Image Processing Reference

In-Depth Information

Proposition 1

d
p
(
F
,
G
) is invariant under a translation. Let
F
+
a
(
x
) =
F
(
x
−
a
) be the CDF of
X
+
a
, a transla-

tion of the original random variable. Then

Proof

The CDF of
X
+
a
is
F
+
a
(
x
) =
F
(
x
−
a
)

Proposition 2

d
p
(
F
,
G
) is invariant under a reflection. Let
F
− 1
(
x
) be the CDF of −
X
, a reflection of the ori-

ginal random variable. Then

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