\section{Introduction}\label{sec:intro}

Digital pathology has rapidly expanded with the adoption of whole-slide imaging and large annotated datasets, enabling computational models to support routine diagnostic workflows. Cell-level quantification---including nucleus detection, instance segmentation, and phenotype classification---is central to tasks such as Ki-67 assessment, immune profiling, and tumour microenvironment analysis, yet remains time-consuming and variable when performed manually. Fast and reliable automated systems are therefore essential. Within this context, DualU-Net \cite{anglada2025dualunet}, developed inside the DigiPatICS project \cite{digipatics} from the Institut Català de la Salut (ICS) of Catalunya, was designed as a lightweight, single-pass architecture capable of accurate and efficient cell instance segmentation.

Beyond accuracy, reliability is equally crucial: \emph{a model should know what it does not know}. Uncertainty estimation is particularly important in digital pathology, where ambiguous morphology, heterogeneous staining, artefacts, and domain shifts routinely lead to failure cases that must be flagged for review. Crucially, uncertainty must be available \emph{at inference time} without the computational burden of ensembles or sampling-based methods. Existing approaches for uncertainty estimation often require multiple forward passes, making them impractical for high-throughput clinical pipelines. Evidential Deep Learning (EDL) offers a promising alternative, providing closed-form aleatoric, epistemic, and vacuity estimates from a single prediction. However, prior work has focused almost exclusively on semantic segmentation; no existing method provides interpretable, instance-level evidential uncertainty or applies EDL to multi-task cell instance segmentation. Furthermore, current uncertainty methods for instance segmentation remain complex and computationally demanding, underscoring the need for simpler and more principled formulations.

Up to the authors knowledge, this work introduces the first evidential approach to multi-task cell instance segmentation, enabling instance-level uncertainty derived from pixel-level evidence.
Our key contributions are: 
i) we extend DualU-Net with a Dirichlet-based evidential segmentation head and a multi-term loss, producing calibrated aleatoric, epistemic, and vacuity estimates at both pixel and instance level, while preserving the previous segmentation and classification performance; 
ii) we introduce simple, closed-form geometric uncertainty cues for the centroid decoder (peak and mass), enabling reliable detection-oriented uncertainty without auxiliary models or sampling; 
iii) through extensive evaluation on multi-tissue and multi-stain histopathology datasets, we show that the proposed evidential scheme matches or improves deep ensembles and Monte Carlo Dropout in error separation at a fraction of the computational cost, generalises across datasets without retuning, and yields interpretable uncertainty maps that clearly expose classification and detection issues relevant for digital pathology workflows.