Biomedical Engineering Reference
In-Depth Information
8.4.1 Method Description
We have formulated our approach to 3D reconstruction of geometric models
from multiple nonuniform volumetric datasets within our level set segmentation
framework. Recall that speed function
F
() describes the velocity at each point
on the evolving surface in the direction of the local surface normal. All of the
information needed to deform a surface is encapsulated in the speed function,
providing a simple, unified approach to evolving the surface. In this section we
define speed functions that allow us to solve the multiple-data segmentation
problem. The key to constructing suitable speed terms is 3D directional edge
information derived from the multiple datasets. This problem is solved using a
moving least-squares scheme that extracts edge information by locally fitting
sample points to high-order polynomials.
8.4.1.1 Level Set Speed Function for Segmentation
Many different speed functions have been proposed over the years for segmen-
tation of a single volume dataset [5, 6, 8, 41]. Typically such speed functions
consist of a (3D) image-based feature attraction term and a smoothing term
which serves as a regularization term that lowers the curvature and suppresses
noise in the input data. From computer vision it is well known that features, i.e.
significant changes in the intensity function, are conveniently described by an
edge detector [53]. There exists a very large body of work devoted to the problem
of designing optimal edge detectors for 2D images [14, 16], most of which are
readily generalized to 3D. For this project we found it convenient to use speed
functions with a 3D directional edge term that moves the level set toward the
maximum of the gradient magnitude. This gives a term equivalent to Eq. (8.8),
F
grad
(
x
,
n
,φ
)
=
α
n
·∇∇
V
g
,
(8.10)
where
α
is a scaling factor for the
image-based
feature attraction term
∇∇
V
g
and
n
is the normal to the level set surface at
x
.
V
g
symbolizes some global
uniform merging of the multiple nonuniform input volumes. This feature term is
effectively a 3D directional edge detector of
V
g
. However, there are two problems
associated with using this speed function exclusively. The first is that we can-
not expect to compute reliable 3D directional edge information in all regions
of space simply because of the nature of the nonuniform input volumes. In
