Zhou Zicong, Liao Guojun
Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd, Minhang District, Shanghai, Shanghai 200240, China.
Deparment of Mathematics, University of Texas at Arlington, 701 S. Nedderman Dr, Arlington, Texas 76010, USA.
Proc SPIE Int Soc Opt Eng. 2022 Feb-Mar;12032. doi: 10.1117/12.2611973. Epub 2022 Apr 4.
Medical image segmentation annotated by experts provides the labeled data sets for many scientific researches. However, due to the unevenly experienced backgrounds of the experts and limited numbers of patients with certain diseases or illnesses, not only do such labeled data sets have smaller samples but their quality and normality also can range in wide variabilities and be ambiguous. In practice, these segmentations are usually assigned to be the ground truths for the scientific studies, so it may undermine the trustworthiness of the resulting findings. Therefore, it is meaningful to consider how to give a more unified opinion of the annotations among different experts. In this paper, a novel approach to form normal distributions of segmentation is proposed based on multiple doctors' annotations for the same patient. The proposed approach is developed through the following steps: (1) utilize a framework of averaging images to construct an averaged annotation based on different given annotations; (2) determine the image registration deformations from the averaged annotation to the given annotations; (3) build a joint multivariate Gaussian distribution over the logorithm of Jacobian determinants and curls of the registration deformations; lastly, (4) simulate a normal distribution of segmentation by the joint Gaussian distribution of registration deformation. This work translates the problem of forming a normal distribution of the image segmentation into a problem of forming joint Gaussian distribution of image registration deformations, which the latter can be reasoned by Jacobian determinant (models local size of pixel cells) and curl (models local rotation of pixel cells) information. In the following sections, a detailed walk-through of the proposed approach is provided along with its analytical mathematics and numerical examples for its effectiveness. A synthetic example of 3 manually defined label image is made to show how to construct a mean label image, and an example of a real cancer image annotated by 3 doctors demonstrates the formation of the normal distribution and the effectiveness of the propose method.
由专家标注的医学图像分割为许多科学研究提供了标记数据集。然而，由于专家的经验背景参差不齐，以及患有某些特定疾病的患者数量有限，此类标记数据集不仅样本量较小，而且其质量和正态性也存在很大差异且模糊不清。在实践中，这些分割结果通常被指定为科学研究的基本事实，因此可能会削弱所得研究结果的可信度。因此，考虑如何在不同专家之间对标注给出更统一的意见是有意义的。本文基于对同一患者的多位医生标注，提出了一种形成分割正态分布的新方法。所提出的方法通过以下步骤开发：(1)利用图像平均框架，基于不同的给定标注构建平均标注；(2)确定从平均标注到给定标注的图像配准变形；(3)在雅可比行列式的对数和配准变形的旋度上建立联合多元高斯分布；最后，(4)通过配准变形的联合高斯分布模拟分割的正态分布。这项工作将形成图像分割正态分布的问题转化为形成图像配准变形联合高斯分布的问题，后者可以通过雅可比行列式（模拟像素单元的局部大小）和旋度（模拟像素单元的局部旋转）信息来推导。在接下来的章节中，将详细介绍所提出的方法，并给出其解析数学和数值示例以验证其有效性。给出了一个由3个手动定义的标签图像组成的合成示例，展示了如何构建平均标签图像，以及一个由3位医生标注的真实癌症图像示例，展示了正态分布的形成以及所提方法的有效性。
