Morse theoretic concepts are today widely employed for the formal characterisation of surfaces and surface features. Although nowhere explicitly mentioned, several core concepts of surface metrology, such as the geometrical feature terms being specified in ISO 25178-2 and ISO 16610-85, are also closely related to Morse theory. The current lack of adequate formal definitions, however, implies that several inconsistencies and ambiguities can actually be found within the two standards. As a consequence, in the present paper the focus is laid on (a) the investigation of the interrelationships between Morse theory and the geometrical feature terms and (b) the presentation of some modifications of the existing definitions in order to eliminate the addressed ambiguities. Apart from the benefit of a consistent topological framework with respect to the definitions of the geometrical feature terms, the application of Morse theory would have the additional advantage that a powerful mathematical tool could be exploited in order to gain new insights into surface structures.

莫尔斯理论概念今天被广泛用于表面和表面特征的形式表征。尽管没有明确提及，但表面计量学的几个核心概念，例如几何特征术语ISO 25178-2 和 ISO 16610-85 中的规定也与莫尔斯理论密切相关。然而，目前缺乏适当的正式定义意味着在这两个标准中实际上可以发现一些不一致和模糊之处。因此，在本文中，重点放在 (a) 研究莫尔斯理论与几何特征术语之间的相互关系，以及 (b) 对现有定义进行一些修改以消除所解决的歧义。除了关于几何特征项定义的一致拓扑框架的好处外，莫尔斯理论的应用还有一个额外的好处，即可以利用强大的数学工具来获得对表面结构的新见解。