In the case of SPAMM grids, from following grid line intersections, we obtain displacement information at a set of loci in the image. In the case of star-burst images, tracking the tag lines will yield displacement information at points where the tag lines intersect the heart wall. Clearly, it is desirable to obtain a dense field of displacement vectors so that myocardial motion can be inspected at all points falling within the myocardium.
As with the case of tag lines, we perform
spline approximation of the data [4][5]
for providing dense motion information. Two variational principles
are
posed which we numerically solve, yielding components of the
displacement vector field for all pixels in the LV
myocardium
:
In the above expression,
is used to denote the
, or
component of displacement,
is in general a non-negative function of
and
and
controls the degree of smoothing, and
is the set of points with known displacement information.
Successive Over Relaxation (SOR)
is used to solve the resulting discrete linear systems of
equations to obtain dense displacement information.
This method calculates
LV displacement at all points of a 2D tagged
cardiac MR image utilizing the tracked image tag information.
Results of dense motion estimation from 2 consecutive frames of
a SPAMM tagged MR image sequence
are shown in figure 4.