PD Dr.-Ing. habil. Björn Gottfried

Spatial Patterns

My research is about the analysis of spatial patterns. Among others, this is of interest in vision and in spatiotemporal reasoning. Concerning the former my focus lies on shape analysis methods, concerning the latter I am investigating motion patterns.

From the methodological point of view I am devoted to the school of qualitative spatial representations. I am investigating how far one gets when describing spatial patterns as compact as possible.

Spatial patterns can in particular be analysed using the notion of positional-contrast. The idea is to decompose objects into parts and to describe the resulting patterns by positional relations. Then, two objects are distinguished by their differences in positional relations: they show a high positional-contrast. But similar objects decompose into similiar patterns, and consequently, show a low positional-contrast. One set of positional relations is shown in the following.

   

The diagram on the left hand side shows all possible 23 Bipartite Arrangement relations, arranged in their neighbourhood graph.

These relations have been introduced in (Gottfried 2004) and are the generalisation of their one-dimensional analogon introduced by J. F. Allen, “Maintaining knowledge about temporal intervals”, CACM 26 (11), 832-843, 1983.

Each relation describes how a line segment relates w.r.t. its position to another line segment. Provided that line segments are arranged intersection-free in the Euclidean plane those relations show all possibilities of pairwise qualitative arrangements.

   
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