Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
Figure 8.
Likelihood map enhancement using the two-class approach: (a) original image;
(b) original likelihood map; (c) enhanced likelihood taking into account the bubbles region
and the background region.
4.2.2. Two-class enhancement of the likelihood map
In several applications the knowledge of the domain allows for definition of
two classes: the first one, related to the region of interest, and the second, related
to everything else. This can be done if the non-desired areas are well known
and a model of them can be built. Therefore, if a two-class problem arises, the
likelihood map can be improved provided that an
a priori
knowledge about the
desired properties of the different regions is available. In this case, we can enhance
the likelihood map using the following expression:
λ
L
(
x, y,
Θ
,
Θ)=(
)
·
L
(
x, y,
Θ)
,
(9)
λ
+
|
L
(
x, y,
Θ)
−
L
(
x, y,
Θ)
|
where
L
(
x, y,
Θ) is the likelihood map for image
I
(
x, y
) using a likelihood model
with parameters Θ. The parameter Θ corresponds to the pa
ra
meters of the like-
lihood model for the region of interest, and the parameter Θ are the model pa-
rameters of the complement of the target region.
λ
is a weighting pa
ra
meter.
Note that when both likelihood values are similar (
L
(
x, y,
Θ)
∼
L
(
x, y,
Θ)), the
likelihood map (
L
(
x, y,
Θ)) is emphasized. It remains smooth elsewhere. This
enhancement highligh
ts
the likelihood map in a range near the border given by
L
(
x, y,
Θ) =
L
(
x, y,
Θ). In this way, we enhance edges near the classification
border weighted by their li
ke
lihood value in the map. The proposed enhanced
likelihood map (
L
(
x, y,
Θ
,
Θ)) partially overcomes one of the drawbacks of the
likelihood map, giving better accuracy and removing non-prominent edges.
Figure 8 shows the procedure when taking into account the background infor-
mation. Figure 8a shows the original image, (b) displays the likelihood map for
the region of interest (the bubbles), and (c) shows the enhanced likelihood map.
We can see that the definition of the region of interest is much more accurate.
