Geography Reference
In-Depth Information
a.
create a vector
+1
(that is a vector of size
+1
) in a dimension such as the
relation below (equation 6) is verified:
2=
∑
(6)
That means that the vector
is calculated by the following expression (equation 7):
=∑ |−|+|−|+⋯+|−|
;
(7)
,
b.
initialize the vector
with 0 (the value 0 is affected in all the entries of the vector);
c.
for the entry
of vector
, one adds the value
|−|
, provided that pixel
exist
and respect the rule of connexion
,
.
being pixel in position
,
on the generic tree (figure 1), if the condition
(respectively the condition
) is verified
will be the pixel in position
,,
,
(respectively in position
,,
,
+180°
). In other words, the entry
of vector
will be evaluated in the following way (equation 6):
=|−,|+−
,,
,
+−
,,
,
+180°
(8)
,
,
,,
,
and
,,
,
+180°
being levels of gray of the
pixels positioned in
,
,
,,
,
and
,,
,
+180°
on the generic tree,
respectively;
d.
repeat the process of stage 3 for all the entries
of the vector
, with
=
0,1,⋯,
.
These entries
represent the levels of gray of the pixels being in the considered image
window. It is about the image window centered on the current pixel, which is the pixel
for which one wants to determine the value of the textural parameter;
e.
make the summation of all the elements of the vector
. The result of this
summation represents the value of the textural parameter for the current pixel
(equation 9):
2=∑
.
(9)
The results produced by this new approach and those obtained by the classical approach are
exactly the same, but the last method requires the evaluation of the co-occurrence matrix,
which is very expensive in time of calculation and memory space of the computer. This is
due to the fact that the new formulation needs only the evaluation of a one-dimension
vector the size of which being equal to a side of the co-occurrence matrix. Furthermore, the
evaluation of the co-occurrence matrix makes intervene a lot of operations of multiplication
linked in multiple reminders, and these operations are expensive in time machine. It is
important to notice that the complexity of calculation increases with the order of the textural
parameter.
