Dilated Balanced Cross Entropy Loss for Medical Image Segmentation

Mahdieh Soleymani Baghshah; Seyed Mohsen Hosseini

REVIEW 4 major objections 6 minor 24 references

Dilated Balanced Cross Entropy Loss for Medical Image Segmentation

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A weighted cross-entropy loss that also weights each object's surrounding pixels can match the performance of Dice+CE in medical segmentation.

desk verdict A simple new weighting scheme for cross-entropy that performs comparably to Dice+CE, but single-run results and per-dataset tuning of the one hyperparameter leave the practical claim conditional. read the letter →

arxiv 2412.06045 v1 pith:TRTAOAVX submitted 2024-12-08 eess.IV cs.CVcs.LG

Seyed Mohsen Hosseini , Mahdieh Soleymani Baghshah This is my paper · ORCID

classification eess.IVcs.CVcs.LG

keywords dilatedbalancedcrossentropylossweightedclassimbalancemedicalimagesegmentationpolypskinlesionmulti-organfunctiondesign

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

Sparse foreground objects and large backgrounds make medical segmentation a class-imbalance problem. The proposed dilated balanced cross-entropy (DBCE) loss reweights plain cross-entropy not by raw class frequency but by the area of each class mask after dilation, so small objects and the ring of background around them receive high weight. On three medical segmentation tasks the paper reports that DBCE beats both plain CE and balanced CE and matches the popular Dice+CE combination. The intended upshot is that a weighted CE loss with the right spatial weighting can handle imbalance as well as a region-based loss.

What carries the argument

The machine is the pixel-wise weight map $M = \max_c W_c$, where $W_c$ is the dilated, area-normalized mask of class $c$. Given binary ground-truth masks $B_c$ and a disk structuring element of radius $R$, each mask is dilated to $B'_c$, normalized by its area to $W_c = B'_c / \sum B'_c$, and the per-pixel maximum over classes is the loss weight. The CE loss map is then multiplied pointwise by $M$ and summed. This construction carries the argument: it moves balancing weight from the object to its uncertain boundary zone, bounds the weight of tiny classes through dilation, and lets the smallest object dominate where masks overlap.

What would settle it

Select $R$ by cross-validation on a validation split for each task, then compare DBCE against plain CE and Dice+CE on the same held-out test sets; if DBCE no longer beats CE or matches Dice+CE, the claim is settled false. A more mechanism-specific test would measure the false-positive rate in the ring around each object, since DBCE should cut it relative to balanced CE.

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Extended reading notes

Core claim

The central claim is that balanced cross-entropy fails because it over-weights the object and under-weights the surrounding background, and that this can be fixed by dilating each class mask before computing balancing weights. In DBCE, each binary class mask is dilated with a disk-shaped structuring element, the dilated mask is normalized by its own area, and at every pixel the loss weight is the maximum of these normalized values across classes; this weight map is multiplied into the CE loss map. Because the max operation makes the smallest object dominate overlapping dilated regions, and because dilation sets a floor on the effective area of tiny classes, the weighting is both stronger for small structures and less noisy than inverse-frequency balancing. The paper's experimental claim is that, with only the dilation radius as an added hyperparameter, this weighting outperforms CE and balanced CE on polyp, skin-lesion, and multi-organ segmentation, and is similar to Dice+CE.

Load-bearing premise

The method's advantage rests on choosing the dilation radius $R$ per dataset, and the paper sets $R$ empirically (20 pixels for two tasks, 10 for the third) without reporting a validation-based selection rule; if $R$ was chosen to fit the test results, the reported improvements over plain cross-entropy may not transfer.

Editorial extensions

If this is right

With the right spatial weighting, a weighted cross-entropy loss can match a region-based loss like Dice+CE on binary and multiclass medical segmentation.
Per-sample weights can be computed on the fly from each label map, removing the need to precompute class frequencies over the whole training set.
The method specifically lowers false positives in the area around objects, the failure mode that plain balanced CE worsens.
The dilation radius $R$ is a single interpretable knob: $R=0$ reproduces balanced CE, large $R$ erases the balancing effect, and intermediate values give the reported improvement.
DBCE reaches Dice-comparable accuracy without changing the network, data, or training schedule, so the reported gains are attributable to the loss function.

Reading between the lines

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

The paper leaves implicit that the dilation radius could be annealed over training: a large radius early would stabilize learning, and shrinking it later would sharpen boundary emphasis; this is a testable extension the authors do not report.
Because the weight map is built from normalized dilated masks, DBCE behaves like a soft distance-to-object attention; connecting it to boundary losses or distance-transform losses could yield variants the paper does not discuss.
A portability test the paper does not run is to fix one radius across many datasets or choose $R$ by validation rather than by inspecting test performance; until such a rule exists, the claimed advantage over plain CE remains conditional on dataset-specific tuning.
The weighting recipe is class-agnostic, so it could transfer to non-medical sparse-object segmentation, such as aerial or satellite imagery, though the paper only evaluates medical benchmarks.

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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

What you should know: the paper proposes DBCE, which replaces class-frequency weights in balanced CE with inverse dilated-area weights, combined by a max across classes. The idea is simple and the motivation is sound: put weight on the object plus a rim around it, where false positives concentrate. I haven't seen this exact weighting in the literature, so it is a modest but real variant.

The evaluation is honest in scope: three datasets (polyp, skin, multi-organ), same network and training conditions across losses, and balanced CE plus Dice+CE as baselines. The qualitative figures show the expected effect—balanced CE gives many boundary false positives, and DBCE reduces them. The paper also shows a dilation-radius sweep with an optimum at R=20, which is more than many loss papers do.

Soft spots: all results are single runs with no error bars or significance tests. The gains over CE are small—+0.61, +0.97, +0.58 mDice across the three datasets—so the differences could easily be noise. Second, the per-dataset dilation radius is set "empirically" without a described validation protocol. Figure 5 shows strong dependence on R; if R was chosen by looking at test performance, the comparison is biased, and the small advantage over CE may not survive a clean tuning rule. The paper is transparent about the radii, but not about how they were selected. Third, no code is released, which makes reproduction harder. The Synapse results show DBCE matching Dice+CE on some organs and losing on others, consistent with "similar" but not a clear win.

I don't think the central argument collapses. A weighted CE with spatially aware weights can plausibly imitate Dice+CE, and the experiments point that way. But the reported advantage over CE is small and unquantified, and the one hyperparameter is tuned without a stated validation split. This is a legitimate empirical loss-design paper, and I would send it to review, but with a strong request for multiple seeds, confidence intervals, validation-based radius selection, and code. With those additions it would be a solid incremental contribution to the segmentation loss literature.

This is for people working on loss functions for imbalanced segmentation; it gives a clear description of a new weighting and a useful baseline. It won't change the field, but it's worth a look after the statistical gaps are addressed.

Referee Report

4 major / 6 minor

Summary. The paper proposes a pixel-wise weighting scheme for cross-entropy loss in medical image segmentation. Instead of weighting each class by the inverse of its global frequency, as in balanced CE, the method dilates each class mask with a disk structuring element, computes the inverse of the dilated area, and assigns each pixel the maximum of these inverse-area weights across classes. The resulting dilated balanced CE (DBCE) loss is compared against CE, balanced CE, and Dice+CE on three tasks: polyp segmentation (Kvasir-SEG to CVC-ClinicDB), skin lesion segmentation (ISIC 2018), and Synapse multi-organ segmentation. The reported results show that DBCE outperforms CE by small margins (mDice gains of +0.61, +0.97, +0.58 on the three tasks) and is close to Dice+CE, with the conclusion that a properly weighted CE can match a region-based loss.

Significance. If the reported results hold, the paper would provide a simple and inexpensive alternative to region-based losses: a weighted cross-entropy loss whose weights are derived from dilated masks, applicable to both binary and multi-class segmentation. The method is easy to implement, and the experiments span three commonly used public datasets with a standard U-Net backbone, which lends practical relevance. The paper also honestly discusses the sensitivity of the loss to the dilation radius in Figure 5. However, the significance is tempered by the absence of uncertainty quantification and by the small, possibly within-noise improvements over CE. The core claim is that DBCE is a generalizable replacement for Dice+CE, but the evidence is conditional on the choice of the dilation radius and on single-seed evaluation.

major comments (4)

[Sec. 3.2, Fig. 5] The dilation radius R is the only method-specific hyperparameter, and it is set "empirically" per dataset (R=20 for polyp and skin lesion, R=10 for Synapse). Figure 5 shows a pronounced performance optimum near R=20 for the polyp task, with a large drop for other radii. The manuscript does not describe a validation-based selection procedure (e.g., a held-out split or cross-validation). If R was chosen by inspecting test-set performance, the reported gains over CE in Tables 1-3 are optimistically biased, and the method's advantage over CE is conditional on dataset-specific tuning. The paper should either report a principled tuning rule (e.g., pick R on a validation split) or show results for a fixed, transferable R across all datasets.
[Sec. 3.3, Tables 1-3] All experiments are based on a single training run per loss, and no error bars, confidence intervals, or significance tests are reported. The central claim that DBCE outperforms CE and matches Dice+CE rests on small differences: e.g., Table 1 shows mDice of 88.85 for DBCE vs. 88.24 for CE, and Table 3 shows mDice of 81.68 for DBCE vs. 81.75 for Dice+CE. These differences are within a few tenths of a point and cannot be distinguished from run-to-run variation without at least multiple seeds and a paired test. Please report mean and standard deviation over multiple seeds (3-5) and, if possible, per-fold comparisons for the Synapse dataset.
[Table 3] The aggregate claim that DBCE produces "similar results" to Dice+CE hides notable organ-level differences. For example, DBCE is 0.95 points worse on Aorta (90.84 vs. 91.79) and 1.54 points worse on Pancreas (66.54 vs. 68.08), while being 1.33 points better on Spleen (91.12 vs. 89.79). These differences are not discussed. If the conclusion is that DBCE is comparable to Dice+CE across organs, the organ-wise pattern should be addressed; if not, the conclusion should be restricted to the aggregate metric.
[Sec. 4, Conclusion] The wording "produces superior results compared to CE" appears in the Conclusion and is also implied in the Abstract. Given the small margins (mDice gains of 0.6-1.0 points) and the absence of statistical support, this is stronger than the evidence warrants. Either provide significance testing or revise the claim to "comparable to, or slightly better than, CE" to avoid overstating the finding.

minor comments (6)

[Abstract] In the abstract, "improved my modifying" should read "improved by modifying".
[Eqs. (2)-(5)] The mathematical typesetting of Equations (2) through (5) appears garbled in the manuscript, particularly the normalization in Eq. (4); please provide a clean, unambiguous formulation of the weight map.
[Fig. 5] Please state in the caption or text what metric is plotted on the vertical axis (presumably mDice on the test set) and clarify whether the curve represents a single run or an average.
[Sec. 3.2] The training details list epoch counts (600, 200, 300) but not batch size or whether the same training budget was kept for all losses; these details are needed for reproducibility.
[References] Reference [5] appears twice in the text: once for the U-Net architecture (Ronneberger et al.) and once for Bertels et al. on optimizing the Dice score; please fix the citation numbering.
[Figs. 2-4] The qualitative examples are illustrative, but the selection criteria for the displayed slices are not stated; please specify whether they are selected randomly or by other criteria.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: DBCE is defined by construction and evaluated on external benchmarks.

full rationale

The paper's central object, the DBCE loss, is explicitly defined in Eqs. (2)-(5) as a weighted CE loss whose pixel-wise weights are derived from dilated class masks; no quantity in the definition presupposes the reported segmentation results. The experimental claims are supported by comparisons on external datasets (Kvasir-SEG/CVC-ClinicDB, ISIC 2018, Synapse) against CE, balanced CE, and Dice+CE baselines, with training conditions kept fixed across losses. The only method-specific hyperparameter, the dilation radius R, is stated to be set empirically per dataset (Sec. 3.2), and its effect is directly investigated in Fig. 5; this is a tunable hyperparameter rather than a fitted quantity renamed as a prediction. There is no self-citation chain, no imported uniqueness theorem, and no known result merely renamed. Possible test-set selection of R is a reproducibility concern, not a circularity concern, because the method's benefit is asserted empirically rather than derived from the choice of R.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The only free parameter is the dilation radius. The two listed axioms are assumptions about error distribution and the design of the weighting scheme. No new physical or conceptual entities are introduced.

free parameters (1)

dilation radius R = 20 pixels (polyp, skin lesion), 10 pixels (multi-organ)
The radius is set empirically per dataset and is the main hyperparameter of the loss. Figure 5 shows performance varies strongly with R, with zero radius (balanced CE) performing worst.

assumptions (2)

domain assumption Segmentation errors are concentrated in and around object boundaries, so weighting the dilated surround reduces false positives.
Section 2: 'most errors usually happen in the object and its surrounding areas'.
ad hoc to paper Dilating masks with a disk structuring element and taking the max of inverse-area weights yields an effective balancing strategy.
The choice of disk and max operation is introduced specifically for this method and is not derived from first principles.

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Cite this review

Pith. "Pith review of Dilated Balanced Cross Entropy Loss for Medical Image Segmentation." pith.science (2026). https://pith.science/paper/TRTAOAVX

@misc{pith2026241206045,
  author       = {Pith},
  title        = {Pith review of: Dilated Balanced Cross Entropy Loss for Medical Image Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TRTAOAVX}},
  note         = {Machine review of arXiv:2412.06045}
}

read the original abstract

A novel method for tackling the problem of imbalanced data in medical image segmentation is proposed in this work. In balanced cross entropy (CE) loss, which is a type of weighted CE loss, the weight assigned to each class is the in-verse of the class frequency. These balancing weights are expected to equalize the effect of each class on the overall loss and prevent the model from being biased towards the majority class. But, as it has been shown in previous studies, this method degrades the performance by a large margin. Therefore, balanced CE is not a popular loss in medical segmentation tasks, and usually a region-based loss, like the Dice loss, is used to address the class imbalance problem. In the pro-posed method, the weighting of cross entropy loss for each class is based on a dilated area of each class mask, and balancing weights are assigned to each class together with its surrounding pixels. The goal of this study is to show that the performance of balanced CE loss can be greatly improved my modifying its weighting strategy. Experiments on different datasets show that the proposed dilated balanced CE (DBCE) loss outperforms the balanced CE loss by a large margin and produces superior results compared to CE loss, and its performance is similar to the performance of the combination of Dice and CE loss. This means that a weighted cross entropy loss with the right weighing strategy can be as effective as a region-based loss in handling the problem of class imbalance in medical segmentation tasks.

Figures

Figures reproduced from arXiv: 2412.06045 by the authors.

**Figure 1.** Calculating the dilated balanced cross entropy (DBCE) loss. (a) Input image, (b) ground truth labels, (c) the cross entropy (CE) loss map before applying any weights (values are normalized for better visualization), (d) pixel-wise loss weight, which are the inverse of the area of dilated shapes of labels, the boundaries of the original labels are also included as a reference, (e) the weighted loss map, obtained by … view at source ↗

**Figure 2.** Visual comparison of predictions obtained by 4 different losses from the polyp segmentation task. For each image the first row contains the binary predictions and the second row shows raw probability predictions. In binary predictions false positives and false negatives are marked by red and blue [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Visual comparison of predictions obtained by 4 different losses from the ISIC 2018 skin lesion segmentation task. For each image the first row contains the binary predictions and the second row shows raw probability predictions. In binary predictions false positives and false negatives are marked by red and blue [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Visual comparison of predictions obtained by 4 different losses from the Synapse multiorgan segmentation task. For each slice the first row contains the label predictions and the second row shows the error map (incorrectly labeled pixels are marked in red) [PITH_FUL…

**Figure 5.** Figure 5: The effect of the amount of dilation on performance for the polyp segmentation task. The radius of the dilation structuring element is increased from zero (simple balanced CE) to 150 pixels. 4 Conclusion For addressing the class imbalanced problem in medical segmentati…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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

[1] [1]

In: Medical Image Analysis

Ma J, Chen J, Ng M, Huang R, Li Y, Li C, Yang X, Mar tel AL.: Loss odyssey in medical image segmentation. In: Medical Image Analysis. (2021)

work page 2021

[2] [2]

In: Proceedings of the IEEE international conference on computer vision (2017)

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work page 2017

[3] [3]

In: Proceedings of t he IEEE conference on computer vision and pattern recognition (2017)

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work page 2017

[4] [4]

In: Medical Image Computing and Computer-Assisted Intervention–MICCAI (2015)

Ronneberger O, Fischer P, Brox T.: U-net: Convoluti onal networks for biomedical image segmentation. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI (2015)

work page 2015

[5] [5]

In: Medical Image Computing and Computer Assisted Intervention–MICCAI (2019)

Bertels J, Eelbode T, Berman M, Vandermeulen D, Maes F, Bisschops R, Blaschko MB.: Optimizing the dice score and jaccard index for med ical image segmentation: Theory and 10 practice. In: Medical Image Computing and Computer Assisted Intervention–MICCAI (2019)

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Fitzgerald K, Matuszewski B.: FCB-SwinV2 Transformer for Polyp Segmentation. arXiv preprint arXiv:2302.01027. (2023)

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In: Multimed ia Modeling: 26th International Con- ference, MMM (2020)

Jha D, Smedsrud PH, Riegler MA, Halvorsen P, de Lan ge T, Johansen D, Johansen HD.: Kvasir-seg: A segmented polyp dataset. In: Multimed ia Modeling: 26th International Con- ference, MMM (2020)

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