Computational models for computing fuzzy cardinal directional relations between regions

In this paper, we investigate the deficiency of Goyal and Egenhofer’s method for modeling cardinal directional relations between simple regions and provide the computational model based on the concept of mathematical morphology, which can be a complement and refinement of Goyal and Egenhofer’s model for crisp regions. To the best of our knowledge, the cardinal directional relations between fuzzy regions have not been modeled. Based on fuzzy set theory, we extend Goyal and Egenhofer’s model to handle fuzziness and provide a computational model based on alpha-morphology, which combines fuzzy set theory and mathematical morphology, to refine the fuzzy cardinal directional relations. Then the computational problems are investigated. The definitions for the cardinal directions are not important and we aim to present the methodology and power of using fuzzy morphology to model directional relations. We also give an example of spatial configuration in 2-dimensional discrete space. The experiment results confirm the cognitive plausibility of our computational models.