Biomedical Engineering Reference
In-Depth Information
Such a problem would be avoided if we could define significant areas along
the surfaces and then apply the refinement only in the regions around them.
However, it is difficult to automatically perform this task.
As a consequence, polygonal meshes generated by the T-surface method may
not be efficient for some further applications. For instance, for finite element
purposes, small triangles must be removed. Consequently, filtering mesh pro-
cedures must be applied in order to improve the surface. Mesh smoothing and
denoising filtering methods, such as those proposed in [68], could also be useful
in this postprocessing step.
We tested the precision of our approach when segmenting a sphere immersed
on a uniform noise specified by the image intensity range [0
,
150]. We found a
mean error of 1
.
58 ( pixels) with standard deviation of 2
.
49 for a 5
×
5
×
5 grid
resolution, which we consider acceptable in this case.
This error is due to the projection of T-surfaces as well as the image noise.
Following [49, 50], when T-surfaces stops, we can discard the grid and evolve
the model without it, avoiding errors due to the projections. However, for noisy
images, the convergence of deformable models to the boundaries is poor due to
the nonconvexity of the image energy [31].
Anisotropic diffusion applied to 3D images can improve the result, as already
demonstrated in Sections 7.8 and 7.9.1. The gradient vector flow (see Section 7.8)
can also be applied when the grid is turned off.
Now, let us consider the following question: Would it be possible to imple-
ment the reconstruction method through level sets? The relevance of it will be
clear in what follows.
The initialization of the model through expression (7.20) is computation-
ally expensive and not efficient if we have more than one front to initialize
[75].
The
narrow-band
technique is much more appropriate for this case. The key
idea of this technique comes from the observation that the front can be moved
by updating the level set function at a small set of points in the neighborhood
of the zero set instead of updating it at all the points in the domain (see [46, 61]
for details).
To implement this scheme, we need to pre-set a distance
d
to define the
narrow band. The front can move inside the narrow band until it collides with the
narrow-band frontiers. Then, the function
G
should be reinitialized by treating
the current zero set configuration as the initial one.
