Information Technology Reference
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Fig. 10 Smoothness equalization: the least smooth image (a) is convolved with a Gaussian (c)to
match the smoothness level of (b)
Gaussian needed to smooth (a) to the level of (b) was 0.125 mm. This stage is a pre-
processing step for the following re
nement technique.
2.4.3 Density and Laplacian Based Correction
The last step re
nes the segmentation of the syndesmophytes using the Laplacian
filter allowed us to
pinpoint the boundary between bone and soft tissue. The interface between the two
materials can be modeled as a smooth step function. Its Laplacian is positive on one
side of the step and negative on the other. The Laplacian divides the interface
between 2 materials of different densities with the zero-crossing roughly in the
middle. Figure
11
shows an IDS processed with a Laplacian. The color code is
green for negative values and red for positive ones. Cortical bone is mainly green.
Cortical bone is thin and can be seen as two step functions back to back.
At the boundary between bone and soft tissue, the representation of a continuous
space by discrete voxels leads to the creation of voxels containing both materials, a
phenomenon usually called partial volume effect. Our algorithm incorporates partial
voxels, assigning them a partial volume value depending on their
filter and gray level density. The output of the Laplacian
, that is,
their grey level intensity. The density criterion is obtained in the following manner.
From the initial rough syndesmophyte segmentation we estimate the mean voxel
“
density
”
