Title: Euler Characteristic Surfaces Show Chinese title

Title: 欧拉特征曲面

Abstract: We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random fields. The goal of this paper is to present the extension of using the Euler characteristic in higher-dimensional parameter spaces. While topological data analysis of higher-dimensional parameter spaces using stronger invariants such as homology continues to be the subject of intense research, Euler characteristic is more manageable theoretically and computationally, and this analysis can be seen as an important intermediary step in multi-parameter topological data analysis. We show the usefulness of the techniques using artificially generated examples, and a real-world application of detecting diabetic retinopathy in retinal images. Show Chinese abstract

Abstract: 我们研究在多参数拓扑数据分析中使用欧拉特征。欧拉特征是一个经典且被充分理解的拓扑不变量，在许多应用中都有出现，包括在随机场的背景下。本文的目标是展示在高维参数空间中使用欧拉特征的扩展。虽然使用更强的不变量如同调论对高维参数空间的拓扑数据分析仍然是激烈研究的主题，但欧拉特征在理论和计算上更易于处理，这种分析可以被视为多参数拓扑数据分析中的一个重要中间步骤。我们通过人工生成的例子展示了这些技术的有用性，并且还展示了一个现实世界的应用，即在视网膜图像中检测糖尿病视网膜病变。