Interpolation methods for spatio-temporal geographic data

We consider spatio-temporal interpolation of geographic data using both the reduction method, which treats time as an independent dimension, and the extension method, which treats time as equivalent to a spatial dimension. We adopt both 2-D and 3-D shape functions from finite element methods for the spatio-temporal interpolation of 2-D spatial and 1-D temporal data sets. We also develop new 4-D shape functions and use them for the spatio-temporal interpolation of 3-D spatial and 1-D temporal data sets. Using an actual real estate data set with house prices, we compare these methods with other spatio-temporal interpolation methods based on inverse distance weighting and kriging. The comparison criteria include interpolation accuracy, error-proneness to time aggregation, invariance to scaling on the coordinate axes, and the type of constraints used in the representation of the interpolated data. Our experimental results show that the extension method based on shape functions is the most accurate and the overall best spatio-temporal interpolation method. New color rendering algorithms are also developed for the visualization of time slices of the interpolated spatio-temporal data. We show some visualization results of the real estate data set including the vertical profile of house prices.