An interval approach to fuzzy surroundedness and fuzzy spatial relations

To describe a picture, spatial relations between image regions provide information concerning relative spatial position of two regions. This information could be for example: one region is left of another region. The definition of such entity is not easy in general and the manner in which spatial data is modeled affects important aspects of its use. So how to model a situation in which both the data and relationships are imprecise? The most useful characteristic of the human language is its ability to describe spatial relations. Giving a defined reference, one can describe an object as left or right of the reference. However, under the same description (left of the reference for example), objects could not have the same position which implies the use of the degree of spatial relations. We describe our methodology using examples introduced in (Gader, 1997; Wang and Keller, 1997). These examples were studied by other authors and were difficult to treat because of the complexity of defining degrees of spatial relations conform with the human perception. We also compare our approach with other approaches and introduce our concept for a GIS technology. Our methodology is particularly suitable for the nature of the geographical information. We present a new approach based on successive cuts of the image horizontally, vertically, or following an oblique direction.