Biomedical Engineering Reference
In-Depth Information
estimate is determined by a previous process [6, 7, 11, 12, 14], possibly cal-
culated using feature sets. Other prior estimates can be given by a rotary ta-
ble [10], a robot arm [13], or even the user. Most such estimates are assumed
to be quite accurate so that using one of the various distance thresholds during
matching will prune outliers correctly. Other researchers do their own feature-
based alignment prior to refinement using such characteristics as principal mo-
ments [4] or similar triangles on a mesh representation of the data [8]. If these
distinguishing features are absent, a uniform distribution of starting points can
always be processed [4]. All of the ICP algorithms must use some set of cri-
teria to detect convergence of the final transformation. For those techniques
that compute intermediate motions using least squares methods, convergence
is achieved when the transform implies a sufficiently small amount of mo-
tion [6, 8, 14] or the distance between corresponding points becomes suitably
close [4, 7, 11, 14]. The iterative searches of parameter space typically converge
based on small changes in the parameters or error value, or if the shape of the
cost function at the current value indicates a function minimum. Any method
can be terminated if convergence is not detected after some maximal number of
iterations [3].
1.4.6
A Genetic Distance-based Technique
Another enhancements on the ICP algorithm for fast registration of two sets of
3D curves or surfaces was done by applying a distance transform to the model
surface [3, 9]. The distance transform essentially converts the 3D space sur-
rounding the two data sets into a field in which every point stores the magnitude
and direction of a displacement vector from this point to the nearest surface
element. Thus the cost function is largely precomputed. Such a transform is
called the
grid closest point
(GCP) [9]. A genetic algorithm (GA) is then used to
minimize the cost function.
Genetic algorithms (GAs) [17] provide a powerful and domain-independent
search method for complex, poorly understood search spaces. Genetic algo-
rithms have been applied to a wide diversity of problems such as combinatorial
optimization [18], VLSI layout [19], machine learning [20], scene recognition [21],
and adaptive image segmentation [22].
As mentioned in the previous section, to perform registration most of the
computation time is spent in finding the closest point in the model set to every
