Biomedical Engineering Reference
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of simplices in which the Characteristic Function changes value ( Combinatorial
Manifold ) gives a simple way to reparameterize the model.
This reparameterization process allows to reconstruct surfaces with significant
protrusions and objects with bifurcations. Furthermore, that process can easily deal
with self-intersections of the surface during model evolution. Also, T-Snakes/
T-Surfaces depends on some threshold to define a normal force that is used to
drive the model toward the targets [10].
Based on these elements (discrete surface model, simplicial decomposition
framework, and threshold), we present in this chapter a semiautomatic segmen-
tation approach for 3D medical images based on isosurface extraction methods
and the T-Surfaces model. Among the isosurface methods [12], two types are
considered in this chapter: continuation and marching methods.
The continuation methods propagate the surface from a set of seed cells [12,
13]. Unlike these approaches, in the traditional Marching Cubes, each surface-
finding phase visits all cells of the volume, normally by varying coordinate values
in a triple for loop [14]. As we have already demonstrated in previous works
[15, 16, 17], continuation methods are useful during both the reparameterization
and initialization of the T-Surfaces model if some topological and scale restrictions
for the targets are supposed.
In the present work we discard these restrictions. We show that continuation
methods remain suitable in the reparameterization process. However, Marching
methods should be used to initialize T-Surfaces close to the boundary. These are
the key points of this work.
Specifically, in the first stage, the T-Surfaces grid is used to define a coarser
image resolution by sampling the image field over the grid nodes. The obtained
low-resolution image field is a thresholded to get a binary field, which we call
an Object Characteristic Function . This field will be searched by the isosurface
generation method. The obtained result may be a rough approximation of the
target. However, the obtained surfaces are in general not smooth, and topological
defects (holes) may occur. Besides, due to inhomogeneities of the image field,
some components of the objects may be split as well as merged due to the low
image resolution used. The result is improved by using the T-Surfaces model.
The grid resolution is application dependent. However, an important point of
our method is its multiresolution/multigrid nature: having processed (segmented)
the image in a coarser (grid) resolution, we can detect regions where the grid has
to be refined, and then recursively applying the method only over those specific
regions.
If the extracted topology remains incorrect, even at the finest resolution, we
propose an interactive procedure based on the T-Surfaces framework to force merge
and split operations. This method is an extension of the one described in [15, 16].
In the case of noisy images, diffusion methods can improve both the isosurface
extraction and the T-Surfaces result. We discuss the utility of 3D image filtering by
anisotropic diffusion and implicit deformable models for our approach. Besides,
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