were obtained in all experiments. Lower bound estimates for Og can be
calculated from the transfer function of ES for a grid spacing equal to
the minimum grid spacing of PS. The composed transfer function can
easily be generated from the transfer function of ES as stored in a
library. The experiments with profiles provided sufficient evidence
that, if the limiting fidelity for the composed transfer function is
defined as above, the impact of the threshold, oa, depends on the mag-
nitude of the threshold and the type of input. To achieve sharper
estimates, o must be calibrated for every application.
4. EXODIUM
The accuracy of a DEM obtained by equispaced sampling depends on the
type of terrain, grid spacing, measuring error and interpolation method.
A DEM from progressive sampling is additionally influenced by the choice
of the threshold and the number of densification runs. The influence of
the threshold on accuracy (and efficiency of sampling) is more decisive
than the number of runs. Unfortunately, both influences depend on the
type of terrain.
The "transfer functions of PS" as introduced have a heuristic value, in
the first instance. H(v, T,r) indicates the risk in PS that some high
frequency components of terrain relief may not be captured. The sampling
strategy for surfaces must be designed such that this risk is minimized.
By analyzing the second differences in not only one direction, but along
x- and y-grid lines and areal densification where the threshold is ex-
ceeded (see /5/), finer sampling is also done in the x-direction even if
only the second difference in the y-direction is larger that T. The
reliability of PS is further safeguarded when supplementing PS with
selective sampling of distinct terrain irregularities (i.e., composite
sampling /7/).
The composed transfer function C (v,T,r) also has some potential in as-
sessing the accuracy of an established DEM. Considering profiles only,
upper bound estimates are obtained for the influence of sampling and
interpolation from the composed transfer function and the power spectrum
of the profile. The relevant question, however, is can the accuracy of a
surface-DEM be assessed by the estimate computed from C(v,T,r) and power
spectrum of a profile (or several profiles)?
Three synthetic terrain surfaces were used for an experimental inves-
tigation which permits separating the influences of sampling/
interpolation and random measuring error. In table 1, the actual
r.m.s.e. are given of the DEMs for PS with different minimum grid spa-
cings and threshold values and linear interpolation. The number of
densification runs was r - 3, an empirically-found good compromise be-
tween accuracy and efficiency considerations. The surface Tl can be
categorized as smooth, T5 as undulated, T6 as mountainous (see /10/).
The area covered is 8 km by 12 km, corresponding to a stereomodel from
1:60.000 wide angle photography. Tables 2 show the estimates obtained
from one arbitrary profile. In table 2a the estimates are given using a
limiting fidelity curve with o - 1/8, table 2b lists the estimates for
o * 1/10.
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