Jones Craig K, Wang Guoqing, Yedavalli Vivek, Sair Haris
Johns Hopkins University, Malone Center for Engineering in Healthcare, Baltimore, Maryland, United States.
Johns Hopkins University, Radiology AI Lab, Baltimore, Maryland, United States.
J Med Imaging (Bellingham). 2022 May;9(3):034002. doi: 10.1117/1.JMI.9.3.034002. Epub 2022 Jun 8.
To derive a multinomial probability function and quantitative measures of the data and epistemic uncertainty as direct output of a 3D U-Net segmentation network. A set of T1 brain MRI images were downloaded from the Connectome Project and segmented using FMRIB's FAST algorithm to be used as ground truth. A 3D U-Net neural network was trained with sample sizes of 200, 500, and 898 T1 brain images using a loss function defined as the negative logarithm of the likelihood based on a derivation of the definition of the multinomial probability function. From this definition, the epistemic and aleatoric uncertainty equations were derived and used to quantify maps of the uncertainty along with tissue segmentations. Maps of the tissue segmentation along with the epistemic and aleatoric uncertainty, per voxel, are presented. The uncertainty decreased based on the increasing number of training data used to train the neural network. The neural network trained with 898 volumes resulted in uncertainty maps that were high primarily in the tissue boundary regions. The epistemic and aleatoric uncertainty were averaged over all test data (connectome and tumor separately), and the epistemic uncertainty showed a decreasing trend, as expected, with increasing numbers of data used to train the model. The aleatoric uncertainty showed a similar trend which was also expected as the aleatoric uncertainty is not expected to be as dependent on the number of training data. The derived uncertainty equations from a multinomial probability distribution were able to quantify the aleatoric and epistemic uncertainty per voxel and are applicable for all two-dimensional and three-dimensional neural networks.
为了推导多项式概率函数以及数据和认知不确定性的定量度量，将其作为3D U-Net分割网络的直接输出。从连接体项目下载了一组T1脑MRI图像，并使用FMRIB的FAST算法进行分割，用作地面真值。使用基于多项式概率函数定义推导的损失函数，以200、500和898个T1脑图像的样本大小训练3D U-Net神经网络。根据这个定义，推导了认知不确定性和随机不确定性方程，并用于量化不确定性图以及组织分割。展示了每个体素的组织分割图以及认知不确定性和随机不确定性。不确定性随着用于训练神经网络的训练数据数量的增加而降低。用898个体积训练的神经网络产生的不确定性图主要在组织边界区域较高。对所有测试数据（分别为连接体和肿瘤）的认知不确定性和随机不确定性进行平均，正如预期的那样，随着用于训练模型的数据数量增加，认知不确定性呈下降趋势。随机不确定性也呈现出类似的趋势，这也是预期的，因为随机不确定性预计不会像那样依赖于训练数据的数量。从多项式概率分布推导的不确定性方程能够量化每个体素的随机不确定性和认知不确定性，并且适用于所有二维和三维神经网络。
