Soft Dice Confidence: A Near-Optimal Confidence Estimator for Selective Prediction in Semantic Segmentation

In semantic segmentation, even state-of-the-art deep learning models fall short of the performance required in certain high-stakes applications such as medical image analysis. In these cases, performance can be improved by allowing a model to abstain from making predictions when confidence is low, an approach known as selective prediction. While well-known in the classification literature, selective prediction has been underexplored in the context of semantic segmentation. This paper tackles the problem by focusing on image-level abstention, which involves producing a single confidence estimate for the entire image, in contrast to previous approaches that focus on pixel-level uncertainty. Assuming the Dice coefficient as the evaluation metric for segmentation, two main contributions are provided in this paper: (i) In the case of known marginal posterior probabilities, we derive the optimal confidence estimator, which is observed to be intractable for typical image sizes. Then, an approximation computable in linear time, named Soft Dice Confidence (SDC), is proposed and proven to be tightly bounded to the optimal estimator. (ii) When only an estimate of the marginal posterior probabilities are known, we propose a plug-in version of the SDC and show it outperforms all previous methods, including those requiring additional tuning data. These findings are supported by experimental results on both synthetic data and real-world data from six medical imaging tasks, including out-of-distribution scenarios, positioning the SDC as a reliable and efficient tool for selective prediction in semantic segmentation.