Biomedical Engineering Reference
In-Depth Information
The most widely used technique for extracting polygonal models from vol-
ume datasets is the Marching Cubes algorithm [72]. This technique creates a
polygonal model that approximates the isosurface embedded in a scalar volume
dataset for a particular isovalue. While the Marching Cubes algorithm is easy to
understand and straightforward to implement, applying it directly to raw vol-
ume data from scanners can produce undesirable results, as seen in the first
images in Figs. 8.13 and 8.16. The algorithm is susceptible to noise and can pro-
duce many unwanted triangles that mask the central structures in the data. In
order to alleviate this problem, we utilize the tools in our level set framework
to smooth the data and remove the noise-related artifacts.
8.5.3 Segmentation
In this section we demonstrate the application of our methods to the segmenta-
tion of DT-MRI data of the human head. We use a high-resolution dataset from a
human volunteer which contains 60 slices each of 128 × 128 pixels resolution.
The raw data is sampled on a regular uniform grid.
We begin by generating two scalar volume datasets based on the invariants
described in Section 8.5.1. The first scalar volume dataset ( V 1 ) is formed by
calculating the trace ( C 1 ) of the tensor matrix for each voxel of the diffusion
tensor volume. It provides a single number that characterizes the total diffusiv-
ity at each voxel within the sample. Higher values signify greater total diffusion
irrespective of directionality in the region represented by a particular voxel. A
slice from this volume can be seen in Fig. 8.12 (left). The second scalar volume
Figure 8.12: Isotropic C 1 (left) and anisotropic C a (right) tensor invariants for
the tensor slice shown in Fig. 8.11.
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