Quantifying uncertainty in medical image segmentation applications is essential, as it is often connected to vital decision-making. Compelling attempts have been made in quantifying the uncertainty in image segmentation architectures, e.g. to learn a density segmentation model conditioned on the input image. Typical work in this field restricts these learnt densities to be strictly Gaussian. In this paper, we propose to use a more flexible approach by introducing Normalizing Flows (NFs), which enables the learnt densities to be more complex and facilitate more accurate modeling for uncertainty. We prove this hypothesis by adopting the Probabilistic U-Net and augmenting the posterior density with an NF, allowing it to be more expressive. Our qualitative as well as quantitative (GED and IoU) evaluations on the multi-annotated and single-annotated LIDC-IDRI and Kvasir-SEG segmentation datasets, respectively, show a clear improvement. This is mostly apparent in the quantification of aleatoric uncertainty and the increased predictive performance of up to 14 percent. This result strongly indicates that a more flexible density model should be seriously considered in architectures that attempt to capture segmentation ambiguity through density modeling. The benefit of this improved modeling will increase human confidence in annotation and segmentation, and enable eager adoption of the technology in practice.

Generative modelling has been a topic at the forefront of machine learning research for a substantial amount of time. With the recent success in the field of machine learning, especially in deep learning, there has been an increased interest in explainable and interpretable machine learning. The ability to model distributions and provide insight in the density estimation and exact data likelihood is an example of such a feature. Normalizing Flows (NFs), a relatively new research field of generative modelling, has received substantial attention since it is able to do exactly this at a relatively low cost whilst enabling competitive generative results. While the generative abilities of NFs are typically explored, we focus on exploring the data distribution modelling for Out-of-Distribution (OOD) detection. Using one of the state-of-the-art NF models, GLOW, we attempt to detect OOD examples in the ISIC dataset. We notice that this model under performs in conform related research. To improve the OOD detection, we explore the masking methods to inhibit co-adaptation of the coupling layers however find no substantial improvement. Furthermore, we utilize Wavelet Flow which uses wavelets that can filter particular frequency components, thus simplifying the modeling process to data-driven conditional wavelet coefficients instead of complete images. This enables us to efficiently model larger resolution images in the hopes that it would capture more relevant features for OOD. The paper that introduced Wavelet Flow mainly focuses on its ability of sampling high resolution images and did not treat OOD detection. We present the results and propose several ideas for improvement such as controlling frequency components, using different wavelets and using other state-of-the-art NF architectures.