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Singly‐ and Doubly‐Constrained Methods of Areal Interpolation for Vector‐based GIS
Author(s) -
Mrozinski Richard D.,
Cromley Robert G.
Publication year - 1999
Publication title -
transactions in gis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.721
H-Index - 63
eISSN - 1467-9671
pISSN - 1361-1682
DOI - 10.1111/1467-9671.00022
Subject(s) - overlay , interpolation (computer graphics) , partition (number theory) , computer science , class (philosophy) , multivariate interpolation , spatial analysis , data mining , geography , algorithm , mathematics , bilinear interpolation , remote sensing , computer graphics (images) , artificial intelligence , computer vision , combinatorics , animation , programming language
Traditionally, areal interpolation has referred to techniques for transferring attribute values from one partitioning of space to a different partition of space but this is only one of several situations that create the need for estimating unknown data values for areal units. This paper presents a categorization of four areal interpolation problems that includes the “missing” data problem, the traditional “alternative geography” problem, the overlay of a choropelth and an area‐class data layer, and the overlay of two choropleth data layers and demonstrates the relationship between the last three problems and general spatial interaction modelling. The “alternative geography” and overlay of choropleth and area‐class data layers mirrors a singly constrained spatial interaction model while the overlay of two choropleth layers is analogous to a doubly constrained interaction model. Iterative proportional fitting techniques with and without ancillary data are developed to solve these three classes of problems.