论文标题
使用离散的摩尔斯理论学习概率拓扑表示
Learning Probabilistic Topological Representations Using Discrete Morse Theory
论文作者
论文摘要
精确描述细尺度结构是一个非常重要但充满挑战的问题。现有方法将拓扑信息用作额外的培训损失，但最终会做出像素的预测。在本文中，我们提出了学习拓扑/结构表示的第一种基于深度学习的方法。我们使用离散的摩尔斯理论和持续的同源性来构建一个单参数的结构家族作为拓扑/结构表示空间。此外，我们学习了一个概率模型，该模型可以在这种拓扑/结构表示空间中执行推理任务。我们的方法生成真实的结构而不是像素图，从而在自动分割任务中获得更好的拓扑完整性。它还通过对结构和结构感知的不确定性的采样来促进半自动交互式注释/校对。
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose the first deep learning based method to learn topological/structural representations. We use discrete Morse theory and persistent homology to construct an one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks. It also facilitates semi-automatic interactive annotation/proofreading via the sampling of structures and structure-aware uncertainty.
