Fig. 2 | Scientific Reports

Fig. 2

From: Osteoporosis prediction from hand X-ray images using segmentation-for-classification and self-supervised learning

Fig. 2

Overview of the proposed uncertainty-aware segmentation framework. The model features a shared U-Net encoder and multiple decoder modules, each designed to capture a distinct mode of the segmentation distribution. For each decoder, stochasticity is introduced via a module-specific latent vector sampled from an isotropic Gaussian prior, which is transformed into feature-wise scale and bias terms before modulating the decoded feature maps. This Gaussian prior imposes no directional bias in the latent space, ensuring an unbiased representation of uncertainty. The resulting stochastic features are passed through \(1\times 1\) convolution layers to produce multiple plausible segmentation hypotheses. A routing function, operating on global encoder features, assigns input-dependent weights to each module’s output. The final predictive distribution is a weighted mixture of all module outputs, trained with an optimal transport-based loss to align the predicted and annotated segmentation distributions.

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