Qualitative similarity measures—The case of two-dimensional outlines

In this paper qualitative similarity measures are introduced. Depending on the underlying representation such similarity measures are based on specific qualitative distinctions which are frequently motivated by perceptual clear distinctions. Here, we discuss one such representation and show how it applies to different domains. In particular, qualitative methods are useful as soon as specific qualitative features can be defined for the purpose of characterising specific objects. Accordingly, we set two examples, namely for a domain of historical objects and for the geographic domain. Afterwards, however, we also demonstrate that our qualitative representation performs quite well when applied to a well-known test data set, without specifying any specific features. Instead, frequencies of qualitative relations are taken into account. The results indicate that qualitative measures not only relate to distinctions which can be easily comprehended by vision but that they are especially efficient in terms of runtime complexity, both issues being of particular importance in the case of image databases.