Method for Searching for Artificial Objects on Planetary Surfaces†
Mark J. Carlotto and Michael
The Analytic Sciences Corporation
55 Walkers Brook Drive
Reading, MA 01867 USA
The focus of the search for extra-terrestrial intelligence (SETI) has
been to look outside our solar system at radio frequencies for signs of intelligent
life. Such a strategy is consistent with current information which suggests
that it is unlikely that intelligent life could have evolved on the other
planets in our solar system. Our knowledge to date cannot, however, rule
out the possibility that extra-terrestrials or their probes may have reached
this solar system. If so, they may have altered planetary surfaces in ways
that are detectable through remote sensing. An alternative strategy is proposed
which involves extending SETI to include a systematic search for anomalous,
i.e., possible non-natural objects on planetary surfaces. An approach for
detecting anomalous objects in planetary imagery based on the fractal modeling
of terrain is described. Fractals have been successfully used to model a
wide range of physical and biological phenomena, including natural terrain.
This success is due, in part, to a property of fractals known as self-similarity,
i.e., fractals look the same, in some sense, across a range of scales or
resolutions. The anomaly detection technique described in this paper is based
on identifying areas in terrain that lack self-similarity. Preliminary results
of applying the technique to Viking orbiter imagery suggest that certain
objects on the Martian surface currently under investigation may not be natural.
Key Words: Search for Extraterrestrial Intelligence (SETI), Mars, Viking
orbiter, fractals, object detection, image processing.
The search for extra-terrestrial intelligence at radio frequencies began
with project Ozma  and has, as of yet, produced no evidence for their
existence. The success of such an endeavor requires that: 1) there are advanced
technological civilizations in the galaxy that are either communicating
with one another or trying to communicate with us, 2) we are able to detect
their signals, and 3) we will be able to decipher the message when we receive
The Drake equation  has been a starting point for speculating on the
number of technological civilizations in the galaxy. At one extreme, some
say that we are the only advanced civilization in the galaxy since if there
were others we would know about them. This is known as the Fermi Paradox
due to a question asked by Enrico Fermi in the 1940s. At the other extreme,
others have estimated upwards of billions of advanced technological civilizations
in the galaxy. Evidence in favor of either extreme is scarce. Estimates derived
from the Drake equation depend on parameter values which are obviously based
on our very limited experience in contacting extra-terrestrials (ETs). Freitas
 argues that the Fermi Paradox cannot be proven. In any case, the consensus
is that the number of advanced civilizations is somewhere in between the
two extremes and is sufficient to warrant some kind of search.
Many believe that the best channel for ET communications is at 1420 MHz,
the frequency at which atomic hydrogen radiates . Even with this as
a starting point, as the bandwidth of spectrum analyzers decreases and the
angular resolution of radiotelescopes increases, the number of frequencies
and directions that we must search will continue to increase. Most feel that
the lack of success is due to the very limited portion of the "search space"
covered to date. Others believe that we do not yet have the technology to
detect and decipher ET radio transmissions or may be looking for a signal
that is simply not there .
An alternative strategy has been put forth more recently that involves
searching for ET probes or artifacts. Freitas  has proposed that we
search for messenger probes in the vicinity of the earth. Based on the
argument that intelligent life has the natural tendency to expand into
and occupy space, and requires raw materials to support such expansion,
e.g., for building space colonies, Papagiannis  argues that if ETs are
in our solar system, they may be in the asteroid belt. Using arguments
similar to those based on Drake equation, Foster  estimates frequencies
of visitations by ETs or their messenger probes and goes on to suggest
the possibility that past encounters may have left behind artifacts or
indirect evidence (e.g., deranged planetary terrain).
This last idea is the point of departure for this paper, that there may
be artifacts that have already been imaged by probes such as the Viking Orbiter.
For example, there has been considerable interest recently in a collection
of unusual surface features in the Cydonia region of Mars [9-12]. Is there
a way to objectively assess these and other surface features so that future
missions such as the Mars Observer can gather more data?
In order to carry out an objective search for artificial features, detection
criteria must be established. Current SETI strategies have been criticized
on epistemological grounds, i.e., we are looking for what we think is out
there . Since we do not really know what we are looking for, it is not
possible to define in a direct way what is "artificial". However, one can
attempt to define what is natural and proceed to measure the "naturalness"
of unknown features. Artificial features are then identified as those farthest
from "natural" in some sense.
The contributions of this paper are: 1) to attempt to define objective
criteria for identifying possible artificial objects, 2) to describe a
technique based on fractal geometry for detecting such objects, 3) to present
some preliminary results of applying the technique to Viking orbiter imagery
that suggest that certain unusual Martian surface features may not be natural,
and 4) to outline a strategy for continuing the search as part of on-going
planetary exploration programs.
Natural Landscapes Using Fractal Geometry
Mandelbrot  has defined a fractal as an object whose Hausdorff-Besicovitch
dimension is strictly greater than its topological dimension. For example,
a fractal surface in 3-d space whose topological dimension is 2 would have
a fractal dimension between 2 and 3. Fractals have been shown to be good
models for diverse physical and biological phenomena such as the length
of coastlines, stream flow volume, terrain surface area, volume of blood
vessels and many more . A reason is that natural phenomena often possess
the property of being self-similar at different scales or resolutions. Self-similarity
is defined by the relation
r f (D)M(X)
where M(X) represents any measurable property of the fractal (e.g.,
surface area), X represents a scale of measurement of the metric property,
r is a scaling factor between zero and one, and
(D) is a simple function of the fractal dimension that depends
on the metric property. This equation states that the metric property computed
at a reduced scale of measurement is equivalent to scaling the metric property
of the fractal at the original scale. This implies that the metric property
obeys a power law function of the scale of measurement
M( X) =
where K is a constant.
For the purpose of modeling landscapes, a class of statistical fractals
known as fractional Brownian motion  has been used extensively. Fractional
Brownian surfaces may be described by their second order difference statistics,
BH (t ) - BH (t +
their surface area,
r 2 - D
or their power spectral density,
where D = 3 - H . Eq. 3 states that the variance
of the difference between any two points on the fractional Brownian surface
a distance T apart increases at a constant power of the distance (since
0 < H < 1; Eq. 4 states that the surface area decreases as a
constant power of the scale (since 2 < D < 3); Eq. 5 states
that the power spectral density (power per unit frequency) varies as a power
of the spatial frequency.
Mark and Aronson  analyzed 17 topographic data sets in the United
States using variograms which plot variance versus distance as defined in
Eq. 3. They found that most of the data sets could not adequately be characterized
by a single fractal dimension, i.e., the logarithm of the variance was
not linearly related to the logarithm of the distance over all distances
or scales. Rather, the behavior of topography tended to be divided into
scale ranges. Over small scales (< 0.6 km) many of the surfaces could
be modeled as fractional Brownian surfaces with D around 2.2 - 2.3.
Over larger scales, higher dimensions around 2.75 were noted while at still
larger scales many surfaces exhibited periodicities. A similar result was
noted by Clarke  who suggests that a combination of fractals, to model
local behavior, and Fourier methods, to model longer-term variations, be
used to describe topography. Locally, at least, fractals seem to be good
models for topography. Clarke goes on to suggest that on planets like Mars
where the types of processes that shape terrain over larger scales on Earth
are for the most part absent, fractals may be adequate by themselves. For
example, Woronow  shows that fractals can be used for classifying certain
kinds of large scale Martian impact craters.
The above suggests a reason why the generation of realistic synthetic
terrain using fractional Brownian motion has been so successful as demonstrated
by Voss  and by Fournier et al . Fig. 1 is
a 3-d plot of a synthetic terrain surface (D = 2.1) produced by Voss'
method for generating fractional Brownian surfaces using discrete Fourier
synthesis. The method is based on passing the discrete Fourier transform
of a 2-d white Gaussian noise field through a linear filter with transfer
function proportional to 1/ (k 2 + l2
)4 - D where k and l are the spatial
frequencies in the x and y directions, and inverse transforming
the result. Fig. 2 shows several views of this synthetic
terrain surface. A Lambertian reflectance function was used to first create
a shaded rendition of the terrain surface (left). The sun is south (solar
0 = 180°) at a zenith angle
0 = 45°. An oblique view was then generated
by viewing the shaded rendition mapped onto the elevation surface via an
oblique parallel projection (right). The image was computed from a view at
an azimuth angle
1 = 180° and a zenith angle
1 = 60°. (Rendering techniques are described
further in Appendix B.)
A major focus in artificial intelligence and machine vision has been
on the problem of recognizing instances of known objects in imagery (see,
for example Ballard and Brown .) The problem of recognizing an unknown
object as an instance of a known object or class of known objects involves
comparing features of the unknown object that can be computed from the
available data to those of known objects and selecting the object with
the best match.
The problem of recognizing unknown or unexpected objects, and the related
problem of detecting man-made objects embedded in natural terrain are fundamentally
different. One possible approach might be to try to determine the characteristics
that are common to all man-made objects. For example, one thinks of man-made
objects as having flat surfaces, sharp boundaries, and different brightness
from the background. Unfortunately, due to lighting conditions, imaging
geometry, and obscuration, the strong linear features that one might expect
are often not there.
An alternative approach based on modeling the background has recently
been proposed by Stein . His approach does not rely on an explicit model
for man-made objects (e.g., that they are rectangular in shape or brighter
than the background); rather, it is based on the observation that man-made
objects tend not to be self-similar in structure and so fractals should
be poor models for man-made objects. The method is based on estimating the
fractal dimension of the image intensity surface within a rectangular window
that is about the size of the objects one would like to detect, along with
the error that results from assuming fractal or self-similar behavior. The
technique used to estimate the fractal dimension involves computing the surface
area A(r) of the image intensity surface as a function of scale r
(see Appendix A). The metric properties of self-similar sets scale according
to a power law as noted in Eq. 4. The fractal dimension of the image intensity
surface is estimated by performing a linear regression of log A(r)
vs. logr . A measure of the degree to which the image intensity surface
lacks self-similarity e is estimated by summing the residuals of the linear
regression over scale, i.e.,
Surfaces that are not self-similar will not follow a power law relationship,
hence the residuals in Eq. 6 will be large and so e will be large.
An entire image is processed by repeating the above process on a pixel-by-pixel
basis within a "sliding window". Two images are produced: one is the local
fractal dimension D(x, y) , i.e., the fractal dimension of the portion
of the image intensity surface within the rectangular window centered at
(x,y); the other is the local fractal model-fit image
(x, y). Fig. 3 shows an image of military vehicles
embedded in natural terrain (a) along with the computed fractal dimension
image (b) and fractal model fit error image (c) for R = 10 scales
and a 21 by 21 window. For natural textures on earth, typical ranges can be
used for thresholding the fractal dimension image in order to generate detections.
At the upper end, terrestrial observations by Mark and Aronson  indicate
that fractal dimensions over short scales are less than about 2.5. At the
end, it has been observed that discontinuities in the image intensity
surface (e.g., due to shadows, object boundaries, and obscuration) produce
fractal dimension estimates that are below the topological dimension. Thus,
for detecting man-made objects, regions whose fractal dimension is not greater
than 2.0 and less than 2.5 are considered anomalous.
The fractal model fit is another independent measure of anomalous behavior.
Unfortunately, since the fractal model fit error is a relative measure,
absolute thresholds do not exist. If the relative frequency of occurrence
of man-made objects is small however, the model fit image can be thresholded
at a given false alarm rate (the probability that a man-made object may
be detected when one is not actually present). The detection result (d) in
Fig. 3 indicates possible man-made objects where the
fractal dimension is not between 2.0 and 2.5, and where the fractal model
fit error is greater than the 90th percentile. Three of four vehicles have
been detected with two "false alarms". Lack of data like that compiled by
Mark and Aronson limits the use of the fractal dimension for anomaly detection
on Mars. For the imagery processed in the next section, the fractal dimension
is used only to remove some object and shadow boundary effects by eliminating
regions whose fractal dimension is less than 2.0. The unthresholded fractal
model fit error image is used by itself in the remaining areas to indicate
the degree to which the data lacks the self-similar behavior of terrain on
a local basis.
Mars/Viking Orbiter Results
Fig. 4 is a mosaic of parts of three Viking frames: 35A72, 35A73,
and 35A74. A 1280 by 1024 pixel area is shown. This is the area in Cydonia
that is currently under investigation by a number of individuals [9-12].
The resolution is about 50 meters per pixel and the total area shown is approximately
3000 sq. km.
The result obtained by applying the anomaly detection technique to the
imagery over this area is shown in Fig. 5. The image
was produced by combining the fractal dimension and model fit images as
described in the previous section and shows the top four detections. R =
10 scales and a 21 by 21 pixel analysis window were used. The analysis window
thus covers an area about 1 sq. km and is near the upper scale limit for
self-similarity based on Mark and Aronson's results for terrestrial landscapes.
The "face"  was found to have the largest fractal model fit error which
implies that it is the least natural object in this area. Close-ups of the
face are shown in Fig. 6. A number of objects
in the "city"  also have large fractal model fit error. Close ups of
one of those objects, the "fortress"  are shown in Fig.
As was seen earlier in the example in Fig. 3 the
object detection technique may indicate the presence of a man-made object
when there is no such object (false alarms) and may fail to detect a man-made
object when one is there (missed detections). In Figs. 4
and 5, several features which appear to be natural seem
to exhibit a certain degree of non-fractal behavior. On the other hand, several
other unusual objects (e.g., the "cliff"  and the "D&M pyramid" )
do not appear to be anomalous by this technique.
As for the false alarms, it is certainly possible for nature to conspire
to produce a structure that is not self-similar over short scales. In fact,
this has been said of the face and the other nearby objects in Cydonia.
It is also noted that there are many features on Mars as well as on the
earth that exhibit aperiodic structure over short scales and are therefore
not locally fractal.
In regard to the missed detections, it was observed earlier that images
of fractal surfaces are also fractal. The converse is not necessary true
however. If a man-made object is illuminated so that its 3-d structure
does not induce significant shading and shadowing effects, structural information
will be lost in the image formation process. The image of the object will
look smoother than it really is and will thus appear less anomalous. In
other words, the ability to discriminate anomalous objects from the background
may be reduced at certain sun and viewing angles. This is illustrated in
Fig. 8 which shows two images of the face (Viking frames
35A72 and 70A13) and surrounding terrain. In 35A72 where the sun is more
than 15° lower than in 70A13, the ability to discriminate the face from
the background is much greater.
To verify that the technique does not detect a plethora of natural objects,
it was applied to the full Viking frame containing the above objects (35A72)
as well as three other nearby frames: 35A70, 35A71, and 35A73. The strength
of the strongest detection in 35A72, the "face", was 1.75, 1.88, and 4.31
times greater than the strongest detections in these three other frames,
respectively. It is noted that the size of these objects (1-2 km) precludes
a comparative analysis of terrestrial analogs (e.g., the Great Pyramid)
using imagery such as Landsat or SPOT. It is also worth noting that it would
be difficult, if not impossible to obtain images of facial profiles such
as those carved on Mt. Rushmore since they were not meant to be viewed from
Finally, a result from Viking frame 70A10 is presented that suggests
that there may be other objectson Mars worth investigating. Fig. 9 shows a 512 by 512 pixel region from 70A10. It
is over 100 km from the Cydonia region in Fig. 4. Also
shown in Fig. 9 is the fractal model fit error image
obtained with the same parameters used earlier. Ignoring the bright areas
caused by periodic noise in the data, a strong anomaly is present over an
unusual rectangular structure having a circular depression and a tapered
"access ramp". Nearby are a pyramidal object and sharp angular features
etched into the surrounding terrain.
This paper has presented criteria for identifying objects of possible
artificial origin on planetary surfaces, described a technique based on fractal
geometry for detecting such objects in planetary imagery, and presented some
preliminary results of applying the technique to Viking orbiter imagery.
The results presented in this paper suggest there are a number of surface
features on Mars that may not be natural. Although it is beyond the scope
of this paper to speculate on their origin, the results warrant further investigation.
In particular, higher resolution imagery must be collected by the planned
U.S. Mars Observer. More importantly, current thinking in the SETI community
[22-24] needs to be broadened to include a systematic search for ET artifacts
in our solar system. The criteria and techniques discussed in this paper
are a starting point for beginning an objective and systematic search for
ET artifacts. It is well within the state-of-the-art to process the current
Viking orbiter imagery archive (about 60,000 images). Estimated costs of
the order of ten million dollars to process existing planetary imagery and
create an automated system for screening future imagery is many orders of
magnitude less than some of the more ambitious radio search projects that
have been proposed.
To paraphrase Van Leeuwenhoek and Denton, perhaps they are not only "dancing
in our lenses" but were, or are, at our very doorstep.
The authors wish to thank Keith Hartt for the 3-d surface reconstructions
used in the paper.
A - Object Detection Algorithm
The object detection technique  is briefly presented here so that
others can independently verify the results presented in the paper. Given
an image x(i, j) a series of grayscale erosions and dilations are computed
. These are used to compute the volume of a covering of the image intensity
surface as a function of the scale parameter
(i, j) = tr (i, j) - br
To obtain an estimate of the surface area for an m x n rectangular
patch centered at (i, j) thecovering volume at each pixel over a window
of the same size is summed and divided by twice the scale parameter:
The fractal model is formally a linear regression model relating the
logarithm of the surface area estimates Ar (i,
j) to the logarithm of the scale parameter r
(i, j) =[2 - D(i, j)]log r + Er (i, j)
where Er (i, j) is the residual of the
linear fit at scale r (i.e. the difference between the actual value
of the logarithm of the surface area and the value predicted by the linear
model). D(i, j ) is the fractal dimension and is related to the slope
of the linear regression of log Ar (i, j)
onto log r . The fractal model fit error is the average of the squared
where R is the number of scales.
B - Image Formation Model
The anomaly detection technique tacitly assumes that the self-similar
structure of terrain is preserved through the imaging process. Pentland 
and Kube and Pentland  have analyzed the properties of images of fractal
surfaces and show that under certain conditions the image of a fractal Brownian
surface is also fractal Brownian, and hence, self-similar.
The simplified model of the image formation process shown in Fig. B1 was used to verify experimentally that images of
fractal surfaces are also fractal. The model ignores atmospheric effects and
sensor degradation. It assumes a single point source (the sun), a Lambertian
surface reflectance function, constant albedo, and an imaging sensor that
is far enough away for a parallel projection to hold. These assumptions appear
to be reasonable over small areas on Mars under limited illumination and
viewing conditions . A computational model of the image formation process
can be divided into two parts: 1) computing a shaded rendition of the surface,
and, 2) projecting the shaded surface onto the focal plane of the imaging
The shaded rendition i(x, y) is related to the elevation surface
z(x, y) by the reflectance map R( p, q) where the gradients p =
x and q =
y are the partial derivatives of the elevation in the x and y directions.
The reflectance map depends on the reflectance properties of the surface
and on the position of the sun. The use of the reflectance map in computing
shaded renditions of terrain is discussed by Horn . The location of the
sun in gradient space is (p0 ,q0
) where p0 = tan
0 , q0 = tan
0 are the azimuth and zenith angles of the sun.
The reflectance map for a Lambertian reflectance function is
Areas that face away from the sun, i.e., where the numerator is negative
are assigned zero reflectance.
It is assumed that the imaging sensor is far enough away for a parallel
projection to hold . For oblique viewing along the x axis, the point
(x,y) is mapped to the point (
1 is the zenith angle of the sensor. That is,
the surface is foreshortened along the viewing direction (in this case along
the x direction). For viewing from another azimuth, the surface is simply
rotated so that the line-of-sight is along the x axis. Since for
1 > 0, obscuration can occur, the hidden
surfaces must first be removed. Then, the shaded rendition i(x, y)
is mapped onto the image plane via Eq. B2 and intermediate pixel locations
are interpolated to obtain the projection i(
) . Fig. B2 summarizes the fractal properties of
images of the fractional Brownian surface shown in Fig.
1. The stability of the fractal dimension and model fit error over a
wide range of illumination and viewing conditions implies that images of
natural terrain are also fractal. It does not imply however that images
containing man-made objects will not also be self-similar. For example,
at low solar zenith angles where shading effects are reduced it may be difficult
to discriminate man-made objects from the natural background. This phenomenon
was noted in Section 4.
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Fig. 1 3-d plot
of synthetic terrain produced by Voss' method for generating fractional Brownian
surfaces (fractal dimension = 2.1)
Fig. 2 Orthographic
view of shaded rendition of synthetic terrain (left) and an oblique parallel
Fig. 3 Detection
of man-made objects. (a) Original image (upper left) has four military vehicles
embedded in a complex natural background. (b) Fractal dimension (upper right)
and (c) fractal model fit (lower left) images indicate that man-made objects
are different than the background. (d) Areas whose fractal dimension is outside
of range 2 < D < 2.5 and whose model fit is greater than 90%-ile are
shown (lower right).
Fig. 4 Mosaic
of Viking orbiter frames 35A72, 73, and 74. Landmarks shown are the "face",
the "city", the "D&M pyramid", and the "cliff".
Fig. 5 Detection
results show four largest anomalies over the "face" and within the "city".
Fig. 6 Close
ups of the "face": down-looking (left) and an oblique view near ground level
on the sunlit side (right).
Fig. 7 Close
ups of the "fortress" within the "city": down-looking (left) and an oblique
view looking into the inner space (right).
Fig. 8 Effect
of variable illumination on the detection of anomalous features. Part of
35A72 and fractal model fit error image (top left and right). Part of 70A13
and fractal model fit error image (bottom left and right). Note the difference
in the number of false alarms between the right top and bottom images. Square
"rings" are caused by noise in imagery.
Fig. 9 Analysis
of part of 70A10 frame (top). Fractal model fit error image indicates strong
anomaly over rectangular feature with central depression and v-shaped opening.
Note pyramidal object and linear features above and to the right.
Fig. B1 Image
formation model. Shaded rendition i(x,y) is a function of the reflectance
properties of the surface and the position of the light source. An oblique
view i(x',y') is generated by a parallel projection.
Fig. B2 Stability
of fractal dimension and model fit as a function of sun zenith (top) and
view zenith(bottom) angle.
† Corrected and revised
version of original paper published in the Journal of the British Interplanetary
Society, Vol. 43, pp 209-216, 1990.
† Descriptive terms
such as the "city" and "fortress" have been used by various investigators
for the sake of convenience and consistency. They do not imply an endorsement
of particular interpretations of these objects.