Biomedical Engineering Reference
In-Depth Information
expression and environmental factors is an exciting area of research, but it is
likely to be many years before such models can be used to align images from
different subjects.
2.5.2
Intrasubject Registration
Almost all registration work so far has been applied to the brain, which is
assumed to be held rigid by the confines of the skull, or to other bony structures.
We are beginning to see extension of registration algorithms to other structures
that deform over time. These deformations may either be due to natural invol-
untary motion (e.g., the heartbeat) or voluntary motion (e.g., change in body
position within the scanner), or may be induced by an intervention. In the
former, we need to align images to establish correspondence point by point. In
image-guided interventions, tissue can distort and deform between preopera-
tive scans and the intervention. Anatomical structures may move in relation to
each other. Intraoperative data in the form of point coordinates, optical images
from microscopes or endoscopes, ultrasound, or x-ray may provide updated
information on location and deformation of anatomical structures. This new
information might be used as a basis for predicting deformation of adjacent tis-
sues. The general problem, as in matching to an atlas described above, is often
poorly constrained, but in this case we may use the physical constraints of the
tissues involved. For example, bony structures will usually remain rigid, and
soft tissues will obey the laws of physics when deforming. Known information
about the tissue such as volume preservation or local rigidity might be incorpo-
rated to constrain what would otherwise be a wide range of possible solutions.
For example, the breast is unlikely to change in volume over the course of a
20-minute dynamic, contrast-enhanced MR sequence of acquisitions.
While devising effective nonrigid registration methods remains a research
topic, there are a number of algorithms undergoing evaluation that show
great promise, e.g., Rueckert et al.
3
Perhaps surprisingly, it appears that the
transformation mapping one individual's anatomy to another might obey
rather similar smoothness constraints to that which occurs naturally in soft
tissue deformations. Algorithms tend to fall into two classes: those based on
modeling, if only approximately, some physical process such as viscous
fluid flow or elastic deformation, and those based on some interpolating or
approximating function. These issues are discussed in more detail in Chapter 13
along with an introduction to the mathematics involved in the more success-
ful approaches.
2.6
Optimization
Only two regularly used algorithms directly calculate a transformation to
establish correspondence. The first is the Procrustes method based on point
correspondence, described earlier. The other is when two images have very
