In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and predicting multiple plausible hypotheses is of great interest in many applications, yet this ability is lacking in most current deep learning methods. In this paper, we introduce stochastic segmentation networks (SSNs), an efficient probabilistic method for modelling aleatoric uncertainty with any image segmentation network architecture. In contrast to approaches that produce pixel-wise estimates, SSNs model joint distributions over entire label maps and thus can generate multiple spatially coherent hypotheses for a single image. By using a low-rank multivariate normal distribution over the logit space to model the probability of the label map given the image, we obtain a spatially consistent probability distribution that can be efficiently computed by a neural network without any changes to the underlying architecture. We tested our method on the segmentation of real-world medical data, including lung nodules in 2D CT and brain tumours in 3D multimodal MRI scans. SSNs outperform state-of-the-art for modelling correlated uncertainty in ambiguous images while being much simpler, more flexible, and more efficient.

We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank parameterisation of previous methods and show that Flow-SSNs can estimate arbitrarily high-rank pixel-wise covariances without assuming the rank or storing the distributional parameters. Flow-SSNs are also more efficient to sample from than standard diffusion-based segmentation models, thanks to most of the model capacity being allocated to learning the base distribution of the flow, constituting an expressive prior. We apply Flow-SSNs to challenging medical imaging benchmarks and achieve state-of-the-art results. Code available: https://github.com/biomedia-mira/flow-ssn.

In image segmentation, there is often more than one plausible solution for a given input. In medical imaging, for example, experts will often disagree about the exact location of object boundaries. Estimating this inherent uncertainty and predicting multiple plausible hypotheses is of great interest in many applications, yet this ability is lacking in most current deep learning methods. In this paper, we introduce stochastic segmentation networks (SSNs), an efficient probabilistic method for modelling aleatoric uncertainty with any image segmentation network architecture. In contrast to approaches that produce pixel-wise estimates, SSNs model joint distributions over entire label maps and thus can generate multiple spatially coherent hypotheses for a single image.

Segmentation uncertainty models predict a distribution over plausible segmentations for a given input, which they learn from the annotator variation in the training set. However, in practice these annotations can differ systematically in the way they are generated, for example through the use of different labeling tools. This results in datasets that contain both data variability and differing label styles. In this paper, we demonstrate that applying state-of-the-art segmentation uncertainty models on such datasets can lead to model bias caused by the different label styles. We present an updated modelling objective conditioning on labeling style for aleatoric uncertainty estimation, and modify two state-of-the-art-architectures for segmentation uncertainty accordingly. We show with extensive experiments that this method reduces label style bias, while improving segmentation performance, increasing the applicability of segmentation uncertainty models in the wild. We curate two datasets, with annotations in different label styles, which we will make publicly available along with our code upon publication.