Fuzzy Spatial Objects Model

Spatial objects that are represented in a conventional GIS are generally considered to be crisp and represented by determinate boundaries. When objects change gradually and continuously over space, there are no crisp boundaries to differentiate them. They are called fuzzy objects, which have indeterminate spatial extent and boundaries. The concepts of fuzzy spatial objects have been proposed and applied in a coastal geomorphological ase of the Netherlands (Cheng, 1999). How to apply these concepts in other application domain (social & economical phenomena) needs further investigation although the concept doesn't exclude other application fields.

• Fuzzy objects without showing uncertainties
  
• Fuzzy objects showing uncertainties
  

Therefore, the objectives of this study are further application (in terms of cases) and development of the fuzzy object concepts (in terms of different data sources). The key issue is to define the objects of interests in the application domains and build the procedure to extract the object from testing data sources.

The following figures present the case study of extracting land cover types of Hong Kong from TM images. We apply the SMA (spectral mixture analysis) method to classify the image. We considered four types of land cover for image classification, man-made objects, bare-hill, vegetation and water. Through SMA, we quantify the areal fraction of these four type components at subpixel scales and interpret the fraction of individual component (end-member) as surrogates for the fuzzy membership function value.

• SMA classification result of land cover of Hong Kong. (End-member fraction of man-made, bare-hill, vegetation, water)

Based upon the fuzzy classification results and fuzzy object models, the core of FC-objects and FC-objects are formed, which are shown below.