2 resultados para Geographic information science and geodesy

em DigitalCommons - The University of Maine Research


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The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

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Current research in the domain of geographic information science considers possibilities of including another dimension, time, which is generally missing to this point. Users interested in changes have few functions available to compare datasets of spatial configurations at different points in time. Such a comparison of spatial configurations requires large amounts of manual labor. An automatic derivation of changes would decrease amounts of manual labor. The thesis introduces a set of methods that allows for an automatic derivation of changes. These methods analyze identity and topological states of objects in snapshots and derive types of change for the specific configuration of data. The set of change types that can be computed by the methods presented includes continuous changes such as growing, shrinking, and moving of objects. For these continuous changes identity remains unchanged, while topological relations might be altered over time. Also discrete changes such as merging and splitting where both identity and topology are affected can be derived. Evaluation of the methods using a prototype application with simple examples suggests that the methods compute uniquely and correctly the type of change that applied in spatial scenarios captured in two snapshots.