The Mathematica Journal
Volume 9, Issue 2


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Updating a Geographic Database
Leendert van Gastel
Harry Uitermark


When collecting new information--most of the time using a theodolite, which is a surveying instrument that measures bearings and distances--all observations are done in a redundant way. This redundancy makes it possible to check the observations for errors. But at the same time, due to the stochastic nature of measurements, small discrepancies are introduced. So before adding new information to the database, we check our measurements for errors and filter out the small discrepancies by least squares methods. A statistical test is performed to ensure the quality of the data: the covariance of the measurements should be within standardized bounds.

A second stage, called warping, fits this internal local computation into the external global world of the database. There are several methods in use for warping. We mention:

  • A similarity transformation, where the coefficients are determined by interpolation
  • A quadratic bilinear extension
  • An elastic rubber-sheet transformation [2]

At the Dutch Cadastre, we chose the last method because it deals best with the information already in the database. We will illustrate this later with an example.

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