Model-Based Segmentation, Reconstruction and Analysis of the Vertebral Body from Spinal CT - Spinal Imaging and Image Analysis - page 377

2.2 Spine Cord Extraction

As a pre-processing step, the spinal cord is extracted using the Matched filter. This

process helps to remove the spinal processes roughly; hence the shape model will
be registered to the image domain easily. In the

filter (MF)
[ 14 , 15 ] is employed to detect the VB automatically. This procedure eliminates the
user interaction and improves the segmentation accuracy. Let f

rst step, the Matched

be
template and test images, respectively. To compare the two images for various
possible shifts s x and s y , one can compute the cross-correlation c ðs x ; s y Þ

ð x ; y Þ and g ð x ; y Þ

as

ZZ g

c ðs x ; s y Þ ¼ ð x ; y Þ f ð x s x ; y s y Þ dxdy ; ð 4 Þ

where the limits of integration are dependent on g ð x ; y Þ . The Eq. ( 4 ) can also be

written as

ZZ G

F ð

c ðs x ; s y Þ ¼ ð f x ; f y Þ f x ; f y Þ exp ð j2 pð f x s x þ f y s y ÞÞ df x df y

ð Þ

5

FT 1 F ð ¼ ð G ð f x ; f y Þ f x ; f y ÞÞ;

where G ð f x ; f y Þ and F ð f x ; f y Þ are the 2-D FTs of g ð x ; y Þ and f ð x ; y Þ , respectively with

f x and f y denoting the spatial frequencies. The test image g ð x ; y Þ is filtered by

F ð

H ð f x ; f y Þ ¼ f x ; f y Þ to produce the output c ðs x ; s y Þ . Hence, H ð f x ; f y Þ is the corre-

lation filter which is the complex conjugate of the 2-D FT of the reference image

f ð x ; y Þ . Figure 3 a shows the reference image used in the Matched filter. Some

examples of the VB detection are shown in Figs. 3 b filter is tested

using 4,000 clinical CT images. The detection accuracy for the VB region is
97.2 %. The detection accuracy is increased to around 100 % by smoothing all
detected points of a dataset in the z-axis.
To extract the spinal processes and ribs roughly, some simple steps are followed
as shown in Fig. 4 . These steps are required to: (i) extract the spinal processes and
ribs roughly, (ii) crop the ROI minimize the execution time. Figures 5 and 6 show
different examples of this stage in the sagittal view.

d. The Matched

-

2.3 Vertebrae Separation

This process is required in the proposed framework hence the shape model is
registered to each VB in an easy way. In this process, two methods are suggested to
separate each vertebrae. The first suggestion is the manual separation, and the

second one is the previously proposed automatic framework [ 16 ] as shown in
Fig. 7 c.