Formalizing fuzzy objects from uncertain classification results

Concepts of fuzzy objects have been put forward by various authors (Burroug h and Frank 1996) to represent objects with indeterminate boundaries. In mo st of these proposals the uncertainties in thematic aspects and the geometr ic aspects are treated separately. Furthermore little attention is paid to methods for object identification, whereas it is generally in this stage th at the uncertainty aspects of objects become manifest. When objects are to be extracted from image data then the uncertainty of image classes will dir ectly effect the uncertainty of the determination of the spatial extent of objects. Therefore a complete and formalized description of fuzzy objects i s needed to integrate these two aspects and analyse their mutual effects. T he syntax for fuzzy objects (Molenaar 1998), was developed as a generalizat ion of the formal syntax model for conventional crisp objects by incorporat ing uncertainties. This provides the basic framework for the approach prese nted in this paper. However, the model still needs further development in o rder to represent objects for different application contexts. Moreover, the model needs to be tested in practice. This paper proposes three fuzzy obje ct models to represent objects with fuzzy spatial extents for different sit uations. The Fuzzy-Fuzzy object ( FF-object) model represents objects that have an uncertain thematic description and an uncertain spatial extent, the se objects may spatially overlap each other. The Fuzzy-Crisp object ( FC-ob ject) model represents objects with an uncertain spatial extent but a deter mined thematic content and the Crisp-Fuzzy object (CF-object) model represe nts objects with a crisp boundary but uncertain content. The latter two mod els are suitable for representing fuzzy objects that are spatially disjoint . The procedure and criteria for identifying the conditional spatial extent and boundaries based upon fuzzy classification result are discussed and ar e formalized based upon the syntactic representation. The identification of objects by these models is illustrated by two cases: one from coastal geom orphology of Ameland, The Netherlands and one from land cover classificatio n of Hong Kong.