Data uncertainties, such as sensor noise or occlusions, 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. Latent density models can be utilized to address
this problem in image segmentation. 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 inhomogenous. As a
result, the effectiveness of gradient descent is inhibited and the model
becomes extremely sensitive to the localization of the latent space samples,
resulting in defective predictions. To address this, we present the Sinkhorn
PU-Net (SPU-Net), which uses the Sinkhorn Divergence to promote homogeneity
across all latent dimensions, effectively improving gradient-descent updates
and model robustness. Our results show that by applying this on public datasets
of various clinical segmentation problems, the SPU-Net receives up to 11%
performance gains compared against preceding latent variable models for
probabilistic segmentation on the Hungarian-Matched metric. The results
indicate that by encouraging a homogeneous latent space, one can significantly
improve latent density modeling for medical image segmentation.

通过在医学图像分割中鼓励一个均匀的潜在空间，可以显著提高潜在密度建模的效果。

医学影像中确定性不确定性量化的潜密度分割模型的研究与改进

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

Quantifying uncertainty in medical image segmentation applications is
essential, as it is often connected to vital decision-making. Compelling
attempts have been made in quantifying the uncertainty in image segmentation
architectures, e.g. to learn a density segmentation model conditioned on the
input image. Typical work in this field restricts these learnt densities to be
strictly Gaussian. In this paper, we propose to use a more flexible approach by
introducing Normalizing Flows (NFs), which enables the learnt densities to be
more complex and facilitate more accurate modeling for uncertainty. We prove
this hypothesis by adopting the Probabilistic U-Net and augmenting the
posterior density with an NF, allowing it to be more expressive. Our
qualitative as well as quantitative (GED and IoU) evaluations on the
multi-annotated and single-annotated LIDC-IDRI and Kvasir-SEG segmentation
datasets, respectively, show a clear improvement. This is mostly apparent in
the quantification of aleatoric uncertainty and the increased predictive
performance of up to 14 percent. This result strongly indicates that a more
flexible density model should be seriously considered in architectures that
attempt to capture segmentation ambiguity through density modeling. The benefit
of this improved modeling will increase human confidence in annotation and
segmentation, and enable eager adoption of the technology in practice.

使用正则化流 (NFs) 的方法来模型化分割模型中的不确定性，相较于严格使用高斯密度模型，可以让模型更具表现力，有效提高单标注和多标注分割数据集的分割性能，并明确提出了更灵活的密度模型应该在该领域内被认真考虑。

使用归一化流提高多注释医学图像分割中的不确定性度量

Improving Aleatoric Uncertainty Quantification in Multi-Annotated  Medical Image Segmentation with Normalizing Flows

The accurate estimation of predictive uncertainty carries importance in
medical scenarios such as lung node segmentation. Unfortunately, most existing
works on predictive uncertainty do not return calibrated uncertainty estimates,
which could be used in practice. In this work we exploit multi-grader
annotation variability as a source of 'groundtruth' aleatoric uncertainty,
which can be treated as a target in a supervised learning problem. We combine
this groundtruth uncertainty with a Probabilistic U-Net and test on the
LIDC-IDRI lung nodule CT dataset and MICCAI2012 prostate MRI dataset. We find
that we are able to improve predictive uncertainty estimates. We also find that
we can improve sample accuracy and sample diversity. In real-world
applications, our method could inform doctors about the confidence of the
segmentation results.

本文利用多个标注者的变异性作为 “地面真相” 不确定性的来源，将其与概率 U-Net 相结合，并在 LIDC-IDRI 的肺结节 CT 数据集和 MICCAI2012 前列腺 MRI 数据集上进行测试，发现能够以提高预测不确定性的估计，同时提高样本准确度和样本多样性。在实际应用中，该方法可以告诉医生有关分割结果的置信度。