  The performance of the state-of-the-art image segmentation methods heavily
relies on the high-quality annotations, which are not easily affordable,
particularly for medical data. To alleviate this limitation, in this study, we
propose a weakly supervised image segmentation method based on a deep geodesic
prior. We hypothesize that integration of this prior information can reduce the
adverse effects of weak labels in segmentation accuracy. Our proposed algorithm
is based on a prior information, extracted from an auto-encoder, trained to map
objects geodesic maps to their corresponding binary maps. The obtained
information is then used as an extra term in the loss function of the
segmentor. In order to show efficacy of the proposed strategy, we have
experimented segmentation of cardiac substructures with clean and two levels of
noisy labels (L1, L2). Our experiments showed that the proposed algorithm
boosted the performance of baseline deep learning-based segmentation for both
clean and noisy labels by 4.4%, 4.6%(L1), and 6.3%(L2) in dice score,
respectively. We also showed that the proposed method was more robust in the
presence of high-level noise due to the existence of shape priors.
