Automated Determination of the Spine-Based Coordinate System for an Efficient Cross-Sectional Visualization of 3D Spine Images - Spinal Imaging and Image Analysis - page 253

Fig. 12 An axial cross-section of a CT spine image I. a Edge points f p m g , extracted by the 3D

Canny edge detector. b Image intensity gradient vectors , extracted by the 3D Sobel

gradient operator (the number of gradient vectors was considerably reduced for visualization
purposes). c An illustration of the determination of a pair of opposite edge points

f g ð p m Þg

p m Þ ð p m ; in the

direction of gradient vector þ g ð p m Þ . d The resulting accumulator A I with superimposed edge

points

extracted edges in the 3D image, while their magnitude is proportional to the
strength of the extracted edges in the 3D image. For a given 3D image, the edge
points of anatomical structures (Fig. 12 a) can

be extracted by the 3D Canny edge detector (using e.g. high threshold t high that
captures 50 % of image pixels and low threshold t low ¼

f p m ¼ ð x m ; y m ; z m Þ; m ¼ 1 ; 2 ; ...; M g

4t high for hysteresis
thresholding), while the corresponding image intensity gradient vectors

0 :

f g ð p m Þ ¼

½ (Fig. 12 b) can be extracted by the 3D

Sobel gradient operator (using e.g. kernel size of 3

g x ð x m Þ; g y ð y m Þ; g z ð z m Þ; m ¼ 1 ; 2 ; ...; M g

3mm 3 ) and normalized 3

so that 1. Before computing the edges and gradient

vectors, the images can be smoothed with a 3D Gaussian

8 g ð p m Þ) 0 k g ð p m Þ k

filter (with e.g. standard

deviation of r ¼ 5mm).

For each edge point p m , a search for the opposite edge point p m is therefore
performed in the direction of the normalized gradient vector g

1 :

ð p m Þ , however,