n of the
resence.
e of the
. NOT
of pixels
remotely
ly if the
e of the
ites that
cs of the
1rements
Accord-
(4)
| identify
equation
?), which
ire inter-
case we
etric (x,
ues w of
spection)
es of (x,
y, z) which can be considered to be the means of the cor-
responding pure classes. Clearly we must perform a different
Hough transform for each band. Since x, y and z are lumi-
nances, they can take integer values in the range 0 to 255, so
we have a 3-D accumulator array 256 x 256 x 256. Instead
of searching exhaustively for all possible combinations of x, y
and z we can select three samples from three different sites
at a time. Thus instead of computing one parametric plane
for a given w, we solve a system of three equations similar
to equation (4) for the values of z, y and z. Then only the
corresponding cell in the accumulator array is incremented.
After the training part of the classification is concluded, it
follows the testing part when we are going to use these derived
values for x, y and z to classify any mixed set. Therefore, we
need to know the intraclass variability in z, y and z in order
to calculate the bin size for a and b. The intraclass variability
can be estimated by examining the steepness of the peak in
the Hough space. Let us assume that for a derived triplet
(xo, yo, Zo) we have a peak value f;,,,,,44 in the Hough
space. Then at the point (oz, yo, zo) we have:
J (20.30.20) e ec
fo ,y0,20)
Form the above we can derive c; and in a similar way c, and
G;. These standard deviations are likely to be different. In
such a case we use the biggest one to calculate the bin size
for a and b from equations (3).
5 APPLICATION TO REAL DATA
Since the simulation results showed that our model performs
well, we then tested it with some real data. The aim was to
decide on the type of vegetation in an area located close to
Athens, the capital of Greece in the province of Attica. Four
test areas (Penteli, Pateras, Varnavas and Lavrio) have been
selected because there were forest fires in each of these areas
within the last ten years. The training site data used in this
work were collected by the Institute of Mediterranean For-
est Ecosystem - National Agricultural Research Foundation
(NARF) of Greece for evaluating the risk of desertification.
The primary vegetation in this study area is composed of
conifers, mainly Aleppo pine and a variety of shrub species.
So the vegetation cover is categorised in three main classes:
bare soil, aleppo pine and other vegetation. For training we
used different sites for which ground data were available. We
have no regions solely composed of one class so we derive the
spectral characteristics of the real pure classes from sites for
which we know their composition, using the Hough transform.
39 training sites were used for this purpose. The algorithm
was then tested on 14 sites which had not been used for train-
ing and for which the composition was known from ground
inspection as well. Two criteria were used to evaluate the ob-
tained results. According to the first criterion a classification
result is considered a “hit” if the dominant class is identified
correctly, otherwise we have a “miss”. The second criterion is
more strict, a classification result is considered a “hit” if the
dominant class is identified correctly with accuracy +15%.
The results of the Hough transform were compared with the
results obtained by the Least Square Errors method.
In Tables 4 and 5 S stands for soil, AP for Aleppo Pine, V for
Other vegetation. The numbers are percentages of coverage
by the corresponding class. Under the heading “LSE” we give
89
the results obtained by using the Least Square Errors. Under
the heading "Hough" we give the results obtained by using
the Hough transform. All the results presented in the fol-
lowing tables were calculated using only two bands, the ones
that give the maximum discrimination for the three "pure"
classes (in our case bands 3 and 5).
With the LSE method according to the first criterion 24 sites
out of the 39 were classified correctly and according to the
second criterion 18 sites out of the 39 were classified correctly.
Using the Hough model, according to the first criterion 25
sites were classified correctly, while according to the second
criterion we had 19 "hits". The detailed results obtained for
these sites are shown in Table 4.
At the second stage of the evaluation of our method, we
tested our model using 14 sites that they had not been used
for the derivation of the pure classes. According to the first
and second criteria the LSE method classified correctly 5 sites.
The Hough model had 8 "hits" in accordance to the first
criterion and 6 "hits" according to the second criterion. The
detailed results obtained for these sites are shown in Table 5.
6 DISCUSSION AND CONCLUSIONS
The simulation results showed that the Hough transformed
method can tolerate large amount of outliers and still retain
an acceptable performance. So the Hough method seems
more attractive in terms of performance, but the price that
one has to pay is the increase in computational complexity.
The problem of exponential explosion of the number of
quadruples one can use has also to be considered. Indeed,
if each one of the distributions that represents a pure class
and the mixed distribution consists of 30 points, we have to
consider 30* possible combinations which is about 109 com-
binations. This is really the limiting factor in our approach:
It is not feasible to use it for large data sets or for many
"pure" classes. However, the method is not really meant for
large data sets as it is only introduced for the case that the
datasets are not sufficiently large to allow reliable statistics
to be extracted from them.
The problem of multiple peaks in the Hough space when more
than the mixtures are present can basicly be tackled by con-
sidering pairs of equations and solving for a single (a, 5)
and incrementing only one cell in the accumulator array at a
time. The problem of combinatorial explosion is dealt with
in [Kälviäinen et al., 1996]
7 ACKNOWLEDGEMENTS
This work has been supported by the CEC project 0025 under
the Environment programme.
REFERENCES
[Adams et al., 1986] J.B. Adams, M.O. Smith, P.E. John-
son, "Spectral mixture modeling: A new analysis of
rock and soil types at the Viking Lander 1 site", Journal
of geophysical re search, vol.91, no.B8, pp. 8098-8112,
1986.
[Bosdogianni et al., 1994] P. Bosdogianni, M. Petrou, J. Kit-
tler, 1994. "Mixed pixel classification in Remote Sens-
ing". Proceedings of the EUROPTO series, Image and
Signal Processing for Remote Sensing, Vol 2315, pp 494-
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
