stantial for both methods. The classifier based in
Neural Networks presented satisfactory results, com-
pared with the Maximum Likelihood. This indicates
that this method demonstrated that it is suitable for
the classification of satellite images. However it is
observed that both methods tend to confuse the ar-
eas of the deforestation class with the no-forest class.
It is believed that that confusion happen because the
grayscale values of the p
´
ıxeis of those two classes are
very close. For that reason it was started the study of
Fractals as a Minimization Error Technique.
2.1 Study of the Minimization Error
Technique
Through the study and of the accomplished experi-
ments it was verified that the classification neural is
suitable for the images of the satellite CBERS. How-
ever, this classification still has a significant error. It
is intended to give continuity to this study through
the incorporation of new techniques of treatment of
the images before the submission to Neural Networks
training and of techniques for Minimization of Error.
One of these techniques intend to decrease the error
of the classification that happens in the borders, or
transition limits between a class and another. It is ob-
served in the images that some classes present very
defined limits and with different characteristics. If it
is applied border detection in these images is noticed
that those limits have visibly patterns or irregularities
that could be used as additional information for iden-
tification of a class. It is supposed that those differ-
ences can be quantified by Fractal Dimension calcu-
lus (Feder, 2000), whose definition supplies the need
of establishing patterns for those borders or limits.
Fractal Dimension study verifies the adaptation of
that technique to determine areas that the ANNs and
the method ML doesn’t get to distinguish.
2.2 Fractal Dimension
Fractal objects are not measured by length or area.
They are “more” than lines and “less” than a plane.
To measure them, it is used the concept of Fractal Di-
mension. Fractal Dimension is a measure that quanti-
fies the fractal density in the metric space it is defined,
being used for compare it. (Feder, 2000) (Conci,
2004) .
2.3 Fractal Dimension Calculus
In geometric objects (with dimension 1, 2 or 3) it is
used a simple relation among dimension, number of
blocks that is necessary to recover them and the size
of the blocks. It is expressed such as:
d =
log N
log (1/L)
where N is the number of blocks with side L of que
recovering and d is the dimension. In a log-log graph,
this relation is translated as a line. The line’s slope is
the Fractal Dimension d (Feder, 2000) (07, 2004).
2.4 Methodology
For the calculus of the Fractal Dimension of each
class, it was developed an algorithm that obtains the
approximate values of the Fractal Dimension of an
image fragment. The algorithm receives for its in-
put a fragment of satellite image whose its borders
were identified. It is a binary image, just containing
the information of the limits of the interest class. The
input image is splitted in squares (or blocks) every
time minor, counted in number of pixels. For each
square size L, are counted the number of squares ”N”
that contain a piece of the image (it embroiders). The
output generated is a file containing the values of the
logarithm of L and the logarithm of N. At the end, it is
made the linear regression of the data of that file, and
the angular coefficient of that straight line represents
the Fractal Dimension of the image. The experiments
were accomplished with the images classified by ML.
That classified image was submitted to the detection
of borders by the Method Canny (W. Gonzalez, 2000)
in the Software MATLAB. The image was submitted
to the detection of borders several times, modifying
the thresholds of the method Canny, in order to ob-
serve the results with more or less ”noise” of the de-
tection. The initial thresholds, given automatically by
the Software, they were 0,0063 and 0,0156. These
are, respectively Low Threshold and High Thresh-
old (parameters), in other words, the thresholds min-
imum and maximum. After the detection of borders,
they were cut out of the image areas according to the
classes of interest. Those cut out areas were used
as data of entrance of the algorithm of counting of
blocks for Dimens
˜
ao Fractal’s determination. The re-
sults of those initial experiments are presented in the
next item.
2.5 Results of the Experiments with
Fractals
Table 1 illustrates the results obtained for the varia-
tion of the thresholds of the Fractais Dimension of the
classes Not-forest and Deforestation.
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