Fuzzy adjacency languages and applications to spatial reasoning

Syntax-based and semantic image analysis appear as natural and significant fields for applying fuzzy theory, especially in geographical information systems and diagrammatic reasoning. This paper presents fuzzy visual languages as a formal mechanism to analyze images and spatial patterns. Images are described as fuzzy visual sentences using a new class of generative mechanisms, the fuzzy relational adjacency grammars, which provide an algorithmic tool for approximate reasoning. Previous contributions did not link fuzzy logic with fuzzy relations and fuzzy algebraic structures as in the approach presented here. Our approach is also novel in combining formal languages, algebra, and fuzzy theory. Its expressive power comes from considering spatial relations explicitly on a par with graphical elements to describe images beyond and above low-level primitive extraction. Our methods are applicable not only to off-line image processing but also to interactive applications