Date of Award


Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Science (MS)


Spatial Information Science and Engineering


Max J. Egenhofer

Second Committee Member

Kathleen Hornsby

Third Committee Member

M. Kate Beard-Tisdale


People conceptualize objects in an information space over different levels of details or granularities and shift among these granularities as necessary for the task at hand. Shifting among granularities is fundamental for understanding and reasoning about an information space. In general, shifting to a coarser granularity can improve one's understanding of a complex information space, whereas shifting to a more detailed granularity reveals information that is otherwise unknown. To arrive at a coarser granularity. objects must be generalized. There are multiple ways to perform generalization. Several generalization methods have been adopted from the abstraction processes that are intuitively carried out by people. Although, people seem to be able to carry out abstractions and generalize objects with ease. formalizing these generalization and shifts between them in an information system, such as geographic information system, still offers many challenges. A set of rules capturing multiple granularities of objects and the use of these granularities for enhanced reasoning and browsing is yet to be well researched. This thesis pursues an approach for arriving at multiple granularities of spatial objects based on the concept of coarsening. Coarsening refers to the process of transforming a representation of objects into a less detailed representation. The focus of this thesis is to develop a set of coarsening operators that are based on the objects' attributes, attribute values and relations with other objects, such as containment, connectivity, and nearness. for arriving at coarser or amalgamated objects. As a result. a set of four coarsening operators—group, group, compose, coexist, and filter are defined. A framework, called a granularity graph. is presented for modeling the application of coarsening operators iteratively to form amalgamated objects. A granularity graph can be used to browse through objects at different granularities, to retrieve objects that are at different granularities, and to examine how the granularities are related to each other. There can occur long sequences of operators between objects in the graph, which need to be simplified. Compositions of coarsening operators are derived to collapse or simplify the chain of operators. The semantics associated with objects amalgamations enable to determine correct results of the compositions of coarsening operators. The composition of operators enables to determine all the possible ways for arriving at a coarser granularity of objects from a set of objects. Capturing these different ways facilitates enhanced reasoning of how objects at multiple granularities are related to each other.