Geoscience Reference
In-Depth Information
In real conditions, the study of spots, the acquiring of their statistical charac-
teristics and their using in a problem of detection is enough a complex problem.
Criteria have to be developed to distinguish spots from other phenomena. For
example, it is necessary to determine such threshold the exceeding of which is the
spot indicator. Also it is necessary to develop model presentation of processes of
spots detection.
The method of the thresholds determination is the most obvious and simple way
for spots de
nition. In this case that part of space belongs to area of spots, on which
the parameter of environment measured within the chosen channel exceeds value
(l
+
) or, on the contrary, does not exceed value (l
−
) a threshold. Let y = y (x
1
, x
2
)is
function of coordinates (x
1
, x
2
) of points within considered region. If
”
y = const is outlined at the region surface, then the closed curves of level y that
bound the spots are projected on it.
Algorithms for simulation of spottiness are based on the numerical solution of
the algebraic inequalities determining coordinates of internal points of spots. It is
impossible to write the equation of spots contours in a general.
Therefore contours of spots are described by system of the simple algebraic
equations connected among themselves by equation
“
level surface
ʣˆ
i
(x, y) = 0, where
ˆ
i
φi(x, y)is
the equation of an elementary curve. For simpli
cation of software realization of
ˆ
i
φi(x, y) the equation of a circle with
varied coordinates of the centre and radius is accepted. Complex forms of spots are
formed by overlapping on a plane of the drawing of several circles with different
parameters that is de
simulation of spottiness image as the equations
ned by system of inequalities of a kind:
X
x
a
i
n
o
0
2
2
ð
Þ
þ
y
b
i
ð
Þ
r
i
where x, y are the cartesian coordinates of internal points of spots, a
i
,b
i
, and r
i
are
coordinates of the centre and radius ith circle, respectively, n is quantity of the
circles composing the modeled image.
To simulate the randomness of background distribution for spottiness the
spottiness model parameters a
i
,b
i
, and r
i
are set by means of random-number
generators. By changing laws of distribution of random numbers and their statistical
parameters, it is possible to receive statistically different spottiness images.
The list of software items of the simulation system for classi
cation of the
phenomena on a terrestrial surface is given in Table
2.21
. An important point about
the system
is algorithms and the software is the possibility of spatial interpolation
and data restoration using remote and in situ measurements.
One of main aspects of the practical importance of developed system is quali-
tative interpretation and visualization of results of remote measurements.
For primary processing of remote measurements it is useful to apply an owerage-
connecting method of cluster analysis to detect the speci
'
c informational zones.
That method is effective under small volumes of sampling. Two variants of this
approach can be brought about by the way in which algorithms and index spaces
are organized.
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