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.

翻译：我们研究使用Euler特性进行多参数地形数据分析,Euler特性是一种古典的、非常清楚的表层变异性,出现在许多应用中,包括在随机字段中。本文的目的是介绍在高维参数空间使用Euler特性的延伸。虽然使用同质等较强变异性对高维参数空间进行表层数据分析仍然是密集研究的主题,但Euler特性在理论上和计算上都比较易于管理,这种分析可被视为多参数表层数据分析的一个重要中间步骤。我们展示了使用人工生成的例子的技术的实用性,以及在对视图像中检测糖尿病复古病的实际应用。