On the improvement of combined fuzzy topological and directional relations information

Concept of combined extraction of topological and directional relations information developed by Zahzah et al. [1] by employing the Allen's temporal relations in 1D spatial domain was improved by Matsakis and Nikitenko [2]. This latter algorithm has high computational complexity due to its limitations of object approximation and segment fuzzification.In this paper, fuzzy Allen relations are used to define the fuzzy topological and directional relations information between different objects. Some extended results of Salamat and Zahzah [3] are discussed. Polygonal object approximation allows us to use fuzzy operators and this approach reduces computational complexity of the method for computing the combined topological and directional relations. To validate the method, some experiments are tested giving satisfactory and promising results. Affine transformation are depicted, these properties will be helpful for using the method in other areas of image analysis such as object tracking.

► Combines fuzzy topological and directional relations between objects pair.
► Uses Fuzzy aggregation operators for the treatment of segments of longitudinal section.
► Reduces time consuming from O(nMM) to O(nNlog(N)) where n;M;N are respectively directions, pixels and vertices of two polygons.
► Determines Affine transformations for fuzzy Allen relations, useful in object tracking algorithms.