Biomedical Engineering Reference
In-Depth Information
Figure 8.17: The model is the interface between two densities, which are pro-
jected onto the imaging plane to create p ( s i ).
Applying the radon transform to the model and substituting for p gives
E
δ ( R θ i x s j ) d x , p ij
β 0 K ( s j i ) + [ β 1 β 0 ]
N
M
E data =
,
(8.37)
i = 1
j = 1
where K ( s j i ) is the projection of the background—it depends on the geometry
of the region over which the data is taken and is independent of the surface
estimate. For some applications we know that β 0 = 0, and the term β 0 K is zero.
The integral over results from integrating g over the entire domain.
The proposed strategy is to alternately (i.e. separately) update the shape of
the surface model and the density parameters. For the surface shape, a gradient
descent minimization approach describes the deformation of the surface, with
respect to an evolution parameter t , as it progressively improves its fit to the
Figure 8.18: The reconstruction strategy starts with an initial surface estimate
and iteratively modifies its shape and the associated density parameters to
achieve a good fit to the input data.
Search WWH ::




Custom Search