Appendix B
In the second step of the image segmentation process, we limit the energy to the restricted
domain (the region inside the red curve in Figure 7):
The corresponding functions ( f1 , f 2 ) that minimize F ( f1 , f 2 , ) satisfy
f 1 ( x)
K ( x) [ H ( ( x))H ( 1 ( x))I ( x)]
K ( x) H ( ( x))H ( 1 ( x))
f 2 ( x)
K ( x) [1 H ( ( x))H ( 1 ( x))I ( x)]
K ( x) [1 H ( ( x))H ( 1 ( x))]
and
t
satisfies
( )H ( 1)
1
K (y
x) | I ( x)
f1 ( y ) |2 dy
2
K (y
x) | I ( x)
f 2 ( y ) |2 dy
(
|
|
)
The parameters are chosen as
(
1
(
2
|
1,
|
)
1
0.01 2552 , and
3.