From Video to RCC8: Exploiting a Distance Based Semantics to Stabilise the Interpretation of Mereotopological Relations

Mereotopologies have traditionally been defined in terms of the intersection of point sets representing the regions in question. Whilst these semantic schemes work well for purely topological aspects, they do not give any semantic insight into the degree to which the different mereotopological relations hold. This paper explores this idea of a distance based interpretation for mereotopology. By introducing a distance measure between x and y, and for various Boolean combinations of x and y, we show that all the RCC8 relations can be distinguished. We then introduce a distance measure which combines these individual measures which we show reflect different paths through the RCC8 conceptual neighbourhood – i.e. the measure decreases/increases monotonically given certain monotonic transitions (such as one region expanding). There are several possible applications of this revised semantics; in the second half of the paper we explore one of these in some depth – the problem of abstracting mereotopological relations from noisy video data, such that the sequences of qualitative relations between pairs of objects do not suffer from “jitter”. We show how a Hidden Markov Model can exploit this distance based semantics to yield improved interpretation of video data at a qualitative level.