Investigating and Improving Latent Density Segmentation Models for Aleatoric Uncertainty Quantification in Medical Imaging

TL;DR

This work introduces 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 and indicates that encouraging a homogeneous latent space significantly improves latent density modeling for medical image segmentation.

Abstract

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.

Figures (8)

• Figure 1: Samples of the LIDC-IDRI dataset with significant inter-observer variability where (dis-)agreement in the ground-truth masks is clearly visible.
• Figure 2: Schematic drawing of the Sinkhorn Probabilistic U-Net (SPU-Net) training framework, which is an extension of the PU-Net introduced by Kohl et al.kohl2018probabilistic. The ground truth is denoted as $\mathbf{Y}$, the input image as $\mathbf{X}$, and the model prediction as $\mathbf{\hat{Y}}$. During testing, only the prior density $p_\psi (\mathbf{z}\vert \mathbf{x})$ is used to predict samples.
• Figure 3: Visualization of test set predictions. The mean and standard deviation is taken from 16 predictions for both PU-Net and our proposed model.
• Figure 4: Visualization of the latent vector mean and variances subject to various test images.
• Figure 5: Interpolation of the latent axis-aligned prior density for the LIDC-IDRI dataset (zoomed-in for viewing convenience).