Advancements in image segmentation play an integral role within the broad scope of Deep Learning-based Computer Vision. Furthermore, their widespread applicability in critical real-world tasks has resulted in challenges related to the reliability of such algorithms. Hence, uncertainty quantification has been extensively studied within this context, enabling the expression of model ignorance (epistemic uncertainty) or data ambiguity (aleatoric uncertainty) to prevent uninformed decision-making. Due to the rapid adoption of Convolutional Neural Network (CNN)-based segmentation models in high-stake applications, a substantial body of research has been published on this very topic, causing its swift expansion into a distinct field. This work provides a comprehensive overview of probabilistic segmentation, by discussing fundamental concepts of uncertainty quantification, governing advancements in the field as well as the application to various tasks. Moreover, literature on both types of uncertainties trace back to four key applications: (1) to quantify statistical inconsistencies in the annotation process due ambiguous images, (2) correlating prediction error with uncertainty, (3) expanding the model hypothesis space for better generalization, and (4) Active Learning. An extensive discussion follows that includes an overview of utilized datasets for each of the applications and evaluation of the available methods. We also highlight challenges related to architectures, uncertainty quantification methods, standardization and benchmarking, and finally end with recommendations for future work such as methods based on single forward passes and models that appropriately leverage volumetric data.

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