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Digital Picture Processing, 2nd Edition
book

Digital Picture Processing, 2nd Edition

by Azriel Rosenfeld, Avinash C. Kak
January 2014
Intermediate to advanced content levelIntermediate to advanced
435 pages
18h 42m
English
Morgan Kaufmann
Content preview from Digital Picture Processing, 2nd Edition
82
4
Digitization
We have shown that
the
sampling strategy
and g(r) as
dictated
by (22)
minimize
the
mean square error
e as
given
by (18). We
will
now
show that
for bandlimited random fields (S
ff
(w)
= 0
outside
a
finite region
9* in the
wy-plane) this error
is
indeed zero.
Substituting
(22) in (19), we
have
for the
minimum mean-square error
e
=
R
ff
(0)
- H^fr-y^P-rJ (24)
m η
which
can be
expressed
as
e
=
/?„(0)-J*,,^)^^
(25)
We will
now
examine
the two
terms
on the
right-hand side separately.
From
Eq. (104) of
Chapter
2, the
first term
is
R
ff
(0)
=
js
ff
(w)dw
(26)
As regards
the
second term,
the
Fourier transform
of the
product R
ff
(r")
g(r')
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Publisher Resources

ISBN: 9780323139915