Cluster dice: a simple and fast approach for instance-based semantic segmentation evaluation via many-to-many matching

In some medical image segmentation tasks, it is important to detect and segment several regions per class, e.g. different lesions, that may be of different sizes. This problem is similar to instance segmentation but is typically addressed as a semantic segmentation one followed by a post-processing step to separate the regions. It is key to develop segmentation performance metrics that account for these scenarios, which we coin as instance-sensitive segmentation, where appropriate segmentation of all instances matter. The gold standard performance metric for evaluating standard semantic segmentation tasks is the Dice Similarity Coefficient (DSC). Although its design inherently tackles class imbalance, the DSC fails to faithfully capture segmentation performance across several instances presenting with instance imbalance. Large instances indeed contribute to the majority of the DSC computation and lead to an inflated performance evaluation. Lesion-wise DSC (Lw-DSC) and CC-Metrics (CCDSC) are previous approaches which address this issue by calculating an individual DSC score for each ground truth instance. These metrics rely on specific segment matching choices to pair predicted and ground-truth instances. In this work, we demonstrate that no single metric can holistically evaluate instance imbalance. Further, we propose Cluster-Dice (C-DSC), one of the first segment matching schemes which allows the merging of ground truth instances. This simple framework is easy to define and implement, transparent, and highly efficient to allow for rapid evaluation, and can accommodate boundary-based metrics as well.