IEEE Trans Med Imaging. 2023 Jan;42(1):3-14. doi: 10.1109/TMI.2022.3203309. Epub 2022 Dec 29.
Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.
多类心脏磁共振（CMR）图像分割旨在将数据分离为具有已知结构和配置的解剖成分。基于最流行的 CNN 的方法使用像素级损失函数进行优化，而忽略了特征解剖学的空间扩展特征。因此，尽管与地面实况具有很高的空间重叠，但推断的基于 CNN 的分割可能缺乏一致性，包括虚假的连通分量、空洞和空白。这些结果是不合理的，违反了预期的解剖拓扑结构。为了解决这个问题，已经提出了基于（单类）持久同调的损失函数来捕获全局解剖特征。我们的工作将这些方法扩展到多类分割任务中。通过构建所有类标签和类标签对的丰富拓扑描述，我们的损失函数使用基于 CNN 的后处理框架在分割拓扑方面做出了可预测且具有统计学意义的改进。我们还提出了（并提供）一种基于立方体复合物和并行执行的高效实现，首次能够在高分辨率 3D 数据中实际应用。我们在 2D 短轴和 3D 全心 CMR 分割上展示了我们的方法，在两个公开可用的数据集上对性能进行了详细和忠实的分析。
