Cryptography Reference
In-Depth Information
5.3.1 The Embedding Procedure
The cover image I has hw pixels, and it is first quantized with the color
palette P of n colors to generate the image data X. Before the secret A is
embedded into the image data X, the colors in the palette are clustered by
the proposed clustering technique. The flowchart of the clustering technique
is depicted in Fig. 5.4.
To group the colors in the palette, the frequency of the color in the im-
age data is counted for each color in the palette P . Initially, all clusters can
be represented by S = S
1
,S
2
,,S
m
, where S
i
= c
i
,1≤i≤n, with n
representing the number of the colors in the palette P . Each cluster satisfies
S
i
∩S
j
=∅,fori = j. Therefore, each cluster S
i
has one color c
i
, and the
number of the clusters m is equal to n.
The i-th maximum occurrence frequency of the colors in the palette P
is then selected, beginning with i =1,1≤i≤n. This is included in the
cluster S
i
. To find the closest color of the i-th maximum color occurrence
frequency, the cluster that the closest color belongs to is denoted as S
nearest
.
If the maximum color difference between each color in cluster and each color
in cluster S
nearest
is smaller than the threshold T
γ
, S
i
then S
nearest
can be
merged into the one cluster.
Whether the clusters are merged or not, i is augmented by one for next
round of clustering steps. If two clusters are merged into one cluster the num-
ber of clusters m is decreased by one. The clustering step is terminated when
the number of clusters m reaches the required value, or when i is larger than
the number of colors in the palette n. Fig. 5.5 shows an example of the cluster-
ing scheme. Given a fixed threshold value T
γ
, the clustering result of Fig. 5.5(a)
can be obtained as shown in Fig. 5.5(b).
After the clustering technique is executed, the n colors in the palette are
grouped into m clusters. In the proposed scheme, the cluster ordering-and-
mapping technique and the combination technique are sequentially executed
in order to embed the secret data A into the image data X.
In each technique, we first check the whether the image data X(i, j)ofone
color pixel is embeddable. Only embeddable pixels are used in the embedding
procedure. To determine whether one pixel is embeddable, two threshold val-
ues T
α
and T
β
are adopted. One pixel is embeddable if it satisfies the following
requirements.
1. The number of distinct clusters in the four neighboring pixels is larger
than T
α
.
2. The maximum cluster difference is less than T
β
. The Cluster Difference is
the difference between the center of a cluster and that of another cluster.
3. When the size of a cluster is equal to one, if the replaced cluster of X(i, j)
is embeddable, then the pixel is an embeddable pixel.
On the first round, we embed a secret bit into X(i, j), where the size
of the cluster is one using the Cluster Ordering-and-Mapping Technique.
