IEEE Trans Med Imaging. 2020 Jul;39(7):2316-2326. doi: 10.1109/TMI.2020.2968917. Epub 2020 Jan 23.
Multi-label probabilistic maps, a.k.a. probabilistic segmentations, parameterize a population of intimately co-existing anatomical shapes and are useful for various medical imaging applications, such as segmentation, anatomical atlases, shape analysis, and consensus generation. Existing methods to estimate probabilistic segmentations rely on ad hoc intermediate representations (e.g., average of Gaussian-smoothed label maps and smoothed signed distance maps) that do not necessarily conform to the underlying generative process. Generative modeling of such maps could help discover as well as aide in the statistical analysis of sub-groups in a population via clustering and mixture modeling techniques. In this paper, we propose an estimation of multi-label probabilistic maps and showcase their favorable performance for modeling anatomical shapes such as the left atrium of the human heart and brain structures. The proposed formulation relies on a constrained optimization in the natural parameter space of the exponential family form of categorical distributions. A smoothness prior provides generalizability in the model and helps achieve greater performance in modeling tasks for unseen samples. We demonstrate and compare the effectiveness of the proposed method for Bayesian image segmentation, multi-atlas segmentation, and shape-based clustering.
多标签概率图，也称为概率分割，参数化了一群密切共存的解剖形状，可用于各种医学成像应用，如分割、解剖图谱、形状分析和共识生成。现有的概率分割估计方法依赖于特定的中间表示形式（例如，高斯平滑标签图和平滑符号距离图的平均值），这些表示形式不一定符合潜在的生成过程。对这些地图进行生成建模可以帮助发现群体中的亚组，以及通过聚类和混合建模技术来辅助统计分析。在本文中，我们提出了一种多标签概率图的估计方法，并展示了它们在建模解剖形状（如人心的左心房和大脑结构）方面的良好性能。所提出的公式依赖于指数族形式的分类分布的自然参数空间中的约束优化。平滑先验为模型提供了可推广性，并有助于在对未见样本的建模任务中实现更好的性能。我们演示并比较了所提出的方法在贝叶斯图像分割、多图谱分割和基于形状的聚类方面的有效性。
