Rethinking Model Calibration through Spectral Entropy Regularization in Medical Image Segmentation
Authors: Kun Cheng
Yukun Zhang
William Henry Nailon
Tonggang Zhao
Venue: ICLR 2026 Poster (2026)
Keywords: medical image segmentation
model calibration
spectral entropy
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
TL;DR: We improve medical image segmentation model calibration by addressing spectral bias and confidence saturation through a frequency-domain framework that balances low and high-frequency components in uncertainty estimation.

Abstract: Deep neural networks for medical image segmentation often produce overconfident predictions, posing clinical risks due to miscalibrated uncertainty estimates. In this work, we rethink model calibration from a frequency-domain perspective and identify two critical factors causing miscalibration: spectral bias, where models overemphasize low-frequency components, and confidence saturation, which suppresses overall power spectral density in confidence maps. To address these challenges, we propose a novel frequency-aware calibration framework integrating spectral entropy regularization and power spectral smoothing. The spectral entropy term promotes a balanced frequency spectrum and enhances overall spectral power,  enabling better modeling of high-frequency boundary and low-frequency structural uncertainty. The smoothing module stabilizes frequency-wise statistics across training batches, reducing sample-specific fluctuations. Extensive experiments on six public medical imaging datasets and multiple segmentation architectures demonstrate that our approach consistently improves calibration metrics without sacrificing segmentation accuracy.

Published as a conference paper at ICLR 2026
RETHINKING MODEL CALIBRATION THROUGH SPECTRAL ENTROPY REGULARIZATION IN MEDICAL IMAGE SEGMENTATION
Kun Cheng', Yukun Zhang', William Henry Nailon", Tonggang Zhao Beijing University of Posts and Telecommunications Beijing, China 2HHS Lothian & The University of Edinburgh, Edinburgh, United Kingdom kchengfbupt.eed edu.. en, mailoneed.ac.
cetbbupt.du..c..m zhaotg@bupt.. edu cn
ABSTRACT
Deep neural networks for medical image segmentation often produce overconfi- dent predictions, posing clinical risks due to miscalibrated uncertainty estimates. In this work, we rethink model calibration from a frequency-domain perspective and identify two critical factors causing miscalibration: spectral bias, where mod- els overemphasize low-frequency components, and confidence saturation, which suppresses overall power spectral density in confidence maps. To address these challenges, we propose a novel frequency-awand calibration framework integrat- ing spectral entropy regularization and power spectral smoothing. The spectral en- tropy term promotes a balanced frequency spectrum and enhances overall spectral power, enabling better modeling of high-frequency boundary and low-frequency structural uncertainty. The smoothing module stabilizes frequency-wise statistics across training batches, reducing sample-speciff fluctuations. Extensive exper- iments on six public medical imaging datasets and multiple segmentation archi- tectures demonstrate that our approach consistently improves calibration metrics without sacrificing segmentation accuracy.
INTRODUCTION
Deep neural networks (DNNs) have become essential in medical image segmentation, enabling tasks such tumor delineation and organ identification HHatamizadeh et al. (2021): Chen et al. (2011b) [sensee et al. (2021). Despite their high accuracy, DNNs often exhibit overconfident predic- mions-particulartyy
lesion boundaries, where predicted confidence substantially exceeds actual correctness Yeung et al. (2023): Larrazabal et al. (2023); Murugesan et al. (2025). This overconfi- dence undermines the reliability of automated systems clinical settings and leads to misinformed diagnostic decisions Begoli et al. (2019).
To mitigate such risks, confidence calibration aims align the predicted confidence with the true likelihood of correctness. Existing calibration methods in medical segmentation primarily oper- in the spatial domain. Post-hoc techniques such as temperature scaling and Platt scaling apply dataset-level adjustments to logits Guo et al. (2:17);: Platt et al. (1999), but they often fail to adapt to anatomical and modality variability Tomani et al. (2021). Training-time methods, including label smoothing Müller et al.] (2019), Focal Loss Mukhoti et al. (2020), and regional uncertainty regu- larization Murugesan et al. (2023a/ 2024), add explicit or implicit constraints on output confidence Pereyra et al. (2017). While these approaches partially alleviate overconfidence, they predominantly focus on spatial domain characteristics and neglect potential frequency domain information, which can lead to suboptimal calibration performance.
Recent efforts suggest that frequency-domen information can enhance calibration and robustness. For instance, style-invariant Fourier domain adaptation has been used to stabilize model behav- ior across domains, and hybrid spatial-spectral representations have shown promise in improving
"Corresoonding author

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Figure 1: Frequency-domen analysis of overconfidence in medical image segmentation. (a) Syn- thesized confidence maps for a binary bbrrgrouuddbaccgroondd segmentation example. Boundary pixels are assigned variable foreground confidence levels a, while interior pixels have full confi- dence (confidence
1.0). (b) Resulting confidence maps as boundary confidence varies from overconfident (1.0) to well-calibrated (0.5). binary context, a = 0.5 represents maximum un- certainty, the ideal state for a boundary pixel, the model is equally confident in the foreground and background classes. Confidence values a < 0.5 are not shown, as they would correspond to an incorrect background prediction, which is outside the scope of calibrating correct foreground prediction. (c) Power spectral density (PSD) analysis. A Hamming window Hamming Stearns (1979) is applied before the FFT reduce spectral leakage caused by edge artifacts, ensuring more accurate spectrum. As boundary confidence decreases toward the well-calibrated state, the PSD) becomes richer across all frequency bands.
generalization and uncertainty estimation Chen et al. (023b); Li et al. (2024); Tang et al. 22021), However, such works primarily target domain shift style variation, rather than addressing over- confidence in confidence maps for medical segmentation.
From a spectral perspective, neural networks exhibit an inherent Spectral Bias during optimization, preferentially learning low-frequency patterns while inadequately capturing high-frequency details Rahaman al. (2019) Xu et al. (2019), which further exacerbates overconfidence boundary re- gions where
information is crucial for uncertainty estimation. Besides, illustrated Fig. [ we create synthetic confidence maps by assigning different confidence levels to boundary pixels, while keeping interior pixels fixed. The power spectral density (PSD) analysis shows that overconfident maps (with boundary confidence a 1.0) have sparse spectral energy. In contrast, well-calibrated maps (e.g., 0.5) display richer power across frequency bands. This suggests that overconfidence is linked to both spectral bias and low spectral complexity. Better-calibrated predic- tions distribute spectral power more evenly, capturing both high-frequency boundary uncertainty and low www-freuunccy structural variations. We term this effect spectral suppression in confidence maps Confidence Saturation.
To address these two issues toward trustworthy medical image segmentation models, this paper introduces novel adaptive calibration method from spectral perspective. Our main contributions are as follows:
1. We conduct the first comprehensive spectral analysis of overconfidence in segmentation, revealing strong link between prediction uncertainty and spectral power distributions.
2. We introduce power spectral smoothing mechanism that stabilizes frequency wise power statistics by aggregating spectral information across historical training batches, help- ing maintain segmentation performance while promoting consistent spectral patterns.
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3. We design spectral entropy regularization mechanism that enhances overall spectral power and improves frequency balance in confidence maps, leading to significantly im- proved calibration quality.
2
RELATED WORK
This section reviews research areas closely related to our approach, including confidence calibration methods, uncertainty estimation approaches, and frequency domain approaches in medical image analysis.
2.1 CONFIDENCE CALIBRATION METHODS
Post-hoc Calibration Methods. These methods improve calibration by adjusting output distribu- tions after model training without retraining. Temperature Scaling Guo al. (2017) adjusts soft- max outputs by optimizing a global temperature parameter. Platt Scaling Platt et al. 1999) applies logistic regression transform logits, while non non-parametric methods such as Histogram Binning Zadrozny & Elkan (001) and Isotonic Regression Fawcett & Niculescu-Mizi) (007) map predicted probabilities to empirical accuracies. However, these approaches lack region speecone-eeciiice calibration ca- pabilities for different anatomical structures and show limited generalization under domain shifts across modalities Tomani et al. (202I). In-training Calibration Methods. These methods mod- ify training objectives with regu larization strategies to optimize calibration during training. Label Smoothing Müäler et al. 2019) softens target labels to reduce overconfidence, while Focal Loss Mukhoti al. (2020) reduces the influence of easily segmented samples. Entropy Regularization Pereyra et al. (0117) encourages higher predictive entropy to suppress overconfident predictions. Recent methods such MarginLoss Murugesan al. (2023a) and CRaC Murugesan al. (2024) incorporate regional information and adaptive constraints for spatial calibration. While these approaches demonstrate advantages in medical image tasks, they primarily rely on spatial domain features and lack systematic frequency domain analysis for calibration.
2.2 PROBABILISTIC UNCERTAINTY ESTIMATION METHODS
Uncertainty estimation approaches in deep learning are primarily based on probabilistic model- ing. Bayesian neural networks (BNNs) Vadera et al. (22T)) exemplified by MC-Dropout Gal & Ghahramani (2016), approximate Bayesian posteriors by retaining dropout during inference. Deep ensembles akshminarayanan al. (2077) train multiple models with different initializations and aggregate predictions, while evidential deep learning Sensoy et al. (2018) directly parameterizes probability distributions rather than point estimates. These methods have been applied in medical image analysis, with Nair et al. (2020) evaluating approaches in brain tumor segmentation and Jungo al. (2018) examining the impact of uncertainty estimation on segmentation accuracy. However, computational complexity and multiple inference requirements limit their real-time clinical applica- bility| Murugesan al. (202bb).
2.3 FREQUENCY DOMAIN APPROACUESS IN MEDICAL IMAGE ANALYSIS
Frequency analysis has been widely applied in medical image analysis, from traditional Fourier- based denoising and enhancement to recent deep learning integration. Recent works have explored diverse applications including data augmentation impact analysis Yin et al. (2019), enhanced trans- lation invariance Zhu et al. (202T), skin lesion segmentation optimization Li et al. (202T), MRI organ segmentation with spectral constraints Chen et al. (2023a). and gross-domain sho- segmentation through frequency loss that matches the prediction's 's spectrum to the ground truth 's to improve segmentation accuracy. In addition, while Feng et al. (2023) and Chen et al. (202 aa) also leverage frequency decomposition, they target domain adaptation and robustness via input/feature-level operations, whereas we directly regularize the spectrum of output confidence maps for calibration in fully supervised segmenta- tion setting. contrast, we focus on confidence calibration and directly regularize the intrinsic spectral properties of the model's output itself, without relying ground truth spectrum. To our knowledge, this use of frequency analysis for confidence calibration in medical image segmentation remains underexplored.
matching Bo et al. (2025). ). Notably, Gorade et al. (2024) used a spectral
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3 METHOD
3.1 SPECTRAL ANALYSIS OF MODEL UNCERTAINTY
To motivate frequency-aware calibration framework, we first conduct comprehensive spec- tral analysis to investigate how model confidence relates to uncertainty estimation medical image segmentation. Specifically, we analyze the power spectral density (PSD) of predicted confidence maps and observe that miscalibrated models often exhibit unbalanced spectral power distributions, characterized by the dominance of low-frequency components and suppressed high-frequency re- sponses. as shown in Fig. [ This spectral bias limits the model's 's ability to capture detailed boundary uncertainty and subtle anatomical structures. We observe that uncalibrated models of- ten produce confidence maps that saturate toward uniformly high values, a behavior we define as confidence saturation. This effect results in reduced overall power spectral density (PSD), dimin- ishing the frequency richness required to represent model uncertainty, especially in regions with boundary ambiguity. In contrast, well-calibrated models yield confidence maps with higher overall PSD, preserving richer spectral characteristics that better reflect structural variability and predictive uncertainty.
These findings reveal strong connection between model calibration and the spectral characteris- ties of prediction confidence. The presence of spectral bias and confidence saturation suggests that current models may fail to adequately represent uncertainty across spatial scales, and particularly high-frequenne boundaries. This motivates the design of a calibration strategy that explicitly incor- porates spectral structure, aiming rebalance frequency distributions and increase overall spectral power, thereby enhancing model calibration and improving segmentation reliability.
3.2 SPECTRAL DECOMPOSITION AND WINDOW SMOOTHING
Building on our prior spectral uncertainty analysis, we now introduce a spectral decomposition and temporal smoothing scheme that extracts reliable frequency-domen domain confidence profiles, mitigat- ing per-sample variability and enabling stable, frequency-aware calibration. Given input images where B is the batch size, Cin denotes the number of input channels, and D. H. W denote depth, height, and width respectively, the neural network fo(-) outputs prediction features (logits before softmax) fe(z) RxxCxxx HxW where C is the number of classes. A scalar confidence map is constructed by taking the voxel-wise maximum logit value across the class dimension. While calibration is ultimately assessed on post-softmax probabilities, we operate on logits because they represent the network's raw, unnormalized evidence and offer a more sensitive signal for spectral analysis. Softmax outputs can saturate near 1, which can mask underlying spectral characteristics, whereas logits retain a wider dynamic range. This logit- based map there- fore directly captures the precursors overconfidence, where excessively high values are a primary cause of miscalibration.
IR x
2 (d, h, w) max (d, d, h, w),
emm I...,.
For each sample 6, we transform (d, h, w) into the frequency domain via a 3D Fast Fourier Trans- form (FFT) to analyze its spectral properties:
Fo(u, v, w) SC (Fon [z h w)))
Es(u, v, w) Fblu, v, w)
(3)
where (u, v, w) are frequency domain coordinates, and Es u, w) represents the power spectral density at each frequency for sample b. Here, SC denotes Spectrum Centering, i.e., freeuueeecny component shift to center the spectrum.
To characterize spectral behavior at different scales, we partition the frequency domain into K con- centric spherical shells Ię based on frequency magnitude, following the band decomposition strategy in Bo et al. (2025):
Is { (u, v, rK-1 < Vu² + 22 2² S 3 k= ==
& min(D. which normalizes the frequency bands relative to the spatial dimensions, with 7% K allowing scale-invariant spectral partitioning. This decomposition enables frequency-aware charac- terization of low-frequency structural content and high-frequency boundary information. For each
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sample b and frequency band k we aggregate the spectral power within the corresponding shell:
s
Σ
Es(u, W.).
(5)
To reduce statistical fluctuations and enhance training stability, we apply temporal smoothing over a sliding window of recent batches:
W
5(h)
S b,a0?
(k)
(6)
B
DE
where W is the window size, w W corresponds to the current batch, and w = corresponds to the oldest batch within the window. This smoothing aggregates spectral power statistics over multiple samples and batches reduce noise and sample-specific variance. Let S (St22, S(K) denote the vector of smoothed spectral power across all K frequency bands. During early training, when historical batches are unavailable, we replicate the current batch statisties initialize the window and ensure numerical stability. This temporally smoothed spectral profile provides consistent and robust reference for regulating spectral power distributions frequency bands throughout training, thereby supporting rrequency-awan calibration.
3.3 POWER SPECTRAL ENTROPY REGULARIZATION
Leveraging the temporally smoothed spectral profile vector S, we introduce a power spectral en- tropy regularization term, which encourages the model learn balanced frequency representations that alleviate spectral bias. It also promotes higher, more informative spectral power to counteract confidence saturation, thereby facilitating calibrated segmentation.
To quantify spectral diversity, we first convert the raw spectral power vectors into probability distri- butions. For the smoothed spectral profile Š and each sample's profile S,, we define their normalized counterparts, P and Po,
S(A)
p(k)_
Σ/= SUI +
where S' is either S or Sb, and is small constant (e.g.. 10 to ensure numerical stability in both normalization and entropy calculation steps. The spectral entropy is then computed using standard Shannon entropy formula:
Hapec (P)=
Σ p(k) log(plk) + E).
k=1
Here, can be or Ps- We select Shannon entropy as is a principled measure from information theory for quantifying the uniformity of probability distribution. A higher spectral entropy indi- cates that power is more evenly distributed across all frequency bands rather than being concentrated in few. This directly aligns with our goal of encouraging richer, more balanced frequency repre- sentations for better uncertainty estimation. The entropy Hapec (Pb) is computed independently for summary statistic, it intention-
each sample b batch. While this compresses the spectrum ally quantifies the spectral uniformity of each sample to address spectral bias. By penalizing this per-sample value, our method enhances the frequency representation of each specific prediction, thereby preserving its unique characteristics rather than obscuring them.
To address spectral bias and the resulting confidence saturation, we introduce a hinge-like spectral regularization loss. It encourages each sample's 's spectral entropy Hspee((P) to approach or exceed the dynamically updated target entropy Hapee( P):
1 max 0, Hspeo Hapee (ps)c(P))) B BEB
ESpectral =
The mechanism of this loss directly counteracts spectral bias. The hinge formulation creates a targeted learning signal: penalty is incurred only when sample's spectral entropy is deficient
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compared to the dynamic target. Minimizing this penalty formally encourages spectral distribution by pushing power from dominant low-frequency bands into underrepresented freeufrryeyccy bands. While entropy itself is scale-invariant, this re- b-bbalncing forces the model to increase the total spectral energy of the logit map to avoid compromising the task loss. This prevents the generation of overly smooth, low-energy confidence maps, directly mitigating the effects of confidence saturation.
uniform
The max(:; 0) operation ensures that only samples with spectral entropy below the adaptive target incur penalties. This selective penalization encourages the model to enhance frequency-domal diversity while maintaining calibration performance for already well-calibrated samples.
3.4 OVERALL TRAINING ORJECTIVE
We integrate our spectral regularization with the conventional segmentation objective through a weighted combination:
Liotal = LOE + X.Spoctrall
(10)
where Lce is the cross-entropy loss for pixel-wise accuracy, and À balances the trade-off be- tween segmentation performance and uncertainty calibration. The hyperparameter À allows users to
balance segmentation accuracy and calibration strength. This flexibility is important because differ- ent organs or lesions exhibit varying levels of uncertainty, requiring tailored calibration strategies to reflect the underlying uncertainty characteristics each case optimally.
4 EXPERIMENTS
4.1 DATASETS AND IMPLEMENTATION DETAILS
We conducted experiments on six public medical imaging datasets, covering diverse anatomical structures and imaging modalities, to comprehensively evaluate our method. These datasets are Brain Tumor Segmentation (BraTS) 2020 Menze al. (2014), Automated Cardiac Diagmosis Chal- lenge (ACDC) Bernard et al. (2018), Fast and Low GPU memory Abdominal oRgan sEgmentation (FLARE) 2021 Ma et al. (2022h, MICCAI Grand Challenge on 6-month Infant Brain MRI Segmen- tation (iSeg) 2017 Sun et al. (202T), A Tumour and Liver Automatic Segmentation (ATLAS) 2023 Quinton et al. 2023), ) and Prostate MR Image Segmentation (PROMISE) 2012 Litjens et al. (2014).
All datasets were split into training, validation, and test sets with ratio of 4:1:1.
Experiments were conducted on Ubuntu 22.04 with an NVIDIA RTX 4090 GPU, utilizing the U- Net architecture Ronneberger al. (2015). We adopted consistent training settings across all exper- iments, including a batch size of 2, input patch size of 96 x 96 x 96, and the SGD optimizer (initial learning rate 0.01). Input data were normalized [0, 1].
4.2 EVALUATION METRICS AND COMPARISON METHODS
Segmentation performance was evaluated using Dice Similarity Coefficient (DSC), 95% Hausdorff Distance (HD95), and Average Surface Distance (ASD), which collectively assess overlap accu- racy, boundary error, and surface deviation, respectively. To evaluate calibration, we used Expected Calibration Error (ECE) as the primary metric, following the protocol in Nixon et al. (209)) and included Static Calibration Error (SCE) and Thresholded Adaptive Calibration Error (TACE). SCE generalizes ECE multi-class settings via class-wiz wise binning. while TACE improves robustness through equal-sized binning and probability thresholding. Both ECE and SCE were computed using B 15 bins, and TACE employed a threshold 0.001 as Murugesan et al. (2024).
All comparison methods are in-training calibration strategies built upon the cross-entropy loss, con- sistent with our approach. We implement these baselines using the optimal hyperparameter config- urations reported in their respective original publications, standard practice for fair benchmarking, These include Focal Loss (FL. 7 = 3) Lin et al. (011)). Label Smoothing (L.S a = 0.1) Szegedy et al. (2016), Margin-basse Label Smoothing (MbLS, X 0.1, m 5) Murugesan et al. (2023b),
Spatially Variant Label Smoothing (SVLS, σ = 2) Islam & Glocker (2021), and Class and Region- Adaptive Constraints (CRaC, 7 1.2, μ 0.9. R 2, margin
5) Murugesan et al. 20044)

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5 RESULTS AND DISCUSSION
Table 1: Quantitative comparison of segmentation performance across multiple datasets (DSC1, HD955,, ASDL). o indicates higher is better, + indicates lower is better. Bold denotes the best result, and italics indicate the second-best.
Dutract
Melhed & Publication
DSCT (5)
HDSSL
ASDi
SYLS
CRaC
ICCV
MICCAT
MallA
MICCAI
96.9
$4.5
56.7
35.9
$5.9
85.9
81.2
2.27
2,80
1.50
3.91
2.46
1.58
1.33
0.40
0.44
0.27
0.41
(14]
0..9
[L:7
iSe22017
94.2
92.0
98.1
94.1
94.2
94.2
98.4
1.91
1.46
1.13
1.15
1.15
1.17
0.85
0.05
0.05
0.05
9.96
0.06
0.06
8.15
FLAREM221
91.5
$2.7
91.3
91.3
91.2
91.4
92.5
8.29
6.17
$.37
7.38
$.40
7.48
4.55
2.64
2:23
2.40
2.09
2.22
2.10
1.34
AUII
91.1
39.3
90.7
91.0
0.5
0.90
0.88
0.83
0.80
0.81
8.74
0.10
0.12
0.11
1..0
0.11
AILASINIS
663
2113
08.3
698
20:19
19:76
18.8
20:31
17.82
4:53
3.54
1.07
PROMESE101
79.1
5.51
Table 2: Quantitative comparison of calibration performance across multiple datasets (ECEL, SCEJ,
TACEn).
Donset
Method Publication
ECEJ 0x10
SCEJ (<10
TACELIKGO
SYLS
ICCV
MICCAL
BraTS2020
9.1
5.5
25.2
1.
2.1
22
1.5
10.7
6.4
13
4.0
5.0
5.1
0.5
42.7
57.3
61.4
21.5
32.8
29.4
20.2
18g22017
4.5
6.5
17.7
2.1
26
2.6
2/0
119
4.0
2.5
2.3
2.9
255
2.8
15.6
17.6
33.8
11.8
13.5
13.4
6.4
FLARE1221
25.5
19.4
6.3
2.2
244
08
18.1
11.
130
11.3
9.1
0.4
0.6
17.8
52.1
80.0
30.4
24.2
78.5
AUII
12.5
212
28.1
16.6
16.7
38.1
10.6
133
1.1
31.0
3810
88.1
26.7
338
533
16.3
ATLAS2223
04
7.0
PROMESE101
41.7
SVL8
CRiC
Ours
(0) Confodenns (b) Rolibhlliy
Image
Map
14
Diagram
Grond Trath
(e) Prediction
Figure 2: BraTSS000 brain tumor segmentation: (a) confidence maps with blue (low confidence) and orange (high confidence), (b) reliability diagrams showing calibration quality against the ideal diagonal baseline, and (c) segmentation results comparison with black (background), green (edema), purple (non-enhancing necrosis), and orange (enhancing tumor).
Quantitative Evaluation in Calibration and Segmentation. Table [ shows that our method achieves the best and second-best segmentation performance CE baseline and leading segmentation methods. As shown in Table T our method demonstrates consistently strong and robust performance across Dice, HD95, and ASD metrics, validating its effectiveness across diverse segmentation tasks. As shown in Table 2 our method demonstrates state-of-the-arr calibration, achieving the lowest ECE and SCE scores across all datasets. These results highlight the reliability and robustness of our approach in producing well-calibrated confi- dence estimates across the full probability spectrum. CRaC's superior TACE performance on ACDC and PROMISE2012 stems from its task-specific calibration tailored for fine-grained confidence ad- justments in small, well-defined anatomical structures such as heart chambers and the prostate. By leveraging spatial consistency and localized uncertainty modeling, CRaC effectively reduces subtle miscalibrations high-certainty regions emphasized by TACE, However, this focused calibration strategy can sometimes compromise segmentation accuracy. In contrast, method achieves
all metrics, outperforming the

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FL
10
LS
Spectaal Density (log scale)
CiRa!" Mirbod
10a
Low Frequeney
High Frequency
10"
10
Frequency scale)
Figure 3: Comparison of power spectral density of confidence maps on the BraTS2020 dataset across different approaches.
Model Comparison: Base CE vs Ours (Improved)
0.0200
miNs Bac
UNet Bai
TrasAUNet Buc
0.0175
Nil tnproved
UNat Ingroved
Transthett impeoval
0.0150
SWirLNETR ongrovad
Arsovicet tmprovd
UNe Deproved
0.0125
ECE
0.0100
0.0075
0.0050
0.0025
0.0000
0.870
0.872
0.874
DSC
Figure 4: Generalizability of the method across segmentation architectures: improvements in seg- mentation (DSC) and calibration (ECE) performance compared to the CE baseline.
more balanced calibration reflected in ECE and SCE metrics, alongside consistently superior seg- mentation performance across diverse datasets.
Qualitative Analysis in Calibration and Spectral Analysis. Fig. 8 illustrates how method enhances uncertainty calibration and segmentation performance on BraTS2020. The CE baseline yields disconnected boundaries in the confidence map (Fig. 8(a)) and shows mixed calibration behavior in the reliability diagram (Fig. 8(b)): it is underconfident in the low-confidencee region, yet becomes systematically overconfident in the high-confidence region (under the ideal curve). FL applies overly aggressive confidence suppression to encourage low-confidence boundaries, which produces diffuse and spatially imprecise uncertainty regions the confidence map; correspond- ingly, its reliability curve exhibits consistent underconfidence even in the high-confidence region. Other methods also tend to undercontident to varying degrees, with underconfidence being more pronounced in the low-confidence region for most approaches. LS follows this general trend and is particularly underconfident at low confidence, while still showing some underconfidence in the high-confidence region. In contrast, spectral regularization and smoothing promote balanced frequency representation. enabling sharper and more precise boundary localization in the confidence maps and yielding reliability curve that stays closest to the ideal diagonal across confidence bins.
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Table 3: Ablation study results of method on the BraTS2020 and FLAREE021 datasets. We evaluate the contribution of each key component across segmentation metries (DSC, HD95, ASD) and calibration metrics (ECE, SCE, TACE). The configurations are: Baseline (CCg), adding spectral entropy regularization without temporal smoothing (CCE w/ LSpectral w/o W), and our full method
with smoothing (Leg w/ Speetrral)
Configuration
Br.TS2020
FLARE2021
DSC1
HDD5]
ASD
ECEL
SCEL
TACEL
DSC1
HD951
ASDJ
BCEL
SCEJ
TACEJ
Baseline (Cog)
2.27
0.40
0.0091
2.64
0.0181
0.0378
Cos w/ Capestral w/ W
0.870
2.25
0.39
0.0065
0.0078
0.0315
0.921
6.15
1.98
0.0170
0.0123
0.0210
Cog w/ ESpertral
0.872
2.23
0.37
0.0015
0,0008
0.0202
0.925
4.55
1.34
0.0008
0.0006
0.0031
Fig. 3 provides a spectral perspective on calibration by linking the power spectral density (PSD) dis- tribution miscalibration patterns observed in the reliability diagram (Fig. b)). The CE baseline exhibits the lowest overall spectral power, reflecting strong confidence saturation and a steep PSD slope that indicates significant spectral imbalance. This spectral bias corresponds its overcon- fident predictions in high-confidence regions and underconfident predictions in low-confidence re- gions in the reliability diagram. Focal Loss reinforces lwwfrreuyyccy dominance, which moderately enhances the PSD in low-frequency regions but sharply suppresses begh-frequency components its high-frrequncyy PSD is even lower than CE. This imbalance hinders its ability to represent boundary- level uncertainty, resulting in underconfident predictions in high-confidence regions. Other meth- ods show comparable overall spectral power and insufficient high-frequency representation, which aligns with their mild underconfidence in the reliability diagram. In contrast, our method achieves the highest overall spectral power and the most balanced frequency distribution, particularly in the high-fru greeffrreuency regions critical for boundary uncertainty. This enables accurate modeling of de- tailed confidence variations and contributes to the best overall calibration performance on multiple datasets.
To validate the generality of our approach, we applied it across a diverse set of widely adopted seg- mentation architectures (Fig. 4. including nnUNet Isensee Isesse al. (202T), SwinUNETH Hatamizadeh et al. 2021). UNet++ Zhou et al. (2019), Attention (Nktay et al. (2018), and TransUNet Chen al. (2021b). Using fixed set of hyperparameters for all experiments, our method consistently improved both segmentation accuracy and calibration. This result demonstrates the robustness and plug-and-play applicability of our approach.
Ablation Studies. Our ablation studies (Table 3 evaluate the contribution of each component. Introducing unsmoothed spectral regularization (LcE w/ CSpectral w/o W) improves both segmen- tation and calibration metrics over the baseline, confirming the benefit of frequency/domain analysis. However, the gains in boundary/sensitive metries (HD95, ASD) are modest, suggesting that instan- taneous spectral feedback is noisy. Our full method, which adds temporal smoothing of the power spectrum (CCr. w/ LSpectral), yields substantial improvements across all metrics. This demonstrates that stabilizing the spectral target is crucial for achieving superior segmentation accuracy and robust calibration.
CONCLUSION
In this work, introduced frequency-aware calibration framework address the persistent chal- lenge of confidence miscalibration in medical image segmentation. By analyzing model uncertainty through the lens of frequency domain behavior, we identified spectral bias and confidence saturation as two fundamental causes of miscalibration. Our method combines spectral entropy regularization, which promotes balanced frequency spectrum and increases overall spectral power, with a tempo- ral spectral smoothing module that stabilizes frequency- -iiee statistics across training batches. This joint design enables the model to more accurately calibrate the predictions of both figgufrry boundary and low- freequnqyccy structure. Experiments across six public datasets and multiple seg- mentation architectures confirm that our approach consistently improves calibration quality without degrading segmentation performance. These results demonstrate the potential of frequency domain calibration as a robust foundation for developing more reliable and trustworthy medical image seg- mentation systems.

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ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (No. 62571054).
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A APPENDIX
This appendix provides supplementary materials support the main manuscript. We offer more detailed interpretation of the multi-dimensional performance comparison and a comprehensive sen- sitivity analysis of our method's key hyperparameters. statement regarding the use of Large Language Models (LLMs) in preparing this manuscript is provided in Section A.1
A.1 STATEMENT ON LLM USAGE
In accordance with conference guidelines, we disclose the use Large Language Model (LLM) during the preparation of this manuscript. The LLM was employed exclusively for copyediting to improve the clarity, conciseness, and grammatical correctness of the text. All scientific contribu- innludinn research idcation, methodological design, experimental setup, data analysis, and interpretation of results-wee were conducted entirely by the authors. The LLM did not generate scien- tific content insights. The authors have reviewed, edited, and assume full responsibility for the final content of this paper.
A.2 DATA PREPROCESSING
standard preprocessing pipeline was applied all medical image data to ensure consistency across datasets and stable model training. This pipeline was uniformly applied to all methods under com- parison to ensure a fair evaluation.
Image Resampling and Spacing Normalization: All images were resampled to a unified isotropic voxel spacing, defined as the median voxel spacing of the dataset. Trilinear interpolation was used for intensity images, whereas nearest-neighbor interpolation was applied to segmentation masks to preserve discrete label integrity.
Intensity Normalization: For CT images, Hounsfield Unit (HU) values were clipped to a clinically relevant range [-1000, 400] HU, followed by Z-score normalization (i.c., subtracting the mean and dividing by the standard deviation). For MRI data, Z-score normalization applied exclusively to foreground voxels (i.e., non-zero values) to prevent background regions from skewing the statistics.
During training, suite of data augmentation techniques employed to enhance model robustness and generalization, including gamma transformation, additive Gaussian noise, Gaussian blurring, and brightness adjustment.
Data Augmentation:
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Algorithm Frequency-Aware Calibration Training Procedure
Require: Model fe. training data loader D, loss weight X, window size W, number of frequency
bands K.
Ensure: Trained model parameters
1: Initialize model parameters 6.
2: Initialize historical spectral power buffer Shist +- D.
3: for each batch {zr, y in D do
4:
Forward Pass and Standard Segmentation Loss
5: f far)
Get logits, shape: (B, (B,,,,,HW)
6: LCE < CrossEntropyLLosic
7:
Per-Sample Spectral Analysis
8:
Initialize batch spectral loss LSpectral 4 0.
9:
Let Sharch be an empty list to store spectral vectors for the current batch. for 1,..., B do
10:
> Iterate over each sample in the batch Generate scalar confidence map from logits i Transform to frequency domain D Compute Power Spectral Density (PSD) (k)) be the spectral power vector for sample b.
2/ - max. 2b.e
12:
Fb + Shift(FFT3D(2.)
Eb, < 1F512
Let Sy = (S) .....
14:
for I,..., do
16:
S + E (un.wee Es(u,,ww)
D Aggregate power in frequency band
17:
end for Append Sp to Sbatch end for
19:
20:
Update Smoothed Spectral Profile and Target Entropy
21:
Sourch + 13 Σb=1 Spathh [b]
Average spectral power for the current batch Remove oldest entry from Spist-
22:
Append Stutch to Spist-
23:
if [Sisal W then
24:
25:
end if
26:
S
Es'es. S" P Normalize(S)
Compute smoothed spectral profile
Six
27:
Convert to probability distribution
28:
Harge ShannonEntropy((P
Compute target entropy
29:
// Compute Spectral Regularization Loss for the Batch
for .., do
31:
S6 + Sbuch [b]
Po Normalize (S.)
33:
Hample + ShannonEntropy (P,)
34:
loss; + (0, Harget sample )2
LSpectral LSpectral loss;
36:
end for
Espectral -- CSpectral
38:
// Update Model Parameters
39:
Liotal &- LCF + XLSppecral
40:
Update using gradients from Liotal-
41:
end for
A.3 THEORETICAL MOTIVATION
From Confidence Maps to 3D Signals. Our framework formulates the model's confidence map as a 3D signal. Given a 3D medical image, a segmentation model fe produces logits =(x) at each spatial location
RR3 A scalar confidence map, c(x), is derived from these logits (e.g., via the maximum logit value) to represent the model's spatial confidence distribution. The 3D Fourier Transform decomposes this signal into its constituent frequency components:
=(k)= = F((()) = //] c(x)e 12nk-
(11)
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where is the 3D frequency vector.
Spectral Signatures of Segmentation Quality, The Power Spectral Density (PSD), E(k) = [ē(k)),. quantifies the distribution of the signal's energy across frequencies. By Parseval's the- orem, the total energy is conserved between the spatial and frequency domains. Low-frequency components correspond to large, smooth structures in c(x), whereas high-frequency components capture sharp transitions and fine details. An effective model should produce confidence maps that smooth within homogeneous regions (low frequencies) but sharp at anatomical boundaries (high frequencies). A common failure mode, partieularly for over-confident models, is the suppression of feggferry detail, yielding overly smooth or "blob-like" predictions. This manifests as PSD pathologically concentrated in the low-frequency bands.
Spectral Entropy as an snformation-Thhoreee Regularizer. We employ spectral entropy to quan- tify the structural complexity of the confidence map. The frequency space is partitioned into K dis- joint bands {Ix / and the power in each band is defined as S = -KKET E(k)dk. Normalizing
these values yields probability distribution = { jk=1
where p(k) = 5(h) /, St) The
spectral entropy is the Shannon entropy of this distribution:
K
H(P) = Σ
p()) log P(N) +E)
(12)
This metric aligns with the Principle of Maximum Entropy, where higher-entropy distribution is more uniform and embodies fewer structural assumptions. Low spectral entropy indicates a degen- erate, now-information output (e.g., over-smoothed) characterized by an overly simplistic confidence structure.
Objective Corrective Regularizer. Our objective does not maximize entropy directly but instead acts as a corrective measure against spectral collapse. The loss, LSpectral x max (0, Hurget ssmptt)) )2, penalizes a sample only if its spectral entropy sample falls below a dynamic target H Haggot- This design theoretically motivated to enforce minimum level of structural complexity, thereby preventing the aforementioned failure mode without discouraging valid, spectrally rich predictions. steers the model away from degenerate solutions characterized by overconfidence and excessive structural simplicity.
A.4 ALGORITHM PSEUDOCODE
Algorithm steps:
D details the proposed training procedure. Each training batch undergoes three main
1. Per-Sample Spectral Analysis: Following standard forward pass and cross-entropy loss computation, sealar confidence map is generated from the maximum logits for each sam- ple. This map is transformed into the frequency domain, and its PSD is aggregated into K frequency bands to produce a spectral power vector.
2. Dynamic Target Generation: Spectral power vectors from the current batch are averaged and appended historical buffer of size W. Averaging this buffer yields temporally smoothed spectral profile, providing stable estimate of the desired spectral characteristics. The Shannon entropy of this profile defines the dynamic target entropy for the current iteration.
3. Regularization and Optimization: The spectral entropy of each sample is compared against the dynamic target. A hinge-like loss penalizes samples with entropy below this target, thereby promoting more informative spectral distribution. The final objective is weighted sum of the cross-entropy loss and this spectral regularization loss.
A.S COMPREHENSIVE PERFORMANCE COMPARISON
Fig. 5 presents holistic performance evaluation, visualizing the trade-off between segmentation accuracy and uncertainty calibration. In this visualization, superior methods enclose a larger, more regular polygon. The ideal method would maximize this area, indicating superior performance
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BraT02020
ISeg2017
FLARE2021
ACDC
ATLAS2023
PROMISE2012
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SVES MALS
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SYES XhiL
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ECE
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000
0222
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SVLS SILLS
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SVLS XBLS
SCE
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CE
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Figure Multi-dimensional radar chart comparing eight methods across segmentation (DSC, HD95, ASD) and calibration (ECE, SCE, TACE) metries. A larger, more regular area indicates better overall performance.
across all metries. Our proposed method exhibits a notably balanced and expansive shape, demon- strating consistently high segmentation scores (high DSC, low HD95/ASD) and strong calibration performance (low ECE/SCE/TACE). In contrast, competing methods often display "spiky" profiles; for instance, some achieve a high DSC at the cost of significantly worse calibration metrics (e.g., ECE, TACE), indicating poor uncertainty estimation. This visual analysis underscores the primary strength of our approach: achieving robust balance between segmentation accuracy and uncer- tainty calibration, a critical requirement for clinical applications where both prediction correctness and confidence reliability are paramount.
A.6 HYPERPARAMETER SENSITIVITY ANALYSIS
sensitivity analysis of the key hyperparameters, revealing consistent trends the BraTS2020 and FLARE2021 datasets. The regularization weight À exhibits a clear trade- off: small values provide insufficient regularization (high ECE). whereas excessively large values degrade segmentation performance (low DSC). Optimal values (c.g.. X = 0.01 for BraTS2020, 0.05 for FLARE2021) balance both objectives effectively. Similarly, the temporal smoothing window W is crucial for a stable entropy target. A small window (W = 10) creates a noisy target, whereas large one (W = 100) adapts slowly to distributional shifts; moderate size (W E[25,75) achieves the best results. Finally, the number of frequency bands K determines the granularity of spectral analysis. Too few bands (K = 2) oversimplify the spectrum, while too many (K = 10) sensitive to noise. A value between 3 and 7 provides robust balance, consistent with related work Bo et al. (2025). These results confirm that the parameter response is stable and predictable, providing clear guidance for application to new datasets.
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Table 4: Sensitivity analysis of the key hyperparameters (A, W, on the BraTS2020 and FLARE2021 datasets.
BraTS2020
FLARE2021
Varying Hyperparameter
Value
DSC1
ECE]
DSCT
ECE!
0.001
0.870
0.0045
0.922
0.0028
0.871
0.0020
0.924
0.0015
(Fixed W
50,
0.872
0.0015
0.925
0.0008
0.050
0.871
0.0013
0,925
0.0007
0.100
0.865
0.0012
0.920
0.0008
0.870
0.0025
0,922
0.0014
25
0.871
0.0018
0,924
0.0010
W' (Fixed = 0.01,
50
0.872
0,0015
0,925
0.0008
75
0.872
0,0016
0,925
0.0009
100
0.871
0.0022
0.923
0.0013
0.870
0,0028
0,923
0.0016
0.871
0.0019
0.925
0.0008
K (Fixed À 0.01, 50)
0.872
0.0015
0.925
0.0009
0.871
0.0017
0.924
0.0011
0.870
0.0023
0.922
0.0015
DSC
HD95
ASD
SVLS
MbLS
CRaC
Ours
0.70
0.80
1.000.0
10.0
1.0
ECE
SCE
TАCE
SVLS
MbLS
CRaC
Ours
1.0
1.5
0.02
0.06
0.08
1e-2
Figure 6: Distribution analysis of segmentation (DSC) and calibration (ECE) metrics on the BraTS2020 dataset. Our method demonstrates improved mean performance and reduced variance compared to the baseline.
A.7 DISTRIBUTION ANALYSIS
Fig. iillustrates the performance distributions for the Dice Score (DSC) and Expected Calibration
Error (ECE). Our method's 's distributions exhibit two key characteristics: (1) rightward shift in mean for DSC and a leftward shift for ECE, indicating superior average performance, and (2) reduced variance (a narrower, taller peak). The latter is particularly important, as it demonstrates improved model robustness and reliability. The smaller spread signifies reduction in outlier predic- tions and catastrophic failures, where baseline model might perform poorly challenging cases. This enhanced consistency a direct result of our spectral regularization, which prevents the model from adopting overly simplistic, spectrally biased solutions and ensures reliable performance across the test population.
A.8 COMPREHENSIVE PERFORMANCE RANKING
This analysis evaluates the generalization capabilities of our method across multiple datasets and metrics. As shown Fig. 7 we aggregate performance ranks to provide a holistic comparison. For aggregation, ranks assigned each method every dataset-metric pair (rank 1 is best) and then
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Total Rankings
Rankings Across Different Metries
43
MbLS
120
MBLS
26
16
35
30
CRaC
126
CRaCC
18
24
17
168
CE
16
25
32
37
Ranking Value
20
153
SVLS-
25
28
30
21
23
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Total Rankings on Methods
Figure 7:
Aggregate ranking scores (lower is better). Right: Heatmap of individual metric ranks (darker is better). Our method achieves consistently high rank across diverse metrics and datasets.
Cross-dataset performance ranking. Left:
summed yield overall (lower is better). The left panel confirms method's superior aggregate rank. The heatmap on the right is more revealing: competing methods often exhibit spe- cialized performance, excelling certain metrics datasets while faltering others, suggesting potential overfitting to specific data characteristics. In contrast, our method achieves consistently strong performance across the board. This demonstrates that by operating the frequency domain, our regularizer targets fundamental aspect of the model's 's confidence representation rather than sataset-specific spatial statistics, leading more robust and holistically effective model.
A.9 VISUALIZING THE MITIGATION OF SPECTRAL BIAS
Confidenee High Erequency Power Spectius
the Confifence Map (CE)
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Figure 8: Analysis of
components on a BraTS2020 sample. (a) High-frequency
power from the baseline model's logits. (b) Confidence map reconstructed from (a), showing mis- placed high-confidence "hotspots." (c) Confidence difference map (Baseline Ours), where red indicates overconfidence corrected by our approach, correlating strongly with the hotspots in (b).
This analysis provides direct visual link between the theoretical motivation of spectral bias and method's corrective effect. We isolate the high-frequency components from baseline model's logit output for a challenging sample. Applying an inverse Fourier transform to these compo- nents reveals their spatial manifestation: misplaced, high-confidence hotspots, demonstrating how
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Published as a conference paper at ICLR 2026
unchecked nigh-frequeney power can lead to erroneous predictions at complex boundaries (Fig. 81-b). The confidence difference map (Baseline - Ours) in Fig. B highlights regions where our method reduces overconfidence. The strong spatial correlation between these regions and the base- line's hotspots serves as direct evidence that our spectral regularization working as intended. successfully suppresses problematic high-frequency power, leading better-calibrated and more structurally coherent confidence maps, particularly in anatomically complex regions.
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Reviews:
[{"review_id": "PygM2AoPi4", "reviewer": "Reviewer_2Bao", "summary": "This paper investigates the problem of confidence miscalibration in medical image segmentation and provides a new perspective by analyzing it in the frequency domain. The authors identify two core causes—spectral bias (models’ preference for low-frequency components) and confidence saturation (loss of spectral power in confidence maps)—that contribute to overconfident predictions. To tackle these issues, the paper introduces a frequency-aware calibration framework combining spectral entropy regularization and power spectral smoothing. Experiments across six public datasets and multiple segmentation architectures demonstrate that the proposed method consistently improves calibration metrics while maintaining segmentation accuracy.", "questions": "N/A", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "Novel Perspective: The work provides an original frequency-domain interpretation of model miscalibration, which is rarely explored in medical image analysis.\n\nTheoretical Insight: The identification of spectral bias and confidence saturation as underlying causes is conceptually sound and empirically validated.\n\nMethodological Innovation: The proposed spectral entropy regularization and power spectral smoothing are well-motivated, simple to implement, and complementary.\n\nComprehensive Evaluation: Experiments on multiple datasets and architectures show consistent improvements in calibration without accuracy degradation.\n\nClinical Relevance: By enhancing uncertainty reliability, the approach contributes directly to improving trustworthiness in medical AI systems.", "weaknesses": "While the proposed frequency-aware calibration framework is conceptually interesting, several aspects require further clarification and discussion. The frequency-domain operations in this work are quite similar to those in [1][2], which also explore the distinction between low- and high-frequency components; however, the paper does not explicitly analyze or compare with these prior studies. Moreover, key training details are missing—particularly the batch size used and how it affects frequency statistics. Performing repeated frequency-domain transformations across multiple batches could introduce considerable computational overhead. The penalty minimization is said to promote a more balanced spectral distribution by transferring energy from dominant low-frequency to underrepresented high-frequency regions, but the paper does not explain how this spectral balance is quantitatively measured, nor whether it might degrade segmentation accuracy. Finally, in class-imbalanced scenarios (e.g., when certain anatomical categories have far more samples), it remains unclear whether the proposed approach retains its effectiveness.\n[1]Feng, Wei, et al. \"Unsupervised domain adaptation for medical image segmentation by selective entropy constraints and adaptive semantic alignment.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 1. 2023.\n[2]Chen, Guangyao, et al. \"Amplitude-phase recombination: Rethinking robustness of convolutional neural networks in frequency domain.\" Proceedings of the IEEE/CVF international conference on computer vision. 2021.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "uDHCfqp8yX", "reviewer": "Reviewer_dMRR", "summary": "This paper introduces a power spectral smoothing mechanism for calibrating segmentation models. Specifically, it proposes a spectral entropy regularisation to improves frequency balance in confidence maps, involving spectral decomposition, window smoothing, leading to better model calibration results.", "questions": "1) In Fig.1, why a lower confidence score at boundary indicates better calibrated outputs? Especially if this is for ground truth labels.\n2) Calibration is important for non-segmentation tasks, but how is this important for segmentation? One will have to set a threshold for the segmentation results to be useful, so the accuracy/IoU naturally becomes the focus.\n3) Is there any reason that in experiments Temperature scaling/Platt scaling and IoU is not report? Temperature scaling/Platt scaling may require validation set but since there are already so many hyper-parameters have been tuned this should be doable.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Handle the calibration task from the spectral domain is novel;\nThe paper is easy to follow.", "weaknesses": "1) Motivation is not solid;\n2) Too many sophisticated hyper-parameters to tune;\n3) Missing important baselines (Temperature scaling, Platt scaling) and metrics (IoU).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "60dqdz8lkL", "reviewer": "Reviewer_LwpE", "summary": "This paper addresses the critical problem of overconfidence in deep neural networks for medical image segmentation. The authors propose a novel approach that reframes model calibration from a frequency-domain perspective. They identify two primary causes of miscalibration: spectral bias, where models over-prioritize low-frequency components, and confidence saturation, where overconfidence leads to a general suppression of power spectral density (PSD).\n\nTo solve this, the paper introduces a frequency-aware calibration framework consisting of two main components:\n1. Spectral Entropy Regularization: A novel loss term that encourages a more balanced and informative frequency spectrum in the model's confidence maps (derived from logits).\n2. Power Spectral Smoothing: A temporal smoothing module that stabilizes the spectral statistics used to create a dynamic target for the regularization loss.\n\nThe authors conduct an extensive evaluation on six public medical imaging datasets and multiple segmentation architectures. Their results show that the proposed method significantly improves calibration metrics (ECE, SCE) while simultaneously maintaining or even improving segmentation accuracy (DSC, HD95).", "questions": "1. Could you please provide an analysis of the training-time overhead? For example, what is the percentage increase in training time per epoch when adding the proposed regularization framework compared to the standard cross-entropy baseline?\n\n2. The temporal smoothing uses a simple sliding window of size $W$. Did you consider using an Exponential Moving Average (EMA) instead? An EMA might offer a more flexible trade-off between stability and adaptability, especially in non-stationary settings where the \"target\" spectral profile might evolve.\n\n3. The method relies on the max-logit to create the confidence map. Have you experimented with other scalar representations of confidence, such as the predictive entropy of the softmax output? It would be interesting to see if its spectral properties provide a similar or complementary signal for regularization.\n\n4. The motivation in Figure 1 defines a \"well-calibrated\" boundary pixel as having $\\alpha=0.5$ (maximum uncertainty). This is intuitive for a binary foreground/background decision. How does this intuition translate to a multi-class boundary, for instance, the boundary between \"edema\" and \"enhancing tumor\" in the BraTS dataset (which has 4 classes)? Is the goal still maximum uncertainty, or is the ideal spectral signature more complex in this scenario?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper's primary strength is its highly original approach. Reframing the calibration problem through the lens of spectral bias and confidence saturation is a novel and insightful contribution. While frequency-domain methods exist, this appears to be the first work to build a coherent framework specifically for confidence calibration by regularizing the output's intrinsic spectral properties. The results are highly significant. The method achieves state-of-the-art calibration, showing massive and consistent improvements in ECE and SCE across all six datasets (Table 2).\n\n2. The technical quality of the submission is exceptionally high. The link between overconfidence and a suppressed, low-frequency-dominated PSD is clearly motivated and visualized (Fig. 1) . The methodology is also well-justified, including the sound rationale for operating on logits rather than saturated softmax probabilities. This technical rigor extends to the evaluation, which is both comprehensive and robust. The authors validate their method on six diverse datasets, compare it against five strong baselines, and use a full suite of segmentation and calibration metrics.\n\n3. Furthermore, the method's \"plug-and-play\" nature is convincingly demonstrated, showing consistent improvements across six different segmentation architectures, including U-Net, nnUNet, and SwinUNETR (Fig. 4) . The analysis is also thorough; the ablation study (Table 3) clearly isolates the contribution of each component, and the appendix provides further strong evidence (e.g., radar charts, rank heatmaps). Crucially, this work breaks the common accuracy-calibration trade-off, often improving segmentation performance while fixing calibration (Table 1)", "weaknesses": "1. The weaknesses are minor and do not undermine the contribution.\n\n2. The paper does not quantify the computational overhead of the proposed method. \n\n3. Calculating 3D FFTs, aggregating power, and managing a historical buffer for each batch introduces a non-trivial training cost compared to the baseline, and this information would be valuable for other researchers. Additionally, the entire spectral analysis relies on a scalar confidence map derived from the maximum logit value. \n\n4. This simplification discards information from other classes, and it remains unclear how this approach would scale to problems with many classes. \n\n5. While the sensitivity analysis for $K$ (the number of frequency bands) is good, the paper could benefit from a more qualitative discussion of why $K=5$ provides an optimal balance, perhaps by linking the bands to specific anatomical structures.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)