corresponding domain-level attribute. This method of topologically defining a
domain-level attribute provides a unique way to query, partition, and evaluate the
ranked blobs and their related real-world structures, as many ranked blobs can and do
exist within the full horizontal areal extent covered by a domain level, but no more
than one ranked blob can exist within the same vertical space defined between two
levels (Figure 8.13). Thus the problem of overlapping ranked blobs (Figure 8.12) is
resolved because blobs can be queried and evaluated by the unique levels in which
they exist.
8.3.1.3 Four New Shared-Event Classes Defined Within the (500x by 500y by
200t) SS cube we distinguish 10371 single events of the four known event types
(Table 8.1). However, we also identified four new classes of shared events (composed
of 1429 shares) that to our knowledge have never been defined before (Table 8.2). We
surmise that the reason for these shared events has to do with our choice of scale
increment between successive layers within the stack and/or noise in the original
image.
In our processing, we have defined 200 individual scales, where the scale increment
is unity. Thus, at each layer in the SS stack, the standard deviation of the Gaussian filter
is increased by unity (STD + 1). However, this is an arbitrarily chosen value. We could
have chosen fractional components as has been done by others (ter Haar Romeny et al.,
2000), but in doing so, we would still have to arbitrarily select this value. This is
because in theory a scale continuum is continuous; however, digitally we are limited to
a discrete (i.e., binary) computational environment.
These new shared events include creations and annihilations (C&A), creations
and splits (C&S), merges and annihilations (M&A), and merges and splits (M&S)
TABLE 8.2 Shared-Event Types and Quantities
Event Types
Number
Percent
C & A
949
66.4
C & S
63
4.4
M & A
26
1.8
M & S
391
27.4
Total
1429
100
TABLE 8.1 Single-Event Types and Quantities
Event Types
Number
Percent
Creations (C)
4,516
42.1
Annihilations (A)
1,528
14.2
Merges (M)
3,309
30.9
Splits (S)
1,378
12.8
Total
10,731
100
DISCUSSION
159
domain-level attribute provides a unique way to query, partition, and evaluate the
ranked blobs and their related real-world structures, as many ranked blobs can and do
exist within the full horizontal areal extent covered by a domain level, but no more
than one ranked blob can exist within the same vertical space defined between two
levels (Figure 8.13). Thus the problem of overlapping ranked blobs (Figure 8.12) is
resolved because blobs can be queried and evaluated by the unique levels in which
they exist.
8.3.1.3 Four New Shared-Event Classes Defined Within the (500x by 500y by
200t) SS cube we distinguish 10371 single events of the four known event types
(Table 8.1). However, we also identified four new classes of shared events (composed
of 1429 shares) that to our knowledge have never been defined before (Table 8.2). We
surmise that the reason for these shared events has to do with our choice of scale
increment between successive layers within the stack and/or noise in the original
image.
In our processing, we have defined 200 individual scales, where the scale increment
is unity. Thus, at each layer in the SS stack, the standard deviation of the Gaussian filter
is increased by unity (STD + 1). However, this is an arbitrarily chosen value. We could
have chosen fractional components as has been done by others (ter Haar Romeny et al.,
2000), but in doing so, we would still have to arbitrarily select this value. This is
because in theory a scale continuum is continuous; however, digitally we are limited to
a discrete (i.e., binary) computational environment.
These new shared events include creations and annihilations (C&A), creations
and splits (C&S), merges and annihilations (M&A), and merges and splits (M&S)
TABLE 8.2 Shared-Event Types and Quantities
Event Types
Number
Percent
C & A
949
66.4
C & S
63
4.4
M & A
26
1.8
M & S
391
27.4
Total
1429
100
TABLE 8.1 Single-Event Types and Quantities
Event Types
Number
Percent
Creations (C)
4,516
42.1
Annihilations (A)
1,528
14.2
Merges (M)
3,309
30.9
Splits (S)
1,378
12.8
Total
10,731
100
DISCUSSION
159