Biomedical Engineering Reference
In-Depth Information
The last major problem that the registration process must address is aligning
data sets that represents only a portion of the model data. A correspondence
between the experimental data set and the corresponding portion of the model
data set must be established before correcting for translation and rotation errors.
Once this is accomplished, the error measure must be calculated for only the
overlapping portions of the two sets. For example, consider scanning a tooth
and attempting to calculate the error between the scanned tooth and a model
of an entire human jaw. The registration process must be able to determine
which region of the jaw coincides with the scanned tooth, assuming the tooth
is distinct enough to distinguish between the other teeth, and then calculate the
error measure using only the overlapping regions.
In terms of algorithmic implementations, all of the registration techniques
fall under two global implementation categories:
distance-based
and
feature-
based
approaches. In the distance-based approach, the goal is to calculate the
transformation by minimizing a criterion relating the distance between the two
data sets. In the feature-based approach some differential properties invariant
to rigid transformation (such as gray level value, histogram, curvature, mutual
information, entropy, etc.) are often used.
In the following sections we will discuss in some details examples of algo-
rithms in both the approaches.
1.4
Distance-based Registration Techniques
Among the distance-based techniques, Besl and McKay [4] proposed the
Itera-
tive Closest Point (ICP)
algorithm which establishes correspondences between
data sets by matching points in one data set to the closest points in the other
data set. ICP is an elegant way to register different data sets because it is intu-
itive and simple. Besl and McKay's algorithm requires an initial transformation
that places the two data sets in approximate registration and operates under the
condition that one data set be a proper subset of the other. Since their algorithm
looks for a corresponding scene point for every model point, incorrect registra-
tion can occur when a model point does not have a corresponding scene point
due to occlusion in the scene. Attempts at solving these problems have led to
several variants of the original algorithm.
The ICP algorithm matches points in the experimental data set after applying
the previously recovered transformation (
R
,
t
), where
R
is a matrix represent-
