Fuzzy spatial objects and their dynamics

Many monitoring activities of environmental processes deal with phenomena t hat are fuzzy. Their spatial description cannot be based on the geometry of their boundaries, because these cannot be identified. In fact, such phenom ena have an uncertain thematic description and that is often the reason why their spatial extent can only be determined with limited accuracy. We will therefore present in this paper a formalism for the description of objects without fixed boundaries, i.e., objects with a fuzzy spatial extent. A met hod based on this formalism will be developed for the extraction of fuzzy s patial object data from digital images or from field representations in a r aster format. This method can then be used for monitoring purposes when the spatial exten t of fuzzy objects are identified at different epochs; the dynamics of such objects can then be obtained from these time series. Several parameters wi ll be proposed to estimate the overlap of objects at successive epochs; wit h these parameters the state transitions of objects can be evaluated. Sever al types of state transition can be distinguished with these parameters suc h as shift, merge, and split of objects. These state transitions can then b e combined to form the processes through which the objects evolve over time . The proposed method is applied in a coastal geomorphologic study of a bar rier island in The Netherlands. (C) 2000 Elsevier Science B.V. All rights r eserved.