Geoscience Reference
In-Depth Information
TOTAL AREA = 324 pp X 320 pp
DISTANCE BETWEEN PICTURE POINTS = 259 m
70
60
50
0.0050
40
0.0040
30
0.0030
20
0.0020
10
0.0010
0
0
−
20
−
10
0
10
20
30
EROSION
DILATATION
Fig. 1.17 Percentage of total area occupied by patterns obtained after successive erosions and
dilatations. Histogram indicates probability that deposit point coincides with arbitrary pixel in
shell added after single dilatation or removed after single erosion (Source: Agterberg and Fabbri
1978
, Fig. 4)
The erosion of Fig.
1.14d
can be continued onward until not a single black point
remains. Likewise, the dilatations can be continued from Fig.
1.14e, f
onward until
most or all of the study area (set
T
) consists of black pixels. The relative areas of
these erosions and dilatations are shown in Fig.
1.17
. For dilatations each relative
area can be interpreted as the probability
P
(
nB
) with
mes
A
nB
Pnb
ðÞ¼
,
n
¼
1, 2,
...
mes
T
that a random cell with side (2
n
+1)
259 m contains one or more black pixels
belonging to the original pattern (Fig.
1.14d
). The probability
Q
(
nB
)thatacellwith
size mes
C
P
(
nB
). Likewise
it is possible to measure the probability
P
d
(
nB
) that a cell with side (2
n
+1)
nB
contains no acidic volcanics is equal to
Q
(
nB
)
¼
1
259 m
is a deposit cell containing one or more deposits (see Fig.
1.18
)because
mes
C
nB
P
d
nb
ðÞ¼
n
¼
...
,
1, 2,
mes
T
Another practical result is as follows. A correlation between sets
A
and
C
can be
carried out by determining how many deposit points are contained in the separate
shells added to, or subtracted from the original pattern (Fig.
1.14d
) by dilatation
or erosion. The original pattern itself contains 36 deposit points or mes
A
\
C
¼
36 pixels. The pattern of Fig.
1.15a
consists of 5,360 pixels and contains
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