Biomedical Engineering Reference
In-Depth Information
Figure 7.
Diagrammatic representation of available measurements for model fitting. The
only discernible measurement of the true displacement,
d
, is the orthogonal component at
time
t>
0
to the tag plane configuration at time
t
=0
.
provided by the intersections of the tag planes includes all three components of mo-
tion. We have empirically determined the optimal confidence values for tag plane
intersections, contour/tag intersections, and tag plane normals. This is described
in Section 6.1.
The tag line data are extracted using a previously published method explained
in [13], where a maximum a posteriori framework was used to estimate the tag
line locations based on a sampling of isoparametric surfaces of a cubic B-spline
solid that model the tag surfaces. Once the tag line data are available, we loft the
tag lines to create B-spline surfaces that represent each tag plane of the three sets
of tag planes. The normal displacement of these tag plane surfaces are used in the
model-fitting process. Contours are manually traced as part of the preprocessing
step.
Tag plane data provide three sets of mutually orthogonal sample points cor-
responding to the two sets of short-axis tag planes and one set of long-axis tag
planes. The true displacement of a point on a tag plane consists of both a normal
and a tangential component (Figure 7). However, due to the
aperture problem
[28], only the normal component is discernible. Therefore, for each time point
t>
0, the set of measurements from the tag planes for each time frame is
M
T
=
{
p
i
+(
d
i
ยท
n
)
n
}
,
(30)
where
p
i
is the position of a sample point on one of the tag planes at
t>
0,
n
is
the normal to the undeformed tag plane, and
d
i
is the true displacement for the
i
th
sample point at time
t>
0.
