F. Csillag et al., SAMPLING AND MAPPING OF HETEROGENEOUS SURFACES - MULTIRESOLUTION TILING ADJUSTED TO SPATIAL VARIABILITY, International journal of geographical information systems, 10(7), 1996, pp. 851-875
Mapping by sampling and prediction of local and regional values of two
-dimensional surfaces is a frequent, complex task in geographical info
rmation systems. This article describes a method for the approximation
of two-dimensional surfaces by optimizing sample size, arrangement an
d prediction accuracy simultaneously. First, a grid of an ancillary da
ta set is approximated by a quadtree to determine a predefined number
of homogeneous mapping units. This approximation is optimal in the sen
se of minimizing Kullback-divergence between the quadtree and the grid
of ancillary data. Then, samples are taken from each mapping unit. Th
e performance of this sampling has been tested against other sampling
strategies (regular and random) and found to be superior in reconstruc
ting the grid using three interpolation techniques (inverse squared Eu
clidean distance, kriging, and Thiessen-polygonization). Finally, the
discrepancy between the ancillary grid and the surface to be mapped is
modelled by different levels and spatial structures of noise. Concept
ually this method is advantageous in cases when sampling strata cannot
be well defined a priori and the spatial structure of the phenomenon
to be mapped is not known, but ancillary information (e.g., remotely-s
ensed data), corresponding to its spatial pattern, is available.