A fuzzy model of directional relationships from the phi-descriptor

Abstract

Directional spatial relationships are a category of spatial relationships and have applications in the fields of image processing, geographic information systems, natural language processing, and robot navigation. They can be directly extracted from images or can be interpreted from a type of image descriptors called the relative position descriptors. Examples of relative position descriptors are the angle histogram, the force histogram, and the recently proposed phi-descriptor. So far, fuzzy models of directional spatial relationships from the angle histogram and force histograms have been proposed in the literature. These include the compatibility method, the aggregation method, and the method of effective forces. However, extraction of directional spatial relationships from the phi-descriptor has not been investigated. In this work, the first fuzzy model of directional spatial relationships from the phi-descriptor is presented. The model calculates the truth degree of a directional spatial proposition (e.g., “object A is to the right of object B”) about two objects from the average angle between the objects. Furthermore, it takes into account the angle which the argument object subtends the reference object when calculating the truth-degree. A novelty of the proposed model is the use of the cone concept in the calculation of the average direction and the handling of boundary cases. The model was tested on standard image data and the results were compared with those of the existing models. The performance is found to be satisfactory and the results meet users’ perceptions and expectations.