Biomedical Engineering Reference
In-Depth Information
This solution represents the level set function variation with time. When the
function approaches the steady state, it does not change. It has positive, nega-
tive, and zero parts. We are interested only in the positive parts. Each pixel in the
positive parts belongs to the associated class of its function. By this representa-
tion, the level set function formulation allows breaking and merging fronts since
Eq. 9.72 contains the curvature term which is considered to be a smoothing part.
9.6.2 Volume Segmentation Algorithm
Step 0 : Initialize φ i , i [1 , c ].
Step 1 : t = t + 1.
Step 2 : Update each function using Eq. 9.72.
Step 3 : Solve Eq. 9.67 for each of n iterations to keep the signed distance
function property.
Step 4 : Smooth each function and remove noise.
Step 5 : If steady state is not reached, then go to Step 1, else go to next slice.
Step 0 is very important since bad initialization leads to bad segmentation. Auto-
matic seed initialization is used to speed up the process and it is also less sensitive
to noise. Automatic seed initialization is to divide the image into nonoverlapped
windows of predefined size. Then the average gray level is calculated and com-
pared to the mean of each class to specify the nearest class it belongs to. A
signed distance function is initialized to each window. The connectivity filter
is applied to remove the nonvessel tissues. The filter exploits the fact that the
vascular system is a tree-like structure.
9.6.3 Segmentation Quality Measurement
A 2D phantom is designed to simulate the MRA. This phantom image contains
many circles with decreasing diameters such as the cerebrovascular tree shape
which is a cone-shaped. Then using the level set segmentation algorithm with this
image, we obtain a resultant image containing the vessels. The SA is measured
by Eq. 9.48.
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