Biomedical Engineering Reference
In-Depth Information
Figure 8.21: A weighting coefficient for each voxel determines the portions of
the discrete sinogram influenced by incremental changes to a grid point.
the model projection to reflect those changes. At each iteration, the amount of
change in an active point's value determines the motion of that particular surface
point as well as the percentage of the surrounding voxel that is either inside or
outside of the surface. By the linearity of projection, we can map these changes
in the object shape, computed at grid points along the surface boundary, back
into the sinogram space and thereby
incrementally
update the sinogram. Note
that each 3D grid point has a weighting coefficient (these are precomputed and
fixed), which is determined by its geometric mapping of the surrounding voxel
back into the sinogram, as in Fig. 8.21. In this way the IPU method maintains
subvoxel accuracy at a relatively low computational cost.
8.6.4.4 Initialization
The deformable model fitting approach requires an initial model, i.e.
φ
(
x
,
t
=
0).
This initial model should be obtained using the “best” information available
prior to the surface fitting. In some cases this will mean thresholding a grayscale
reconstruction, such as FBP, knowing that it has artifacts. In practice the initial
surface estimate is impacted by the reconstruction method and the choice of
threshold, and because we perform a local minimization, these choices can affect
the final result. Fortunately, the proposed formulation is moderately robust with
respect to the initial model, and our results show that the method works well
under a range of reasonable initialization strategies.
