Image Processing Reference
In-Depth Information
U
0
U
1
U
2
0
@
1
A
0
@
1
A
0
@
1
A
000
010
000
000
101
000
000
−
101
000
U
3
U
4
U
5
0
@
1
A
0
@
1
A
0
@
1
A
010
000
010
101
000
101
−
101
000
−
101
U
6
U
7
U
8
0
@
1
A
0
@
1
A
0
@
1
A
0
−
10
000
010
−
10
−
1
000
101
10
−
1
000
−
101
F
F
C
0
@
1
A
0
@
1
A
0
@
1
A
124
232
002
3 2 0
1
/
4
/
4
−
1
−
3
/
4
−
1
/
4
124
232
002
Fig. 3.6. The discrete image
F
can be expanded as the sum of the basis vectors
U
0
,
U
1
,
···
,and
U
8
weighted with the expansion coefficients that are placed in the matrix
C
in a
row major fashion, i.e.,
c
0
=
C
(1
,
2),
c
1
=
C
(1
,
3),
c
2
=
C
(1
,
3),
c
3
=
C
(2
,
1)
···
,
etc. The image intensities, representing matrix values, vary uniformly from black to white as
the matrix values change from
−
1 to 1, except in the
bottom row,
where the gray range from
black to white represents the interval [
−
4
,
4]. The matrix
F
is obtained by summing
c
i
U
i
and
should be identical to
F
10, we will discuss the
discrete local spectrum
and the
structure tensor
at each point
of the image. These pixels will have arrays with two indices as values,
tensor values
.
Tensors constitute Hilbert spaces for which addition, scaling, and scalar prod-
uct rules follow the same rules as arrays with multiple indices. The zeroth and the
