Cryptography Reference
In-Depth Information
Step 1: Generate a set of n random vectors P =p
0
, p
1
,, p
n−1
that
are equally distributed in(t
0
,t
1
,φ)0≤t
0
<N
0
,
0≤t
1
<N
1
,
0≤φ≤2π.
Step 2: Evaluate
Q =f (g (t
0
,t
1
,φ) M)(t
0
,t
1
,φ)∈P=q
0
,q
1
,,q
n−1
Here q
i
,i =0, 1,,n−1 are scalars. Here inter-grid positions are
handled applying bilinear interpolation.
Step 3: Approximate T [f ](M)byq =
n−1
i=0
q
i
.
In this chapter, we only use the global feature, that is one floating-typed
value, calculated from luminance component of the color image.
1
n
Statistical Moments of the Color Histogram
Generally speaking, texture feature extraction methods can be classified in
three major categories. These are as follows, Statistical, Structural and Spec-
tral. In statistical approaches, texture statistics such as the moments of the
gray-level histogram, or statistics based on the gray-level co-occurrence ma-
trix are computed to discriminate different textures. In this chapter, statistical
moments of the gray-level histogram are used to describe texture. Let z be a
discreet random variable representing gray-levels in the range [0,L−1], where
L is the maximum gray value. Let p (z
i
) ,i =0, 1,,L−1 be a normalized
histogram. Then the n-th moment with respect to the mean is given by:
L−1
−m)
n
p (z
i
)
µ
n
(z)=
(z
i
(11.29)
i=0
where m is the mean value of z, that is, the average gray level
L−1
m =
z
i
p (z
i
)
(11.30)
i=0
The second-order moment, variance, is a measure of gray-level contrast.
And the third-order moment is a measure of skewness of the histogram and
the fourth-order moment is a measure of its relative flatness. In this chapter,
we use the mean value m and three moments µ
2
(z) ,µ
3
(z) ,µ
4
(z)ofeach
color components histogram in RGB color space. That is, four floating-typed
values per color-component, as the features which are to be embedded.
Hu Moments
Hu moments are a set of algebraic invariants that combine regular moments
[39]. They are invariant under a change of size, translation, and rotation. Hu
