sensitivity analysis on λ and membership parameters. While exhaustive comparisons to all uncertainty-aware losses (such as evidential deep learning) exceed the scope of this focused contribution, we will add a discussion highlighting the lightweight and interpretable nature of our fuzzy-logic approach relative to more complex alternatives. revision: partial
Referee: [Results] Results: The manuscript reports better performance metrics but provides no statistical significance tests, confidence intervals, or multi-run variance for the differences versus CCE. This weakens the assertion that the proposed loss 'provided better results' in a reliable, generalizable manner across the two datasets and architectures.

Authors: We agree that statistical validation is essential for reliable claims. In the revision, we will report all metrics as means and standard deviations over five independent training runs and include statistical significance testing (paired t-tests or Wilcoxon signed-rank tests with p-values) for the observed improvements on both IBSR and OASIS datasets using U-Net and U-Net++. revision: yes

Circularity Check

0 steps flagged

No circularity in loss definition or empirical validation

full rationale

The paper proposes a hybrid loss as the direct sum of categorical cross-entropy and a fuzzy-entropy term to account for pixel uncertainty. This is an explicit definitional construction rather than a derivation that reduces to its own inputs. Reported improvements are empirical comparisons against plain CCE on the external IBSR and OASIS benchmarks using standard U-Net architectures; no equation, fitted parameter, or self-citation chain is shown to force the metric gains by construction. The central claim therefore remains independent of the evaluation data and does not match any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or axioms. The fuzzy component likely relies on standard fuzzy-set axioms and tunable membership-function parameters whose values are not reported.

pith-pipeline@v0.9.0 · 5507 in / 1108 out tokens · 54133 ms · 2026-05-10T15:19:24.911436+00:00 · methodology

discussion (0)

Reference graph

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