Extendingthe Applicability of Viewsheds in
Landscape Planning
Peter F. Fisher
Abstract There follows a summary of the proposed variants, and a re~h~
determination of the visible area or viewshedfrom a view of their sensitivity to database error. Finally, a discusviewing
point looking out on a landscope is a widely availa- sion of how these variants may be used to respond to the
ble function in a GIS. A reconsideration of the oueries which queries is presented.
ma; be made of the viewshed, however, reveal; that often
the function does not address them correctly. This has led to
the specification of alternative viewshed functions intended
to give flexible outcomes which can be used to respond to
the queries directly. The alternatives include the horizons
viewshed, the local offset viewshed, the global offset viewshed,
and reverse viewing versions of all three. Applications
of these alternative viewshed functions to answer queries
about the landscape and the view which the binary viewshed
is not able to respond to either precisely or flexibly are ex-
amined.
Introduction
The determination of the area visible from a location or locations
in the landscape is a process which landscape architects
have dealt with for many years (Smardon et al., 1986).
With the advent of computer processing of spatial information,
and the realization that elevation data can effectivelybe
held in digital form, visible area determination was an early
subject for algorithm development and implementation
(Travis, 1975; Yoeli, 1985).The function has since become
one of the standard operations available within commercial
geographic informati& systems (GIS) which are designed for
orocessine land-surface elevation data. There has been con-"
tinuing research interest in the visible area determination.
Topics have included optimization in selecting sites on the
basis of visibility (Lee,1991;DeFloriani et al., 1994a),influence
of database error (Felleman and Griffin, 1990; Fisher,
1991; Fisher, 1992),reliability of different algorithms
(Sorensen and Lanter, 1993; Fisher, 1993),and implementation
on parallel architectures (DeFlorianiet al., 1994b).
The visible area is determined by defining one location
as the viewing point and then calculating the line-of-sight to
every other point within the area of interest (the target
points). If the land surface rises above the line-of-sight,then
the target is out-of-sight,and otherwise it is in-sight. The result
is based on a Boolean concept of visibility and reported
as a binary field. Consideration of this binary Boolean image
reveals that it does not actually address the types of query
which is asked of it in many investigations. This revelation
has led to a reconsideration of visible area determination and
to the presentation of a set of variant algorithms. That reconsideration
has been published elsewhere (Fisher, 1994b;
Fisher, 1996),and is summarized below. The purpose of this
paper is to show that the application of the variants proposed
enables more precise responses to a range of queries.
The next section includes a review of the types of query
which are not answered by a standard binary viewshed.
Department of Geography, University of Leicester, Leicester
LEI 7RH, United Kingdom.
ProblematicQueries
A binary viewshed answers a basic query, namely, whether a
target location can be seen from the viewing point. Viewshed
analysis is widely used to assess the visual impact of construction
and to plan visible areas for amenity and routing.
In these applications, however, it is rarely sufficient to determine
the viewshed from one, or a set of, viewing locations.
Rather, it is usual that some ancillary property (related to the
line-of-sight)is really required, and the binary viewshed simply
provides an easily determined surrogate.
In locating a forest-fireobservation tower, for example
(Travis et al., 1975; Lee, 1991),the viewable area is not limited
to the area which is directly within lines-of-sightfrom
the tower, but rather the observer can effectively see a forest
fire where the ground surface is beyond the horizon so long
as the vertical differencebetween the ground and the line-ofsight
to the horizon is less than enough for the smoke to be
dispersed by the wind (Figure 1A; Mees, 1978).
Similarly, when determining the visual impact of a new
structure in the landscape, it is necessary to identify whether
the structure rises above the skyline or remains below it, not
whether either the ground surface at that location or even
the top of the structure is in- or out-of-view.The visual impact
of an object which is behind the horizon and completely
masked by the horizon is very different from one
which pierces the skyline, and the impact of a development
which is within the visible area is very different depending
on the degree to which it too pierces the skyline (Middleton,
1952). It is relatively easy to camouflage an object which has
a landscape as a background, as opposed to one which is silhouetted
against the sky (Figure lB), although some objects
can be well designed to avoid visual impact even if they are
backed by the sky. Also, when designing routes through terrain
with concern to visibility, it is essential to know
whether a location is on the skyline with respect to an observer
or not; such locations should probably be avoided.
Similarly, in landscape planning for recreation, locations
should be avoided if they entertain a view of an unsightly
object on the skyline. Furthermore, in archaeology, the visibility
of sites on the skyline is widely held to be of importance
for astronomical alignments, as well as territory
markers (Ruggles et al., 1993).
The standard viewshed algorithm determines the area
Photogrammetric Engineering & Remote Sensing,
Vol. 62, No. 11,November 1996, pp. 1297-1302.
0099-1112/96/6211-1297$3.00/0
0 1996 American Society for Photogrammetry
and Remote Sensing
A Forestfires
edge of edge of fire
viewable area viewable area
Reversing locations
out-of-view
Figure 2. Just because a viewer at one location
can see the ground surface at another location
does not mean that a viewer at the second location
could see the ground at the first.
B Development impact high developmentbeyond
developmentIn the viewshed the honzoncan stlll create
1-indicates a location is simply in-view;
2-indicates what is referred to here as a local horizon
(an intermediate horizon might be another name),
developmententirely
below the skyllne
which is, for example, the top of a landscape feature
gtves no Impact
ment in vlew but
such as a hill which is backed by more land surface;
es not nseabove 34s a global horizon (the skyline) where the landsurthe
skyline mayhave little
visual impact face is seen to meet the sky;
0-again is the area which is not visible.
Figure 1.Examples of situations in which the binary viewshed
will not yield useful results. The Local Offset Viewshed
If the target point is in-view, then the vertical offset (the vertical
height) between the land surface at the target location
which is visible from a particular viewing location. Fre- and the line-of-sightto the next local or global horizon in the
quently (as when planning a new structure, or exploring direction of the line-of-sightis reported as a positive number.
chaeoastronomy) we are actually interested in the area from If the target is out-of-sight,then the offset is reported as
which that location can be viewed, which is not equivalent a negative number which is the height between the land surto
the area which can be seen from the location, because the face at the target location and the line-of-sight to the previheight
of the object at the viewing point may well be differ- ous horizon in the direction of the line-of-sight.
ent from the height of the viewed object (Figure 2). Only if Any location which is on an horizon will have value 0
the heights of the viewer and the viewed are equal will the (Figure 3C).
area which is viewable from a location and the area from
which the location is visible be the same (Franklin and Ray, The Global OffsetViewshed
1994).Under any other circumstances the two are very likely If the target point is in-view, then a positive number is reto
be different, and although we may only be talking of the turned which is the vertical offset (the vertical height) bedifference
between the eye level of a human being and the tween the land surface at the target location and the
ground surface, it may make a significant difference in the line-of-sight to the global horizon in the direction of the linearea
determined. It is both interesting and disturbing to no- of-sight.
tice that the standard viewshed algorithm is actuaIly regu- If the target is out-of-sight,then the height between the
larly used to determine this area in studies of visual impact, land surface at the target location and the line-of-sightto the
for example, and that the option to determine the area- global horizon in the direction of the line-of-sight is reported
which-can-see, as opposed to the visible area (the area- as a negative number.
which-can-be-seen) is only implemented in some GIS, Any location which is on a Global Horizon will have
including, for example, the Visibility command in Arc Info value 0 (Figure 3D).
(ESRI, 1992),and the Vista command in Genacell (Genasys,
1993). ReverseViewing Variants
All the above four versions of the viewshed have a reverse
The AlternativeViewsheds variant. Rather than reporting on whether many target locaThree
alternative viewshed functions have been developed to tions can be seen from a single viewing point, as is the basis
address the shortcomings recognised above. These are re- of all the above, the visibility of a single target or viewed
viewed in this section, but detailed algorithms and imple- point from many viewing points is determined. As noted
mentation details as well as a detailed analysis of the above, the reverse binary viewshed can be determined in
sensitivity to error in the digital elevation model (DEM) are some commercial software, but it would appear that none of
reported by Fisher (1996). these other variants are currently available in any commercial
software.
The Binary Viewshed
The standard viewshed as it is implemented in the majority Error Modeling
of commercial software is the binary viewshed; a location Just as the binary viewshed is very sensitive to the accuracy
which is determined to be in-view is recorded as 1,while an of the digital recording of the elevations (Fisher, 1991;
area which is out-of-viewis 0 (Figure 3A). Fisher, 19921,so these variants are sensitive. Fisher (1996)
shows how it is actually possible to determine error-sensiThe
HorizonsViewshed tized versions of the above products. Using Monte Carlo simThe
horizons variant of the viewshed returns a four-way cat- ulation, as in the earlier work, it is possible to determine the
egorization of the visible area (Figure 3B): probability of a location being in-view, out-of-view, or on a
November 1996 PE&RS
. . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .
Figure 3. The coding scheme of variants of the viewshed.
In the upper part, a profile through the landscape is
shown while below a table gives the values which would
be recorded in each of the four viewshed variants: (A)
The Binary (Standard)viewshed, (B) the Horizons viewshed,
(C) the Local Offset Viewshed, and (D) the Global
Offset Viewshed. Radiating from the viewer are Lines of
Sight (LoS)to the three horizons along the profile shown.
Vertical lines above that profile show the positions of elevation
data (mid-pointsof pixels in the DEM for which visibility
is being determined),which correspond to columns
in the table. On each vertical line in the upper part, a refers
to the vertical height from the ground to the LoS
which passes through the horizon nearest the viewer, b
is the height between that LoS or the ground and the
LoS to the second horizon from the viewer, and c to
height between the LoS to the second or the ground and
third horizons.
Applications
Forest Fire Observation
As discussed above, and illustrated in Figure lA, the area
from which a forest fire is visible is larger than the binary
viewshed. Some amount of vertical offset from the line-ofsight
can be accepted because the smoke can be visible even
when the flames are not and the existence of smoke is a reliable
indicator of fire (Mees, 1978).For a particular geographic
location, a negative vertical offset from the
line-of-sightneeds to be defined and then the actual area
over which a forest fire is visible can be determined from the
local offset by recoding the values to give a new binary
viewshed (Figure 5a). The amount of the negative offset
would be based on the usual wind conditions, especially
when fires may be expected to start (a seasonal phenomenon),
and the amount of offset may be dependent on the
bearing from the observation point.
The mean estimates of the offsets determined in multiple
error simulations can be used to yield alternative versions of
this variant of the viewshed. The means of the estimates of
the local offsets are shown in Figure 5b, where the spatial
autocorrelation in the error fields is I = 0, and Figure 5c
shows the resulting area when I = 0.9 in the error fields. The
resulting viewsheds appear similar, but the former has a
much more speckled appearance due to the irregularity in
the noise fields used to generate it.
The mean and standard deviations of the estimate of the
offset may be used in combination to estimate the probable
area which would be visible. Thus, adding and subtracting
one standard deviation to the mean of the estimated offsets,
and applying the same threshold (-20 m) as above, yields
the areas with 15 percent, 50 percent, and 85 percent probability
(approximately + and - 1 standard deviation) of being
visible (Figure 5d).
Another version of the probabilistic model of the viewshed
with specific offset may also be derived by taking the
acceptable offsetfrom a horizon, but it would need to be delocal
or global horizon. Equally it is possible to generate a termined by generating and summing multiple versions of
mean estimate of the offset and a standard deviation of the the binary viewshed for multiple noisy DEMs. However, this
multiple estimates caused by the Monte Carlo simulation. A would need an investigator to redetermine the
complete error model requires reporting of the mean and viewshed from the DEM. Using the mean and standard deviastandard
deviation of positive, negative, and combined esti- tions of the estimated offsets that the area visible for
mates.
Details of this Study
To exemplify the applicability of these variants of the viewshed,
a small part of the Coweeta Basin, North Carolina was
studied. The dataset itself is a 100 by 100 subset of the UsGS
30-m resolution DEM derived from 1:24,000-scalequad sheet
(Figure4). A single viewing or viewed location is used in all
subsequent discussion and is shown by a cross in Figure 4.
The viewshed variants were all coded in Turbo Pascal 7.0
running on a Pentium-based PC compatible computer. As in
previous work, error simulation was achieved by drawing
random numbers from a normal distribution. The spatial autoconelation
in the error field has been shown to influence
several aspects of the viewshed and its appearance (Fisher,
1991; Fisher, 1992; Fisher, 1996). Spatial autocorrelation was
achieved, as in the previous work, with the variant of the algorithm
proposed by Goodchild (19801, with spatial autocorrelation
measured by Moran's I which varies horn
approximately -1to 1, where a value of just less than 0 represents
a completely disordered distribution and a value
tending to 1indicates that similar values are neighboring
(Goodchild, 1986).The IDRISI raster GIs package was used for
all post processing and display (Eastman, 1992)
PE&RS November 1996
I
rn
,4i#wnn 1;CBB
t+s8.s* rn
i ~ Q D m
II
I
-m
ma0 R
-m
.t
-*BOB m
It.
Figure 4. The digital elevation model of part of the Coweeta
Basin, North Carolina. The area covered is 3 km
square, and the viewing or viewed point is shown by a
small cross.
wI-oI-*IN
I"*...
0% II
15% II
I)% m
m I I
(dl
Flgure 5. (a)Those areas with more than -50 m local
offset derlved from the local offset viewshed; (b)those
areas with more than -50 m local offset In the mean of
20 realisations when the error field has I = 0; (c)as (b),
but when I = 0.9; and (d)the areas wlth 1 5 percent, 50
percent, and 85 percent probabllltles of belng wlthln a
-50-m local offset derlved from estimates of the mean
and standard deviations of the local offset, wlth I = 0.9.
any other offset can be rapidly determined without going
back to the viewshed determination.
It is not possible to choose among all these different versions
of the same viewshed product reliably. The only thing
to say for sure is that Figure 5d, with three different levels of
probability, contains the most information, and so is probably
the best for planning purposes.
PlanningVisual Impact
The visual impact of a new construction seems to be one of
the most widely quoted applications of visibility analysis. If
a new development is proposed at a location, then the viewshed
variants reviewed here give a powerful analytical potential
beyond the use of either the binary or reverse binary
viewsheds. The binary viewshed gives an idea of the area
which can be seen from the construction site. If the viewing
point is an existing building, or is an important scenic location,
then this is an important consideration. The local offset
shows the height the new construction can be at any location
before it pierces the horizon from the viewing point and so
the maximum height of the structure at any location to minimize
visual impact. Figure 6a shows the area where construction
of a feature over 10 m high might be banned if
consideration were being given to the area visible from the
test viewing point, because the structures would be higher
than the next local horizon, although the structures could be
in-view from the viewing location (values of + or - in
the local offset viewshed are included). With greater consideration
to the view, a proposed structure may only be allowed
to be visible if it is at a considerable distance from the
viewing point. Alternatively, less consideration may be given
to the visible area by only banning construction in areas
within + or - 10 m of the global horizon, where it would be
backed by the sky (Figure 6b).
If the viewing point is actually the potential construction
site (a more common situation),then the reverse viewsheds
are more useful in evaluating the visual impact. The locations
with values greater than 10 m in the reverse local offset
viewshed are shown in Figure 6c, and are the areas from
which the construction would impact the horizons.
A set of error analyses similar to those included in the
discussion of forest fire observation would be possible for results
presented in Figures 6.
The height to which a structure could be built at any location
without becoming visible from the viewing point may
also be determined from the offset viewsheds, and error estimates
may be determined. Therefore, it is possible to make
relatively precise statements of the areas which will not be
visible, or the amount of the structure which will be visible,
and so judge the impact of that part of the structure.
Frost Exposure
The distance to the global horizon (Figure 7) allows calculation
of exposure of locations to the sky and to frost hazards, something
not achievable from the binary viewshed. If the distance
is found from the viewing point to the global horizons in various
directions, and the average, maximum, and minimum values
can all be extracted, then the exposure may be calculated
(Dozier et al., 1981).Again, error statements are possible based
on the standard deviation of the offset estimates.
M-d-"LW II
* M W 0
Figure 6. (a)The areas wlth up to + or - 10-m offset from
any horizon are those where a structure 1 0 m hlgh would
be vislble against the background of further land or sky,
even where the ground at these locations is not visible; (b)
those areas with up to + or - 10-m offset from the global
horizon where a structure 10m hlgh would be visible
against the sky; and (c)the areas from which a 10-m high
structure at the vlewed point would back the sky.
November 1996 PE&RS
Wt*ld. 1
x*ke7,*m C3
Figure 7. The area within the global horizon upon which
exposure calculation may be based. The cross marks the
position of the viewing location.
Most
ConcealedObserver Positions
It is often the case that an observer needs to be placed such
that the observer has concealed visibility of a location. In
other words, the observer needs to see a target location, but
also need not be easily seen from it. Candidate locations for
this can be determined by taking the intersection of the area
which is in-view in the reverse binary viewshed and out-ofview
in the standard binary (Figure 8a). In these locations
the standing observer can see the target location, but when
lying on the ground a person standing at that location cannot
see the first person (Figure 3). These locations can be further
prioritized by examining the local offset at those locations,
the site with the highest local offset being the optimal viewing
location.
It is also possible to derive the probability that the locations
are in this category of being able to see when standing
but without being seen when lying down. The intersection of
the probable versions of the binary and reverse binary viewsheds
can be determined by the multiplication rule (assuming
for the sake of simplicity independence of the observations):
i.e.,
p(xA n B) = p(xA).p(xB) (1)
where p(x)is the probability of a location belonging to the
set of points A which can not be seen from the viewing
point, and B which can see it. Figure 8b shows the result of
this operation, and it is apparent that even when I = 0.9 the
pattern is very different from the analysis of binary viewsheds;
the locations with high probabilities do not necessarily
coincide with locations identified in the binary analysis,
and many more candidate locations are present, although
many of those have very low probabilities. Furthermore,
from this probabilistic version it is possible to derive the
path of least probability of being visible in approaching the
viewing point.
Conclusion
There is a very real and ever present risk that GIS users will
misunderstand the logic of the functions they use, and will
use those functions to answer queries for which they are not
designed. Such failures with respect to the viewshed have
motivated the current research, but they are present with respect
to other operations as well. The risks of this may not
Figure 8. (a)The intersection of binary and reverse binary
viewsheds, and (b)the intersection of the inverse of the
probable binary viewshed and the probable reverse binary
viewshed (where I = 0.9 in both error fields). The cross
marks the position of the viewed location. Locations from
which a person standing at the viewed point (Person 1)
can be seen, but where the ground the viewer (Person 2)
stands on cannot be seen by Person 1,and so Person 2
has the best opportunity to remain unobserved.
be sufficient to invalidate all analyses, but the resulting misapplication
may well cause a growing feeling of distrust
among users. That distrust will be to the detriment of the use
of GIS in particular and computer technology in general.
In the work presented here, variants of a basic GIs operation
have been summarized. It has been shown that the
viewshed, as it is implemented within most GIs, has a limited
suitability for the types of query it is frequently used to
answer. The variants improve greatly the analytical potential
of the viewshed operation, giving more appropriate answers
to complex queries, well beyond those which motivated the
research in the first place. Furthermore, not only do the variants
provide complete and precise responses to the queries,
the two offset variants also provide real number images of an
area which allow flexible interrogation and changes in parameters
of the query, without the need to re-calculate the
viewshed, a computationally complex and time consuming
process.
PE&RS November 1996
L
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I
-
B
The American Society for Photogrammetry and Remote Sensing
announces
16th Biennial Worksho~on Color Potogra~hy& Videography in Resource Assessment
WESWCO, TEXAS April 29-May 1, 1997
This workshop, following in the tradition of the previous
workshops, will provide an opportunity to share information
on and experience with application of photographic
and videographic remote sensing for assessing natural
resources. Emphasis will be toward, but is not limited to,
the following areas:
Plant Science Water Quality
Agricultural Crops Wetlands or Riparian
Range Management Vegetation
Forest Resources Geomorphology
Soils FisheriesIWildlife Habitat
Video and Digital Systems
Abstracts (250 words or less) due by 15 January 1997
Send abstracts to:
James H. Everitt
USDA, ARS
Remote Sensing Research Unit
2413 E. Highway 83
Weslaco, TX 78596-8344
Tel 210-969-4824; fax 210-969-4893
j-everitt@tamu.edu
Acceptance letters will be mailed by
15 February 1997.
Proceedings Papers are due 1 May 1997.
November 1996 PE&RS