Biomedical Engineering Reference
In-Depth Information
2.4.2.3
The Iterative Closest Point Algorithm
15
The iterative closest point algorithm,
although originally devised for other
purposes, has been widely applied to surface-based registration of medical
images. In the most usual form of this algorithm, one surface is represented
by a set of points while the other is represented by a surface made up of many
triangular patches or “facets.” The algorithm proceeds by finding the closest
point on the appropriate triangular patch to each of the points in turn. The
closest points form a set, and these are registered using the corresponding
landmark-based registration and the residual error is calculated. The closest
points are found from this new position and the process is repeated until the
residual error drops by less than a preset value.
These methods are described in more detail in the next chapter. They use
more of the available data than landmark identification, and robust and
accurate methods have been reported for some applications. Unfortunately,
the technique is highly dependent on identification of corresponding sur-
faces, yet different imaging modalities can provide very different image
contrast between corresponding structures. The process of delineation is
hard to do accurately. Computer-assisted segmentation currently almost
always requires some manual editing or adjustment. The surface may also
exhibit natural symmetries to certain rotations, leading to poorly constrained
transformations.
Other features, such as lines and tubes, as well as combinations of fea-
tures, have also been used.
16
In principle, adjacent surfaces may be used
for registration incorporating knowledge of the spatial relationships of
different surfaces.
17
2.4.3
Registration Based on Voxel Intensities Alone — Voxel
Similarity Measures
In recent years a number of robust and accurate algorithms have been
devised that use the intensities in the two images alone without any require-
ment to segment or delineate corresponding structures. These are often col-
lectively referred to as voxel similarity-based registration. As these algorithms
have been so successful, it is worth spending a few words to describe their
historical development and to introduce a way of representing the image
intensities of a pair of images that are to be registered. This representation
is called the joint histogram or joint probability distribution. These terms will
be described shortly. Unlike the algorithms described above, these methods
use all (or a large proportion of) the data in each image and so tend to average
out any errors caused by the noise or random fluctuations of image intensity.
The simplest and earliest purely intensity-based registration method was
applied to images from the same modality and therefore the images are
unlikely to have changed very much.
