Formulation and test of a model of positional distortion fields Chris Funk, Kevin Curtin, Michael Goodchild, Dan Montello, UCSB; Val Noronha, Digital Geographic

The model Vector field  Measured positions x+  x, y+  y Vector field continuous and smooth –Kiiveri: function of coordinates –but function loses generality If  is known everywhere then distortion can be removed –variation in magnitude of  could be visualized

The data Street centerline files –multiple vendors, sources many different  Ambiguous messages about location if origin, destination have different databases –which street is (x,y) on? Applications in transportation, generalizes to other domains

Figure 1: Plot of a section of the two databases, superimposed on an interpolated field showing the magnitude of the distortion vector.

Obtaining a sample of  Match points between databases –easiest at nodes Provides a sample set of observations –poor in rural areas

Determining a complete  Interpolate a continuous field But what model to use for the surface? –Kiiveri - function of coordinates –spatial interpolation (e.g. Kriging) maximally smooth –piecewise with linear breaks mosaic of patches

Figure 2: Effect of a cliff on a linear feature (left); editing with a smooth line (right)

Why a mosaic of patches? Constant or linear or affine within each patch Breaks where there are no features –causes no cartographic offense Fits production methods –photogrammetric mosaic, edgematching of different sources

Clustering the error field Variogram of angular differences Ratio of areal dependence –compares variation within lag with predictions from variogram Cluster using RAD

Figure 3: Semivariogram of angular distortion values.

Figure 4: A plot of the RAD values associated with angular distortions.

Figure 5: Initial clustering based on RAD values.

Figure 6: Clustering using only high RAD values.

Conclusions Piecewise approach to modeling  Observable at points Identification of patches –piecewise constant Transportation application generalizes Errors highest where field is least observable