90
Image
F(x)
Reference
Image
R(J)
Joint Histog ram
Estimation
h,; (F,R) '" h(F(i),R(T,. (x)))
3: Hua-mei Chen
Computation of the
MI similarity
measure
IT. (F, R )
Fig. 3.1. General flow chart of intensity based image registration using mutual information
as the similarity maesure
are explained. However, these methods, under certain conditions, suffer from
a phenomenon called interpolation-induced artifacts that hampers the optimization process and may thereby reduce registration accuracy (Pluim et
al. 2000). To overcome the problem of interpolation-induced artifacts, a new
algorithm called the Generalized Partial Volume joint histogram Estimation
(GPVE) algorithm (Chen and Varshney 2003) is also introduced.
3.2
Mutual Information Similarity Measure
Mutual information has its roots in information theory (Cover and Thomas
1991). It was developed to set fundamental limits on the performance of communication systems. However, it has made vital contributions to many different
disciplines like physics, mathematics, economics, and computer science. In this
section, we introduce the use of MI for image registration.
MI of two random variables A and B is defined by
"
PA B(a, b)
I(A,B) = :,;-PA,B(a, b) log PA(~)PB(b) ,
(3.1)
where P A (a) and PB (b) are the marginal probability mass functions, and
P A,B(a, b) is the joint probability mass function. MI measures the degree of
dependence of A and B by measuring the distance between the joint probability
PA,B(a, b) and the probability associated with the case of complete independence PA(a)PB(b), by means of the relative entropy or the Kullback-Leibler
Image
F(x)
Reference
Image
R(J)
Joint Histog ram
Estimation
h,; (F,R) '" h(F(i),R(T,. (x)))
3: Hua-mei Chen
Computation of the
MI similarity
measure
IT. (F, R )
Fig. 3.1. General flow chart of intensity based image registration using mutual information
as the similarity maesure
are explained. However, these methods, under certain conditions, suffer from
a phenomenon called interpolation-induced artifacts that hampers the optimization process and may thereby reduce registration accuracy (Pluim et
al. 2000). To overcome the problem of interpolation-induced artifacts, a new
algorithm called the Generalized Partial Volume joint histogram Estimation
(GPVE) algorithm (Chen and Varshney 2003) is also introduced.
3.2
Mutual Information Similarity Measure
Mutual information has its roots in information theory (Cover and Thomas
1991). It was developed to set fundamental limits on the performance of communication systems. However, it has made vital contributions to many different
disciplines like physics, mathematics, economics, and computer science. In this
section, we introduce the use of MI for image registration.
MI of two random variables A and B is defined by
"
PA B(a, b)
I(A,B) = :,;-PA,B(a, b) log PA(~)PB(b) ,
(3.1)
where P A (a) and PB (b) are the marginal probability mass functions, and
P A,B(a, b) is the joint probability mass function. MI measures the degree of
dependence of A and B by measuring the distance between the joint probability
PA,B(a, b) and the probability associated with the case of complete independence PA(a)PB(b), by means of the relative entropy or the Kullback-Leibler