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F4 overcomes the above drawback by making both even negative and odd positive
coefficients represent a stego-one, and odd negative and even positive represent a
stego-zero. F5 is a combination of F4 and matrix encoding, which embeds
m
bits into
2
m
−1 coefficients using less than one LSB alteration to reduce distortion due to data
embedding. But F5 causes a decrease of image energy because of the magnitude dec-
rement, or shrinkage of histogram. This may provide a clue for steganalysis [10].
By using the LHA approach, a coefficient equal to
j
is changed to either
j
+1 or
j
−1
when it differs from a corresponding hidden bit, where both even negative and odd
positive coefficients are also used to represent a stego-one, and odd negative and even
positive with a stego-zero. There are two exceptions: a coefficient originally equal to
−1 may be changed to −2 or 1, and an original +1 may be changed to −1 or +2. So, the
magnitude and shape of the coefficient histogram is preserved when the LHA technique
is used, and any steganalytic algorithm that explores abnormality in histogram can be
defeated. Fig. 8 shows the histograms of original quantized DCT coefficients and
stego-coefficients of a compressed image Baboon with a quality factor 70. A secret bit
was embedded into the (3,3) coefficient in every 8-by-8 block using F5 and LHA,
respectively. It is clear that the LHA method keeps the histogram of transform coeffi-
cients unchanged whereas F5 causes detectable modifications.
2500
Original histogram
F5-stego histogram
LHA-stego histogram
2000
1500
1000
500
0
-5
0
5
Fig. 8.
Histograms of original quantized and stego-DCT coefficients with F5 and LHA
Quantized values of DCT coefficients (3,3)
4
Conclusion
2
In addition to the χ
test and RS analysis, the presence of secret message based on LSB
replacement can also be revealed by viewing the image as a 3D landscape and counting
the numbers of crossings,
N
0
and
N
1
, through two interleaved families of gray-level
planes,
P
O
and
P
E
. These two families may be referred to as odd and even gray-level
planes. With an increasing amount of embedded information,
N
E
rises whereas
N
O
keeps
unchanged. This leads to a new steganalytic method as named the GPC analysis in this
paper.
All the three steganalytical methods make use of the asymmetry inherent in the
procedure of conventional LSB embedding as only the mapping
F
1
is used. In order to
