Biomedical Engineering Reference
In-Depth Information
those algorithms visually as well as objectively [8, 9, 10]. Among those different
registration algorithms, the voxel similarity approaches to image registration
have attracted significant attention since these full-volume-based registration
algorithms don't rely upon data reduction or segmentation, and involve little
or no user interaction. They can also be fully automated and offer quantitative
assessment. Maintz
et al.
[4] lists the reported paradigms and Studholme
et al.
[11], Penney
et al.
[12], and Holden
et al.
[13] compare many of them. Among
various different similarity measures, mutual information is the most prominent
(see [14, 15, 16], and [17]). Many papers and reports have been published on this
similarity measure since its first publication and advances in this area have been
recently reviewed in Pluim
et al.
[17].
A cross-entropy optimization approach to image registration was reported
recently in Zhu [18]. Cross-entropy minimization as a principle was formally
established by Shore and Johnson [19, 20]. They also studied the properties of
cross-entropy minimization [21]. In addition to image registration, this measure
has been applied to the areas of spectral analysis in Shore [22], image reconstruc-
tion in Zhuang
et al.
[23], biochemistry in Yee [24], process control in Alwan
et al.
[25], non-linear programming in Das
et al.
[26], and electron density estimation
in Antolin
et al.
[27], among many others.
Cross-entropy, also known as Kullback-Leibler divergence, is an information-
theoretic measure that quantifies the difference between two probability den-
sity functions (pdf). It can be either maximized or minimized, depending on
how a priori pdf is given. Cross-entropy maximization degenerates to mutual
information maximization, conditional entropy minimization or joint entropy
minimization under certain conditions. Cross-entropy has two close relatives
known as reversed cross-entropy and symmetric divergence, which have been
applied to spectral analysis (see [28, 29]) and neural networks [30]. It is reported
that cross-entropy, reversed cross-entropy, and symmetric divergence spectral
analyses have comparable performance. However, it is not clear how reversed
cross-entropy and symmetric divergence perform as registration measures. This
chapter explores their use as similarity measures for medical image registration
and compares their performance.
Since 1999, the imaging vendors have been developing new imaging devices
which combine two different imaging modalities into a single apparatus [31].
General Electric Medical Systems, Philips Medical Systems, and Siemens Medi-
cal Solutions/CTI all have released PET/CT devices (Discovery LS, Biograph, and
