Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation we consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.

拓扑和几何分割方法为详细的现场分析和可视化提供了强大的概念。然而，当涉及到需要高度精确的几何分割的定量分析时，有前途的理论与可用的计算方法之间存在很大差异。在本文中，我们比较和评估了各种分割方法，目的是识别和量化这些差异的程度。因此，我们专注于量子化学的一个应用：电子密度场的分析。它是一个可以通过实验测量或理论计算的标量。在评估中，我们考虑源自量子化学和计算拓扑领域的方法。我们将这些方法应用于一组晶体和分子的电荷密度。所以，我们将体积分割成原子区域，并推导出和比较这些区域的总电荷和偶极矩等定量测量。因此，我们得出结论，准确的几何确定对于正确分割和分析标量场至关重要，这里在电子密度场上进行了演示。