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Ambiguity is inevitable in medical images, which often results in differentimage interpretations (e.g. object boundaries or segmentation maps) fromdifferent human experts. Thus, a model that learns the ambiguity and outputs aprobability distribution of the target, would be valuable for medicalapplications to assess the uncertainty of diagnosis. In this paper, we proposea powerful generative model to learn a representation of ambiguity and togenerate probabilistic outputs. Our model, named Coordinate QuantizationVariational Autoencoder (CQ-VAE) employs a discrete latent space with aninternal discrete probability distribution by quantizing the coordinates of acontinuous latent space. As a result, the output distribution from CQ-VAE isdiscrete. During training, Gumbel-Softmax sampling is used to enablebackpropagation through the discrete latent space. A matching algorithm is usedto establish the correspondence between model-generated samples and"ground-truth" samples, which makes a trade-off between the ability to generatenew samples and the ability to represent training samples. Besides theseprobabilistic components to generate possible outputs, our model has adeterministic path to output the best estimation. We demonstrated our method ona lumbar disk image dataset, and the results show that our CQ-VAE can learnlumbar disk shape variation and uncertainty.

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