" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

Segmentation algorithms are prone to make topological errors on fine-scale struc-tures, eg,
broken connections. We propose a novel method that learns to segment with correct …

We address the problem of crowd localization, ie, the prediction of dots corresponding to
people in a crowded scene. Due to various challenges, a localization method is prone to …

Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …

Precision medicine aims to provide personalized care based on individual patient
characteristics, rather than guideline-directed therapies for groups of diseases or patient …

In the segmentation of fine-scale structures from natural and biomedical images, per-pixel
accuracy is not the only metric of concern. Topological correctness, such as vessel …

Local structural information can increase the adaptability of graph convolutional networks to
large graphs with heterogeneous topology. Existing methods only use relatively simplistic …

Deep neural networks are known to have security issues. One particular threat is the Trojan
attack. It occurs when the attackers stealthily manipulate the model's behavior through …

Existing generative adversarial networks (GANs) focus on generating realistic images based
on CNN-derived image features, but fail to preserve the structural properties of real images …

In recent years, algebraic topology and its modern development, the theory of persistent
homology, has shown great potential in graph representation learning. In this paper, based …