Biomedical Engineering Reference
In-Depth Information
Figure 6.
Likelihood map pipeline for STOP and GO active models.
4.2. Likelihood Potentials
A likelihood function, in statistics, is a function proportional to the condi-
tional probability function of its second argument while keeping the first fixed.
Extrapolating from this definition and using the Bayes theorem, we consider the
likelihood function to be any conditional probability density function with one
parameter fixed. In segmentation/classification environments the likelihood func-
tion depends on two random variables,
x
and
c
that represent the feature vector
data and the class label, respectively. Therefore, the likelihood function that we
consider corresponds to the conditional probability function holding the random
variable
c
constant to a certain label of interest (LOI).
L
(
x
)=
αp
(
x
|
c
= ' LOI')
Using the former definition, we define the
likelihood map
as the set of correspond-
ing likelihood values for each of the elements of a given space. In our case, the
likelihood map is composed by the likelihood values for each of the pixel feature
vectors of an image. Likelihood maps contain information related to the probabil-
ity of how much an area of the image represents the class of interest.
Figure 6 shows the place where the deformable model is used in this approach.
The use of likelihood maps to guide a deformable model evolution is important
when an area of interest is under the influence of noise or subject of great vari-
ations. In those scenarios the use of the certainty of a given area belonging to
the region of interest can be exploited. This approach opposes the most tradi-
tional trend of classification techniques that rely on the
a posteriori
probability
Note that in this last
technique the boundaries are strictly fixed by the equality disregarding the value
of the probability. In this sense the one-class approach via likelihood maps has
the desirable effect of avoiding false positive segmented/classified regions. Our
approach exploits this fact to guide the deformation of the deformable model to
the most probable regions.
equality given by
p
(
x
|
c
= ' LOI')=
p
(
x
|
c
= ' NOT LOI').
