CQ-VAE: Coordinate Quantized VAE for Uncertainty Estimation with Application to Disk Shape Analysis from Lumbar Spine MRI Images

TL;DR

This paper introduces CQ-VAE, a discrete latent space generative model that captures ambiguity and uncertainty in medical image interpretation, demonstrated on lumbar spine MRI images.

Contribution

The paper presents CQ-VAE, a novel discrete latent space VAE with Gumbel-Softmax sampling for uncertainty estimation in medical imaging.

Findings

CQ-VAE effectively models shape variation and uncertainty in lumbar disk images.

The model provides probabilistic outputs alongside deterministic estimates.

Demonstrated improved uncertainty quantification in medical image analysis.

Abstract

Ambiguity is inevitable in medical images, which often results in different image interpretations (e.g. object boundaries or segmentation maps) from different human experts. Thus, a model that learns the ambiguity and outputs a probability distribution of the target, would be valuable for medical applications to assess the uncertainty of diagnosis. In this paper, we propose a powerful generative model to learn a representation of ambiguity and to generate probabilistic outputs. Our model, named Coordinate Quantization Variational Autoencoder (CQ-VAE) employs a discrete latent space with an internal discrete probability distribution by quantizing the coordinates of a continuous latent space. As a result, the output distribution from CQ-VAE is discrete. During training, Gumbel-Softmax sampling is used to enable backpropagation through the discrete latent space. A matching algorithm is used to establish the correspondence between model-generated samples and "ground-truth" samples, which makes a trade-off between the ability to generate new samples and the ability to represent training samples. Besides these probabilistic components to generate possible outputs, our model has a deterministic path to output the best estimation. We demonstrated our method on a lumbar disk image dataset, and the results show that our CQ-VAE can learn lumbar disk shape variation and uncertainty.