Cryptography Reference
In-Depth Information
Secondly, our next task is to determine how much image data we can dis-
card without deteriorating the image quality, or, rather at what complexity
does the image data become indispensable. To discard data means to replace
local image areas in a bit-plane with random noise patterns. If we replace all
the local areas having complexity value α
L
≤α, yet the image still main-
tains good quality, then perhaps we can discard more. If the quality is no
longer good, then we can not discard that much. If α
L
= α is the minimum
complexity value to be good, such α
L
is used as the threshold value.
To be indispensable, or rather informative, for an image means the fol-
lowing. If the image data is still picture-like after we have discarded (ran-
domized) a certain amount of image data for such an α that α≤α
U
,and
if we discard more, then it becomes only noise-like. Then, that α
U
is re-
garded as the limit of the informative image complexity. If α
L
and α
U
coincide
(α
0
= α
L
= α
U
), we can conclude α
0
is the complexity threshold to divide
informative and noise-like regions in a bit-plane.
We made a random pattern replacing experiment on a bit-plane of a
color image. Fig. 8.3 illustrates the result. Fig. 8.3 shows that if we randomize
regions in each bit-plane which are less complex than 0.5−8σ, the image can
not be image-like any more. While, we can randomize the more complex re-
gions than 0.5−8σ without losing much of the image information. This means
the most of the informative image information is concentrated in between 0
and 0.5−8σ in complexity scale. Surprising enough, it is only 6.6710
−14
%
of all 88 binary patterns. Amazingly, the rest (i.e., 99.9999999999999333%)
are mostly noise-like binary patterns.
A) Original image
B) Randomization
C) Randomization
(simple side)
(complex side)
Fig. 8.3.
Randomization of the less and the more complex than 0.5−8σ.
The conclusion of this section is as follows. We can categorize the local
areas in the bit-planes of a multi-valued image into three portions: (1) Natural
informative portions, (2) Artificial informative portions, and (3) Noise-like
portions. The reason we categorize the excessively complicated patterns as
informative is based on our experiments [7]. The most important fact here
