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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
142
5
Compression
In order to minimize the mean-square error between f(ra, n) and f(m, n\
the coefficients a(k, I) must satisfy the following orthogonality conditions:
E[f(m,
ή)- ΣΣ
a
^ W(
m
~Kn- I)
\f(ij)
= 0
i and; = 0, 1,
2,...,
Ν + 1, (ij) Φ (m, n) (79)
Substituting (78) in (79), we get
p
\m-i\
p
\n-)\
_ £ £ φ
9
/)
p
l«-k-i|
p
l»-l-j|
=
0
(k,Z)*(0,0)
ι and; = 0, 1,
2,...,
Ν + 1, (U) Φ (m, n) (80)
Proceeding in a manner analogous to the one-dimensional case, one can
show that when (m, n) is one of the interior pixels (i.e., it is not on the bound-
ary),
the coefficients a(k, /) are given by
a(l,0) =
fl
(0, 1) = a(-1, 0) = α(0, -1) = α
and
a(l,
1) =
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Publisher Resources

ISBN: 9780323139915