2004
Verti-
1000
on
tion
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
2. The difference between the hi and transferred lines
shows how the quality of the observer siting is af-
fected by using lo-res data. Even for a very poor 50m
resolution, the difference is only ten percent; siting
with lo-res elevations is poorer, as we would expect.
S REDUCING HORIZONTAL RESOLUTION
Next, we tested the effect of reducing the map’s horizon-
tal resolution, using bilinear interpolation in Matlab, from
1201 rows and columns to 600, 400, and 300. We tested
these combinations of (R,H): (80,10), (100,5), (100,10),
(100,30), (100,50), (300,10), (500,50). When transferring
each observer sited on the lo-res map back to the hi-res
map, if possible, we placed it in the the lower right corner
of the window of possible observers.
Figure 6 samples our observations, showing the joint visi-
bility index of 100 observers sited for R =100, H =5. (In
this and the reduced vertical resolution tests, we set FIND-
MAX to return 1000 top observers, and set the block size
so each block had 2 top observers). For this experiment,
the 100 observers jointly could see 70% of the map cell.
As the cell was gradually scaled down from 1201 x 1201
to 300 x 300, the computed joint visibility index changed
little, and often rose slightly. Perhaps the lo-res data has
fewer small hidden dips. However, when the observers
sited on the 300 x 300 cell were tested on the 1201 x 1201
data, a surprising phenomenon became apparent. The ob-
servers’ joint visibility index fell from 70% to 50%. Even
the 600 x 600 computation was 55% compared to 70%.
That is, how much a set of observers can see depends
strongly on the resolution at which that their siting is com-
puted. Even a factor of 2 reduction in linear resolution is
serious. This shows two different things:
l. Computing viewsheds with lo horizontal resolution
data is inaccurate.
2. Effective observer siting requires hi-res data.
We are now considering whether slightly perturbing the lo-
res observers' locations when they are transferred back to
the hi-res map might increase their joint visibility index.
6 CONCLUSIONS
We have demonstrated. multiple observer siting with in-
tervisibility, and experimented on multiple observer siting
w/o intervisibility while reducing the vertical and horizon-
tal resolution of the map cell.
We observed that even considerably reducing vertical res-
olution (from 0.1m to 10m) does not worsen multiple
observer siting. If this observation generalizes to other
datasets, then expensive efforts to maximize vertical res-
olution are not justified, at least for observer siting.
However, reducing the horizontal resolution had the oppo-
site effect. Siting observers on a cell with even a factor of
1201
2 lower resolution produced a noticeably poorer joint visi-
bility index, when measured on the hi-res data. That is, if
our observations generalize, visibility index computations
and observer sitings must be computed on map cells of the
highest horizontal resolution possible.
Finally, the experiments that we report here, and many
other unpublished tests, are possible only because of our
very efficient (in both time and space) siting toolkit, which
has easily handled map cells with up to 2000 x 2000 ele-
vation posts.
7 THE FUTURE
These experiments, and other experiments with our toolkit,
demonstrate the value of moving beyond mere viewshed
computation to multiple observer siting. Indeed often large
errors in viewshed computations do not significantly affect
the siting. This illuminates a great opportunity: how far
can this idea be pushed, to create faster, yet just as good,
applications of visibility?
Assorted small extensions are also possible, such as com-
putation of the joint viewshed for observers traveling along
specified routes, multiobserver siting so that each target is
covered by at least K observers, for K > 1, and trajectory
planning of an observer to minimize or maximize the total
viewshed.
Another area for investigation is the connectivity of either
the viewshed, or its complement. Indeed, it may be suf-
ficient for us to divide the cell into many separated small
hidden regions, which could be identified using the fast
connected component program described in Nagy et al.
(2001).
There is also the perennial question of how much informa-
tion content there is in the output, since the input dataset
is imprecise, and is sampled only at certain points. A most
useful, but quite difficult, problem is to determine what, if
anything, we know with certainty about the viewsheds and
observers for some cell. For example, given a set of ob-
servers, are there some regions in the cell that we know are
definitely visible, or definitely hidden?
Finally, the proper theoretical approach to this problem
would start with a formal model of random terrain, which
is usually formed by running water. E.g., local maxima are
common but local minima almost nonexistent. Then we
could at least start to ask questions about the number of
observers theoretically needed, as a function of the param-
eters. Until that happens, continued experiments will be
needed.
REFERENCES
Caldwell, D. R., Mineter, M. J., Dowers, S. and Gittings,
B. M., 2003. Analysis and visualization of visibility sur-
faces. In: Proceedings of the 7th International Confer-
ence on GeoComputation, http://www.geocomputation.
org/2003/, University of Southampton, UK.
