The accurate estimation of predictive uncertainty carries importance in medical scenarios such as lung node segmentation. Unfortunately, most existing works on predictive uncertainty do not return calibrated uncertainty estimates, which could be used in practice. In this work we exploit multi-grader annotation variability as a source of 'groundtruth' aleatoric uncertainty, which can be treated as a target in a supervised learning problem. We combine this groundtruth uncertainty with a Probabilistic U-Net and test on the LIDC-IDRI lung nodule CT dataset and MICCAI2012 prostate MRI dataset. We find that we are able to improve predictive uncertainty estimates. We also find that we can improve sample accuracy and sample diversity.
In the Probabilistic U-Net @cite_1 , the approximate posterior distribution is given the form @math , where we have set @math . The hidden variables are thus activations @math dependent on the training data. A (conditional) prior over @math is given by a @math . To train this setup, the authors employ a variant of the ELBO with a @math -weight on the KL-penalty Again, @math represents the variational parameters to be optimized. Since at test time we do not have access to @math , we use the prior network and Monte Carlo sample in @math . The specific form of the likelihood @math can be found in the original paper @cite_1 . This method is known to produce very diverse samples, from which we could estimate aleatoric uncertainty. In this paper, we endow the Probabilistic U-Net with a mechanism to estimate epistemic uncertainty and extend this method yet further, such that the aleatoric uncertainty estimates are automatically calibrated to the training set.
@cite_1
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Many real-world vision problems suffer from inherent ambiguities. In clinical applications for example, it might not be clear from a CT scan alone which particular region is cancer tissue. Therefore a group of graders typically produces a set of diverse but plausible segmentations. We consider the task of learning a distribution over segmentations given an input. To this end we propose a generative segmentation model based on a combination of a U-Net with a conditional variational autoencoder that is capable of efficiently producing an unlimited number of plausible hypotheses. We show on a lung abnormalities segmentation task and on a Cityscapes segmentation task that our model reproduces the possible segmentation variants as well as the frequencies with which they occur, doing so significantly better than published approaches. These models could have a high impact in real-world applications, such as being used as clinical decision-making algorithms accounting for multiple plausible semantic segmentation hypotheses to provide possible diagnoses and recommend further actions to resolve the present ambiguities.