
\section{Introduction}
The remarkable advancements in deep learning have revolutionized numerous fields, largely propelled by the availability of labelled datasets \cite{karimiDeepLearningNoisy2020, zhangDisentanglingHumanError2020, garcia-garciaReviewDeepLearning2017}. However, the presence of label noise is a significant impediment to the generalizability of Deep Neural Networks (DNNs), as their immense capacity makes them prone to memorizing incorrect labels, which harms their ability to generalize to unseen data \cite{lienen2024mitigating, gonzalez-santoyoIdentifyingMitigatingLabel2025, schneider2024potential, schneider2023spml}. This problem is especially pronounced in medical image segmentation, where obtaining clean, pixel-level annotations is notoriously difficult and expensive, and where annotation errors can have direct clinical consequences \cite{karimiDeepLearningNoisy2020, zhangDisentanglingHumanError2020, xuAdvancesMedicalImage2024}. Training on such noisy labels leads to incorrect gradients, causing the model to learn erroneous patterns and fail in critical applications \cite{marcinkiewiczQuantitativeImpactLabel2019}.

To counteract label noise, a variety of robust learning methodologies have been developed, primarily for classification tasks. These include noise filtering techniques \cite{gonzalez-santoyoIdentifyingMitigatingLabel2025}, loss reweighting strategies \cite{karimiDeepLearningNoisy2020}, and curriculum learning \cite{lienen2024mitigating}. While promising, these methods often introduce computational complexity or require strong assumptions about the noise characteristics \cite{gonzalez-santoyoIdentifyingMitigatingLabel2025}. Among the explored directions, noise-robust loss functions are a compelling alternative due to their simplicity, efficiency, and model-agnostic nature \cite{staatsEnhancingNoiseRobustLosses2025}. By leveraging properties like boundedness \cite{zhang2018generalized} and symmetry \cite{wang2019symmetric}, they modify the optimization objective to inherently limit the influence of noisy examples and prevent overfitting \cite{toner2023label, ding2024improve}.

Despite these advances, a research gap remains for robust learning specifically in image segmentation, where existing methods often struggle to address the spatially-correlated inaccuracies inherent in annotation noise \cite{guoImbalancedMedicalImage2025, karimiDeepLearningNoisy2020}. In this paper, we propose to address this gap by adapting and generalizing the \textbf{abstention} mechanism, a powerful technique that has proven effective in mitigating label noise in classification \cite{karimiDeepLearningNoisy2020, thulasidasan2019combating, schneider2024informed}. The abstention mechanism empowers a DNN to abstain from making a prediction on confusing or unreliable samples by integrating an abstention option directly into the training process. Building upon the foundational Deep Abstaining Classifier (DAC) \cite{thulasidasan2019combating} and its extension, the Informed Deep Abstaining Classifier (IDAC) \cite{schneider2024informed}, this paper makes several contributions to advance noise-robust medical image segmentation:

\begin{itemize}
    \item \textbf{Adaptation of Abstention to Segmentation}: We investigate the applicability of the abstention mechanism to image segmentation by adapting the DAC and IDAC loss functions for this domain.
    \item \textbf{Enhanced and Generalized Abstention Definition}: Our contribution improves and generalizes abstention, incorporating an informed regularization term guided by estimated noise rates $\tilde\eta$ and a power-law-based $\alpha$ auto-tuning algorithm.   
    \item \textbf{Loss-Agnostic Integration and Novel Loss Functions}: We integrate the enhanced abstention mechanism with other loss functions, including Generalized Cross Entropy (GCE) \cite{zhang2018generalized}, Symmetric Cross Entropy (SCE) \cite{wang2019symmetric}, and Dice Loss \cite{milletari2016v}, introducing three loss functions: the Generalized Abstaining Classifier (GAC), the Symmetric Abstaining Classifier (SAC), and the Abstaining Dice Segmenter (ADS). ADS introduces architectural adaptations for class-wise abstention and class-specific noise rates $\tilde\eta_c$.  
    \item \textbf{Empirical Validation of Robustness and Versatility}: Through empirical evaluations and quantitative analysis (\figureref{fig:intro}) on medical image datasets (CaDIS \cite{grammatikopoulou2021cadis} and DSAD \cite{carstens2023dresden}) under varying noise levels, we show consistent superiority over non-abstaining baselines.  
\end{itemize}
The remainder of this paper reviews related work (\sectionref{sec:related}), details our proposed abstention framework and novel loss functions (\sectionref{sec:method}), outlines the experimental setup (\sectionref{sec:exp}), and presents a comprehensive evaluation of our results (\sectionref{sec:results}) before concluding in \sectionref{sec:conclusions}.

\begin{figure}[htbp]
    \figureconts
    {fig:intro}
    {\caption{The impact of our noise-robust abstention framework. On a CaDIS sample with 25\% label noise, the baseline Dice Loss (b) produces a noisy and inaccurate mask. In contrast, our proposed \textbf{Abstaining Dice Segmenter (ADS)} (c) yields a result that is visually cleaner and adheres more closely to the ground truth (a).}}
    {
    \subfigure[Ground Truth]{
    \label{fig:intro-gt}
    \includegraphics[width=0.25\textwidth]{samples/cadis-gt.png}
    }
    \subfigure[Dice]{
    \label{fig:intro-dice}
    \includegraphics[width=0.25\textwidth]{samples/cadis-dice.png}
    }
    \subfigure[\bfseries ADS]{
    \label{fig:intro-dads}
    \includegraphics[width=0.25\textwidth]{samples/cadis-ads.png}
    }
    }
\end{figure}