Accurate segmentation of tubular, network-like structures, such as vessels,
neurons, or roads, is relevant to many fields of research. For such structures,
the topology is their most important characteristic; particularly preserving
connectedness: in the case of vascular networks, missing a connected vessel
entirely alters the blood-flow dynamics. We introduce a novel similarity
measure termed centerlineDice (short clDice), which is calculated on the
intersection of the segmentation masks and their (morphological) skeleta. We
theoretically prove that clDice guarantees topology preservation up to homotopy
equivalence for binary 2D and 3D segmentation. Extending this, we propose a
computationally efficient, differentiable loss function (soft-clDice) for
training arbitrary neural segmentation networks. We benchmark the soft-clDice
loss on five public datasets, including vessels, roads and neurons (2D and 3D).
Training on soft-clDice leads to segmentation with more accurate connectivity
information, higher graph similarity, and better volumetric scores.

介绍了一种新的相似度度量方法 centerlineDice 以及通过基于相似度度量的训练方法 soft-clDice 实现了对管状结构，如血管和神经元等的更精确分割和更好的连通性信息提取。

clDice - 一种针对管状结构分割的新型保拓扑性损失函数

clDice -- A Novel Topology-Preserving Loss Function for Tubular  Structure Segmentation

We present a hybrid method that performs the complete parcellation of the
cerebral cortex of an individual, based on the connectivity information of the
white matter fibers from a whole-brain tractography dataset. The method
consists of five steps, first intra-subject clustering is performed on the
brain tractography. The fibers that make up each cluster are then intersected
with the cortical mesh and then filtered to discard outliers. In addition, the
method resolves the overlapping between the different intersection regions
(sub-parcels) throughout the cortex efficiently. Finally, a post-processing is
done to achieve more uniform sub-parcels. The output is the complete labeling
of cortical mesh vertices, representing the different cortex sub-parcels, with
strong connections to other sub-parcels. We evaluated our method with measures
of brain connectivity such as functional segregation (clustering coefficient),
functional integration (characteristic path length) and small-world. Results in
five subjects from ARCHI database show a good individual cortical parcellation
for each one, composed of about 200 subparcels per hemisphere and complying
with these connectivity measures.

本文提出了一种基于脑白质纤维束连接信息对个体大脑皮层进行完整分区的混合方法，分为五个步骤，最终输出不同皮层的子区分标签。在功能分化、功能整合和小世界等方面，经过测试得出其效果良好。

基于个体白质纤维聚类的大脑皮层表面划分

Cortical surface parcellation based on intra-subject white matter fiber  clustering

We propose a novel approach for preserving topological structures of the
input space in latent representations of autoencoders. Using persistent
homology, a technique from topological data analysis, we calculate topological
signatures of both the input and latent space to derive a topological loss
term. Under weak theoretical assumptions, we construct this loss in a
differentiable manner, such that the encoding learns to retain multi-scale
connectivity information. We show that our approach is theoretically
well-founded and that it exhibits favourable latent representations on a
synthetic manifold as well as on real-world image data sets, while preserving
low reconstruction errors.

该研究提出一种新颖的方法，利用持久性同调技术，在自编码器的潜在表示中保留输入空间的拓扑结构，以保存多尺度的连接信息。实验表明这种方法在合成流形和现实世界图像数据集上表现出良好的潜在表示，并保留了低重构误差。