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The Homeomorphism Extension Problem for Triangulations in Conflation

By Gillman, Daniel W.

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Book Id: WPLBN0000597907
Format Type: PDF eBook
File Size: 889,535 KB.
Reproduction Date: 2005
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Title: The Homeomorphism Extension Problem for Triangulations in Conflation  
Author: Gillman, Daniel W.
Volume:
Language: English
Subject: Government publications, Census., Census report
Collections: U.S. Census Bureau Collection
Historic
Publication Date:
Publisher: U.S. Census Bureau Department

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Gillman, D. W. (n.d.). The Homeomorphism Extension Problem for Triangulations in Conflation. Retrieved from http://self.gutenberg.org/


Description
Statistical Reference Document

Excerpt
Introduction: We discuss the problem of extending a one-to-one correspondence between two equinumerous finite sets of points in the plane to a specific type of homeomorphism between two topological spaces containing the sets. To understand the importance of the problem, some background information is necessary. The Census Bureau is developing a computer system for merging two digitized map files. The process of merging these files is known as conflation. Basically, conflation requires three fundamental steps: control point selection, triangulation, and rubbersheeting. Pairs of points, each pair consisting of a point from each map, are selected. The selected points of one map are then used as the vertices of a specific, well-defined triangulation on that map, and for each of the triangles of this triangulation we create a triangle on the corresponding set of vertices on the other map. The set of triangles on the second map need not form a triangulation there, but there is a one-to-one correspondence ...

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