Biomedical Engineering Reference
In-Depth Information
D
olp
for three different ranges of cell motion. The distance selection
is based on topological spatial relations between objects in consecutive frames,
defined similar to the relation in Randell et al.'s region connection calculus (RCC)
[76, 77] and Egenhofer et al.'s 9-intersection model [78, 79]. The correspondence
analysis is largely based on proximity because intensity, texture, and shape are not
distinguishing features for cells since they share the same appearance.
msk
,and
D
⎨
D
)
∩
)=
∅
if bbx
(
W
i
bbx
(
W
j
bbx
D
msk
∩
W
j
=
∅
D
MOD
(
W
i
,
W
j
)=
if W
i
(3.36)
⎩
D
olp
otherwise
The
interbounding-box distance
bbx
(3.37) quantifies long-range displacement
between two regions (cells) in consecutive frames by the distance between their
bounding boxes denoted as bbx().
D
D
bbx
(
W
i
,
W
j
)=
K
bbx
×
D
I
(
bbx
x
(
W
i
)
,
bbx
x
(
W
j
))
2
+
D
I
(
bbx
y
(
W
i
)
,
bbx
y
(
W
j
))
2
(3.37)
where bbx
(
W
)
≡
<
inf
x
(
W
)
,
sup
x
(
W
)
,
inf
y
(
W
)
,
sup
y
(
W
)
>
is the minimum bounding
box of a region; bbx
x
(
W
)
≡
[
inf
x
(
W
)
,
sup
x
(
W
)]
and bbx
x
(
W
)
≡
[
inf
y
(
W
)
,
sup
y
(
W
)])
are intervals obtained by projecting the bounding box bbx
onto
x
and
y
axes;
D
I
is interval distance defined in (3.38); and
K
bbx
is a constant. In the cases of
overlapping bbx
x
or bbx
y
intervals,
(
W
)
D
B
corresponds to the minimum edge-to-edge
distance; otherwise it corresponds to minimum corner-to-corner distance [Figure
3.15(a)].
0
if
I
∩I
=
∅
A
B
D
I
(
I
,
I
)=
(3.38)
A
B
{|I
(
)
−I
(
)
|
,
|I
(
)
−I
(
)
|}
min
1
2
1
2
otherwise
A
B
B
A
D
msk
quantifies mid-range displacement between two
regions (cells) in consecutive frames, by the minimum contour-to-contour dis-
The
intermask distance
Figure 3.15
Object-to-object distance
D
MOD
:(a)
D
bbx
: interbounding-box distance; (b)
D
msk
:
intermask distance; and (c)
D
olp
: tonal-weighted overlap distance.
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