Biomedical Engineering Reference
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(a)
(b)
(c)
(d)
Figure 14. Consider all possible cases in the position of the curve. The fitting term is
minimized only in the case when the curve is on the boundary of the object. (a) The curve
C is outside the object, and F 1 ( C ) > 0 and F 2 ( C ) 0 . (b) The curve C is inside the
object; then F 1 ( C ) 0 and F 2 ( C ) > 0 . (c) The curve C is both inside and outside the
object; then F 1 ( C ) > 0 and F 2 ( C ) > 0 . (d) The fitting term is minimized when the curve
C is on the boundary of the object.
So, the unknown C could be replaced by Φ. Using Heaviside function H and
Dirac measure ∆ 0 , which are defined by
1 , ( z
0)
dH ( z )
dz
H ( z )=
0 =
,
(25)
0 , ( z< 0)
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