Image Processing Reference
In-Depth Information
pi/12
0
−pi/12
−pi/12
0
pi/12
pi/12
0
−pi/12
−pi/12
0
pi/12
Fig. 10.10. (
Top
) A perfectly balanced image
f
, and its power spectrum,
|F |
2
. The
red circles
represent a concentration of the power. (
Bottom
) The same as on top, except that the image is
rotated with the angle
4
the state of equilibrium of directions when both eigenvalues are equal. Accordingly,
the
balanced direction tensor
is given by
I
11
0
0
I
11
Z
B
=
1
2
(10.43)
which is a special case of the complex structure tensor. The tensor is completely
equivalent to the scalar quantity
I
11
, which determines
Z
B
uniquely which is in turn
an average of the magnitude of
(
f
). This tensor has also been called “isotropic”
[225] and being “ball-like” [161] in other studies. The term isotropic should not be
interpreted as an existence of all directions in the image is a necessity. Figure 10.10
shows two images that contain only two directions and yet they are qualified for the
term. Likewise the term ball tensor should not be interpreted too restrictively such
