  Data uncertainties, such as sensor noise, occlusions or limitations in the
acquisition method can introduce irreducible ambiguities in images, which
result in varying, yet plausible, semantic hypotheses. In Machine Learning,
this ambiguity is commonly referred to as aleatoric uncertainty. In image
segmentation, latent density models can be utilized to address this problem.
The most popular approach is the Probabilistic U-Net (PU-Net), which uses
latent Normal densities to optimize the conditional data log-likelihood
Evidence Lower Bound. In this work, we demonstrate that the PU-Net latent space
is severely sparse and heavily under-utilized. To address this, we introduce
mutual information maximization and entropy-regularized Sinkhorn Divergence in
the latent space to promote homogeneity across all latent dimensions,
effectively improving gradient-descent updates and latent space
informativeness. Our results show that by applying this on public datasets of
various clinical segmentation problems, our proposed methodology receives up to
11% performance gains compared against preceding latent variable models for
probabilistic segmentation on the Hungarian-Matched Intersection over Union.
The results indicate that encouraging a homogeneous latent space significantly
improves latent density modeling for medical image segmentation.
