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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
150
5
Compression
Equation (123) is used to obtain the following result:
[β]"
1
®
[ß]"
1
=([Φ][Π[Φ])®([Φ][Γ][Φ])
= ([Φ] ® [Φ])(([Γ][Φ] ® [Γ][Φ])) (124)
where we have used the identity
(M[B])
® ([C][D]) = (M ® [C])([ß ] ® [£>] )
Using th e sam e identit y agai n fo r th e secon d lef t direc t produc t i n (124) , w e
get
[βΓ
1
®
[βΓ
1
= ([Φ] ®])([Π ® [Γ])([Φ] ® [Φ]) (125)
which shows that the matrix of the eigenvectors of] ~
1
®] "
1
is given
by] ® [Φ], since] ®] is an Ν
2
χ Ν
2
diagonal matrix.
Let Η be the Karhunen-Loeve transform of the modified data vector h.
If Ψ„, is the mth eigenvector of [β]"
1
® [β]"
1
(i.e., the N
2
element ...
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Publisher Resources

ISBN: 9780323139915