Medical Image Registration: Theory, Algorithm, and Case Studies in Surgical Simulation, Chest Cancer, and Multiple Sclerosis - Biomedical Image Analysis - page 6

flexible, yet more complex and the methods range from using cross correlation,
variance minimization, histogram clustering and the famous maximization of
mutual information (discussed later in details).

1.2.3 Nature of Transformation

Since the registration process tries to recover the optimal transformation be-
tween two candidate subjects, the nature of such transformation categorize the
registration procedure to be used. The most commonly used is the rigid reg-
istration where the transformation involves only translations and rotations. If
the transformation maps parallel lines onto parallel lines it is called affine .Ifit
maps lines onto lines, it is called projective . Finally, if it maps lines onto curves,
it is called curved or elastic . Each type of transformation contains as special
cases the ones described before it, e.g., the rigid transformation is a special
kind of affine transformation. A composition of more than one transformation
can be categorized as a single transformation of the most complex type in the
composition, e.g., a composition of a projective and an affine transformation
is a projective transformation, and a composition of rigid transformations is
again a rigid transformation. Also a transformation is called global if it applies
to the entire image, and local if subsections of the image each have their own
transformations defined.
Rigid and affine transformations are generally global, and curved transfor-
mations are local. This is due to the physical model underlying the curved trans-
formation type. Affine transformations are typically used in instances of rigid
body movement where the image scaling factors are unknown or suspected to
be incorrect, such as in MRI images due to geometric distortions. The projective
transformation type has no real physical basis in image registration except for
2D/3D registration, but is sometimes used as a constrained-elastic transforma-
tion when a fully elastic transformation behaves inadequately or has too many
parameters to solve.

1.2.4 Interaction

Three levels of interaction can be involved in registration procedures. Auto-
matic , where the user only supplies the algorithm with the image data and pos-
sibly information on the image acquisition. Interactive , where the user does the