Fuzzy spatial objects and their dynamics

The determination of the spatial extent of geo-objects is generally approached through the boundaries or more precisely through the position of the boundary points. The analysis of the geometric uncertainty of the objects is therefore often based on accuracy models for the coordinates of these points. The accuracy evaluation in land surveying and photogrammetry generally refers to the mapping of crisp objects. In many other survey disciplines objects are mapped that are not crisp, in that case the geometric uncertainty is not only a matter of coordinate accuracy, but also a problem of object definition and thematic vagueness. It can not be handled by only a geometric approach such as epsilon band method. This paper proposes an approach to map the spatial extent of the objects and their uncertainties when objects are measured from field observation data. Beyond that, this paper presents a method of detecting the dynamics of these fuzzy objects from time series. They are determined by comparing their spatial extents at successive epochs. Simultaneously, the processes through which objects evolve are identified and are represented by several types of state transition, such as shift, merge, and split of objects. The proposed method is applied in a coastal geomorphologic study of a barrier island in The Netherlands.