IMAGE SEGMENTATION USING THE LEVEL SET METHOD - Deformable Models - page 115

the initial seed by simply clicking on the AOI, as shown in the leftmost
image of Figure 11;

2. Tracking Step: For subsequent image slices, level set segmentation is
performed with the initial curve (the same as the segmented result from
the previous image). The front is propagated with a newly proposed speed
function (Section 5.1), which is designed for tracking.

This segmentation process is demonstrated in Figure 11. The underlying

relationship between the segmentation and trackingmethods relies on the proposed
variational framework (Section 4.2) for the speed function.

5.1. Speed Function for Tracking

The 0.1-mm inter-layer distance of the CVH data makes tracking easier and
more reliable for the segmentation task. We also extended the speed model in Sec-
tion 4 for the tracking problem. Due to the visual consistency constraint between
two continuous layers, we can assume that the transformation of the edge between
images I n and I n +1 is between a narrow band with width δ . All the following
calculations are done only within the narrow band.
We propose a new speed function for evolving the contour, from image I n to
the next slice I n +1 . Taking the segmentation result in I n as the initial contour in
I n +1 , the front propagates under the speed function (Eq. (40)), to attract the front
moving to the new AOI boundary. Here, the curvature term κ is still adopted in
order to avoid a “swallowtail” during the propagation. F D is the cost function
between the two images I n and I n +1 . It can be measured by the sum of square
differences between the image intensities in a window, as shown in Figure 12.
Equation 41 tells us how to determine the magnitude and signal of F D , where
+ n and

n indicate whether the pixels are outside or inside the zero level set,
respectively, in I n . C n

−

and C n
−

are the content models of these pixels in I n . ID
represents the overlapped non-homogenous areas (Figure 12):

+

F = KI n +1 ( κ + F D )+ βF C , (40)

I n +1 ) 2 ,F C = S

F D = S · ( I n − · dist( C n ,C n +1 ) , (41)

Sign(dist( C ID ,C n

+ ) − dist( C ID ,C n

S =

− ) .

(42)

Note that F D , convolved by KI n +1 , forces the front to move in the homogeneous
area and to stop at the boundaries in I n +1 . The sign of F D determines whether
the curve will expand or shrink.