Graphics Reference
In-Depth Information
Fig. 1.4.
Possible behavior of
f
a
(
x
)when
f
(
x
) is constant. (a) Considering local
maxima/minima of
f
a
(
x
); (b) considering global maximum/minimum of
f
a
(
x
),
•
denotes the position of key pixel.
Proof
: When the key pixels are on the horizontal line at
x
=
c
, it follows from
the definition of key pixel that
either f
(
c
)
>f
(
x
)
or
f
(
c
)
<f
(
x
)
in both the intervals [(
k
1
−
δ
1
)
,K
1
] and [
K
2
,
(
k
2
+
δ
2
)], where
f
(
x
) is constant
in [
K
1
,K
2
]and
δ
1
,δ
2
∈{
.Thus,
(1) the pixels at
K
1
and
K
2
are either corner connected or direct connected
or its combination to the neighboring pixels outside the interval [
K
1
,K
2
]; or
0
,
1
}
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