The name is absent

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Chapter 3

Applications using Tri-Iinear Contours

3.1 Building Scalars from Existing Segmentation

In the case where segmented data are given as input, we present a simple heuristic to
produce scalars off of the binary classification of a typical segmentation. Segmentation
inputs are typically defined by associating an integer value at each voxel or by creating
multiple 0-1 mask volumes, where each one represents a segment. Either of the two
representation can be easily converted to the other. Without loss of generality, we
assume the input is n 0-1 (binary) masks, where each masks represents one of n total
segments.

Under our contour representation, we can an assign arbitrary scalar to each voxel,
and the resulting surface should be a smoother surface than a binary classification.
Unfortunately, this type of assignment does not produce desirable rendering of the
segmented map (see Figures 3.1(b) and 3.1(e)). Instead, we blur each of the binary
masks using a truncated 3 × 3 × 3 gaussian function as our kernel [7]. We can view
the output of the blurring as n scalars defined for each voxel, but the final output we
want is a single scalar defined for each voxel. Using the convention defined previously,
we write the following as the final output scalar, t^new(τ), at the voxel x.

f^ιew(x) = t^k(x) -t^j(x)                           (3.1)

where Z^fc(rc) and t^j(x) are the largest and second largest of the n values computed
from the blurring step.

This heuristic is guided by the same intuition given in the gradient discussion of
Section 2.1.2. In the two-material case, the contour will correspond the blurring of a

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