Spatial organization in 2D segmented images: Representation and recognition of primitive spatial relations

Object recognition and scene analysis tasks can be greatly enhanced when information about spatial organization in an image is available. Moreover, for recognition of complex objects a suitable representation of spatial relations between objects' components taking into account shape, size, orientation, etc., is required. This cannot be accomplished by reducing a region to one or a few representative points; instead the region as a whole must be treated. This paper presents a fuzzy logic approach to the representation and recognition of spatial relations between regions in a 2D image. The main source of information on spatial relations is the geometry of the regions in question and we argue that this is complex enough to cause ambiguity in spatial relations, and hence to warrant a fuzzy logic approach. The basic idea is to calculate the angles between the line connecting two points (one in each region) and the horizontal line, to construct a histogram of these angles, and then upon an interpretation of the histogram as a fuzzy set to match it with the fuzzy sets representing a vocabulary of spatial relations. Other expressions of the spatial information which may be context dependent can be easily obtained by adding context knowledge. Several examples are used to illustrate our approach.