Biomedical Engineering Reference
In-Depth Information
processes that lead to individual variability. These issues are explored in
more detail in Chapter 14.
2.3
Types of Transformation
2.3.1
Dimensionality Transformations
The process of registration involves computation of a transformation between
the coordinate systems of the images or between an image and physical space.
We are three-dimensional beings who move, so in principle, registration
should be four-dimensional. In practice, we usually make some approximations
and assumptions so that the body can be represented with fewer dimensions.
2.3.1.1
2D-to-2D
If the geometry of image acquisition is tightly controlled, 2D images may be
registered purely via a rotation and two orthogonal translations. It may also
be necessary to correct for differences in scaling from the real object to each
of the images. However, computationally straightforward, clinically relevant
examples of this are rare, as controlling the geometry of image acquisition is
usually very difficult. One example is the registration of x-ray radiographs of
the hand with
99m
Tc methyl-diphosphonate planar nuclear medicine images
for the diagnosis of suspected scaphoid injury.
1
Color Figure 2.2* shows a
nuclear medicine image overlaid in color on the radiograph, confirming a
scaphoid fracture. In this example, a purpose-built holding device con-
strained the hand to be in identical positions in the two images.
2.3.1.2
3D-to-3D
Of more widespread applicability is the accurate registration of multiple 3D
images such as MR and CT volumes. The assumption is usually made that
the internal anatomy of the patient has not distorted or changed in spatial
relationships between organs, so that the imaged part of the body behaves as
a “rigid body.” In this case three translations and three rotations will bring
the images into registration. Careful calibration of each scanning device is
required to determine image scaling, i.e., the size of the voxels in each modal-
ity. 3D-to-3D registration is the most well developed and widely used method
and is the primary emphasis of this topic.
2.3.1.3
2D-to-3D
2D-to-3D registration may be required when establishing correspondence
between 3D volumes and projection images such as x-ray or optical images.
Another class of 2D-to-3D registration arises when the position of one or
* Color Figures follow page 22.
