Biomedical Engineering Reference
In-Depth Information
on validation conclude the chapter. The following chapter covers the same
ground from a more formal mathematical perspective and with more technical
details on implementation.
All the images that we wish to register or manipulate in any other way on
a computer must be available in digital form. This means that they are stored
in coded form with numbers representing the image intensity or color at each
location. This is usually achieved with a rectangular array of small square or
rectangular elements called
(an abbreviation of “picture elements”),
each pixel having an associated image intensity value. The pixel array pro-
vides a natural coordinate system for the images, and an element in each
image can be accessed by its two-dimensional (2D) position within this array.
A typical CT slice will be formed of 512
pixels
512 pixels, and each will corre-
2
spond to an element of about 0.5
in area. This dimension determines
the limiting spatial resolution of the image. 2D slice images are often stacked
together to form a 3D volume. Many images are now acquired directly as 3D
volumes. Each pixel will now correspond to a small volume element of tissue
or
0.5 mm
voxel
. If the slice spacing is, say, 1.5 mm, the voxel size will be 0.5
0.5
3
1.5 mm
. The number stored in each voxel, the voxel image intensity, will be
some average of the physical attribute measured over this volume. For clini-
cal MR brain images, typical voxels are 0.9
3
0.9
3 to 5 mm
, with 256
256 pixels in a slice. It is also possible to acquire MR images with cubic voxels,
e.g., 1.0
1.0 mm, and MR images with approximately cubic voxels are
often used for registration applications.
1.0
2.2
Correspondence
As stated above, image registration establishes spatial correspondence. We
should consider carefully what this means. Consider a scenario in which we
might have a patient who is imaged with MR and CT over the course of a
few hours, or perhaps on subsequent days, as workup for neurosurgery. The
process of registration will establish which point on one image corresponds
to a particular point on the other. By “correspond” we mean that these
points represent a measurement localized to the same small element of tis-
sue within the patient. We can then deduce something about spatial relation-
ships between different structures, each seen by only one modality. The
computational process of registration yields the appropriate transformation
between the “coordinate systems” of the two sets of scans, which are referenced
to the individual scanners. A coordinate system provides a way of describing a
position in space.
No measurement is perfectly accurate, and there will always be uncer-
tainty, error, or “tolerance” in this estimate of correspondence. For many clin-
ical applications it is important to know what this tolerance is, so as not to
