A TECHNIQUE FOR IMPERCEPTIBLE EMBEDDING OF DATA
IN A COLOR IMAGE
Kaliappan Gopalan
Department of Electrical and Computer Engineering, Purdue University Calumet, Hammond, IN 46323, U.S.A.
Keywords: Image embedding, Spectrum modification, Visual masking, Steganography, Data hiding.
Abstract: A method of embedding data in a color image for applications such as authentication of an employee
carrying a picture identification card is described. By converting the color image to a one-dimensional
signal in red, green, or blue, audibly masked frequencies in the 1-D signal are determined for each segment
or block. Embedding of data, such as key biometric information of the person, is carried out by modifying
the spectral power at a pair of commonly occurring masked frequencies. Preliminary results show that the
spectrum modification technique is simple to process and causes barely noticeable distortion in the
embedded image. Using an oblivious technique and a key consisting of the frequencies where spectrum is
modified, successful data retrieval with no bit errors has been achieved. Embedded image corrupted by low
level noise still retained the hidden data with low bit errors. Higher payload of hidden data can be obtained
at a cost of perceptibility of embedding.
1 INTRODUCTION
Data embedding employing a host image is a useful
means for storing or hiding information.
Information is hidden in a cover image in such a
way that the embedded image (the stego) is
indiscernible from the unembedded cover image.
By concealing information imperceptibly in the
cover image and using a strong key, attempts at
illegal recovery and/or tampering of hidden data are
foiled. An imperceptible embedding technique that
can also accurately recover the embedded
information without requiring the cover image, i.e.,
by an oblivious method, can be used in covert
communication (Petitcolas, et al, 1999
).
Another key application area of image
embedding is in hiding vital medical or biometric
information of employees in their pictures for ready
access in case of an emergency, or for secure
identification (Wu and Liu, 2003). A small amount
of distortion in image quality in such applications
may be tolerable as long as data robustness is
guaranteed. While imperceptibility is critical for
covert communication, data robustness and payload
are vital in personnel authentication applications
with, preferably, oblivious data extraction.
We present a method of embedding data in a
color image that requires a key for retrieval. Image
distortion causing perceptibility of embedding is
minimized at a cost of lower payload. This method
is proposed as an extension to prior work on spectral
domain audio embedding by tone addition (Gopalan,
et al 2003) and gray level image embedding
(Gopalan, 2006), both using spectral domain
modification.
2 SPECTRAL DOMAIN
EMBEDDING
Imperceptibility of embedding data in an image can
be achieved by exploiting the imperfection in the
human visual system (HVS). Based on the results of
secure embedding in the spectral domain of audio
signals, the proposed technique for image
embedding relies indirectly on the masking property
of the HVS. In the case of audio embedding at
psychoacoustically masked audio frequencies, a two
step procedure has been reported (Gopalan, et al
2003). In the first, a set of auditorily masked
spectral points for each frame of a given cover audio
signal is determined. These frequencies depend on
the just noticeable difference (JND) in hearing and a
512
Gopalan K. (2006).
A TECHNIQUE FOR IMPERCEPTIBLE EMBEDDING OF DATA IN A COLOR IMAGE.
In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 512-515
DOI: 10.5220/0001211105120515
Copyright
c
SciTePress
global masking threshold based on a set of critical
band filters.
Modification of the spectrum is carried out in the
second step by setting the power levels at the two
masked frequencies in a known ratio for bits 1 and 0.
The pair of frequencies and the power ratio of the
two masked spectral components (and the frame
indices, if only a selected frames carry hidden data)
form the key for embedding and retrieval of data.
Average power levels set to one-tenth and one-
hundredth of the segment power at masked
frequencies has been observed to result in inaudible
and robust hiding of information. Since spectral
domain modification at the two frequencies is at
relatively low power levels and it is spread across all
time samples in a segment, the embedded (stego)
audio is rendered imperceptible from the original
(cover) audio in waveform, spectrogram and
audibility.
Extension of spectrum modification at selected
frequencies for image embedding and its
implementation are described in the following
sections.
3 IMAGE SPECTRUM
MODIFICATION PROCEDURE
To extend the above two-step audio embedding
algorithm for hiding data in an image, a common
pair of visually masked spectral points can be
determined using psychovisual contrast or pattern
masking frequencies from the discrete cosine
transform (DCT) of each block of an image.
Alternatively, a simpler one-dimensional approach,
similar to the determination of psychoacoustically
masked frequencies for an audio signal, can be used
in place of detecting the JND in the image. This
approach can be further simplified by converting the
two-dimensional intensity level of a color host
image in one of the three primary colors to one-
dimensional signal by appending all the rows (or
columns) sequentially. (It has been shown that by
treating each block of 8x8 subimage as a frame (by
conversion to one-dimensional data) of ‘audio’ and
appending all the blocks together causes noticeable
distortion in the image after spectrum modification
(Gopalan, 2006).
Choosing a high enough ‘sampling frequency,’ a
pair of most commonly occurring masked
frequencies in all frames (of typically 64 pixel
samples each) are obtained by determining global
masking threshold and setting an acceptable level of
spectral density below this level for each frame.
(Although the choice of sampling frequency is
empirical, a high value – above 10,000 Hz – gives
more masked frequencies, which contribute to a
stronger key for embedding and retrieval.) Spectral
power levels at the selected pair of frequencies in
each frame are set by a known ratio for embedding
binary values. An advantage of this conversion and
embedding is that it entails less computational effort
and faster detection of embedding points compared
to a DCT-based procedure.
A pair of most commonly occurring masked
frequencies f1 and f2, in part, form the key for
embedding and retrieval. Complex spectrum at each
of the two frequencies is modified to attain
imperceptibility of embedding. Since the two
audibly masked frequencies may not be present in
all the segments, raising their power levels based on
the global audio masking threshold for a given frame
may result in discernibility of embedding in the
overall audio and, hence, image. To prevent this,
power levels at f1 and f2 are set to low levels in each
segment. If X(f1) and X(f2) are the spectral
components at frequencies f1 and f2 in the original
segment, the spectrum-modified (i.e., data-
embedded) segment is obtained as follows.
To embed a 1:
1
2
'( 1)
'( 2)
j
j
X
fe
X
fe
θ
θ
α
β
=
=
(1a)
To embed a 0:
1
2
'( 1)
'( 2)
j
j
fe
fe
θ
θ
β
α
=
=
(1b)
where
X'(f1) and X'(f2) are the modified spectral
components at frequencies f1 and f2, and
1
θ
and
2
θ
are the phase angles of the original spectrum at f1
and f2. The constants
α
and
β
are adapted based
on the average power of each segment. Typically,
α
is larger than
β
so that the spectrum at one of
the two frequencies is higher than that at the other
frequency. Both values, however, are small enough
so that they are not visible in the spectrogram
(histogram) of the audio (image) signal and large
enough to be not lost in quantization after
embedding. The values for
α
and
β
are set
empirically for a given cover image.
Modified frame spectrum is transformed to time
domain, quantized to the same number of levels as
A TECHNIQUE FOR IMPERCEPTIBLE EMBEDDING OF DATA IN A COLOR IMAGE
513
the cover image, and converted back to two-
dimensional image.
Embedded information in each segment is
recovered by the spectral ratio at the two (key)
frequencies, f1 and f2. That is, the recovered bit rb
in a segment is given by
(1)
1, if 1
(2)
(2)
0, if 2
(1)
Xf
b
Xf
rb
Xf
b
Xf
⎧⎫
>
⎪⎪
⎪⎪
=
⎨⎬
⎪⎪
>
⎪⎪
⎩⎭
(2)
where X(f) is the spectral component of the
embedded and quantized frame at cyclic frequency f,
and b1 and b2 are set empirically. If a segment is
left unembedded for added security or when the data
size is smaller than the available capacity, spectral
levels at the two frequencies are set equal; this
corresponds to a retrieved ‘bit’ of -1.
The key for embedding and retrieval consist of
the indices of the embedded frames and the
corresponding frequency pair used to modify
spectrum. This key, clearly, depends on the cover
image. Both the variability and the presence of
many masked points make it harder for illegal
retrieval and/or tampering of data by an exhaustive
search of possible embedded frequencies.
4 IMPLEMENTATION AND
RESULTS
Results of the two-step image embedding algorithm
using the gray scale cameraman image
(cameraman.tif) available in MATLAB showed that
embedding at a pair of high frequencies, even
though they are not the most commonly occurring
masked frequencies, caused little noticeable
distortion and zero bit error in data recovery
(Gopalan, 2006). Based on these results, the
technique was applied to embedding data in one or
more of the primary colors in a JPEG color image.
This image (kid.jpg) of 289x200x3 pixels was
converted one-dimensional signal in each of the
three colors by appending all the rows of pixel
values together. Using an arbitrary sampling
frequency of 16,000 Hz, the masked frequencies for
each color were obtained. The pair of frequencies,
4875 Hz and 6250 Hz, which were in the masking
set of approximately 30 percent of the segments for
all three colors, resulted in minimal distortion of
embedded image with each of the three colors. For
the size of 289x200 = 57800 values in the one-
dimensional signal, a maximum of 57800/64 = 903
bits can be embedded when all the frames of 64
pixels each are used.
To test the image quality with this full capacity,
(a) all bits of 1, (b) all bits of 0, and (c) a random set
of 903 bits, were used each for the data with the
constants
α
and
β
set at a ratio of 1E-5 from the
average power of each segment. The resulting
image for (a) is shown in Figure 1 along with the
original cover image. Using a spectral ratio of b1 =
b2 = 1 in Eq. (2), all the embedded bits were
retrieved correctly from the modified and quantized
image. Perceptibility of embedding, as can be seen
from the figure, appears to be minimal. Same results
in data recovery were observed for the other two
cases as well. Image distortion was more noticeable
for green and red colors relative to modifying blue,
however, due to lower sensitivity of HVS to small
changes in blue than to green or red.
Extending the embedding procedure to more
than one color using the same pair frequencies
showed a slightly noticeable distortion in the image.
Figure 2 depicts the image resulting from modifying
spectrum in the color pair red-blue. (Although, for
simplicity, the same frequency pair has been used in
all the cases, the key can be made stronger with
different frequency pairs for each case.) Visibility
of embedding appeared to be more for green-blue
modification than for red-green; red-blue pair
showed the least distortion in image quality. As
with the single color modification, this is due to the
higher threshold of HVS in perceiving changes in
red and blue. With a total of 2x903 = 1806 bits, the
doubling of payload can be exploited for embedding
data of larger sizes. Considering that the payload is
doubled, the distortion may be tolerable in pictures
such as in a driver license, for example.
Altering the spectrum at the same pair or, at
different pairs, of frequencies at all three colors
tripled the payload at a cost of higher visibility.
Since data recovery caused no bit errors, the
increased payload can be used to strengthen the key
by selecting frames for embedding, which can also
reduce image distortion.
5 CONCLUSION
A method of embedding data on a color image by
converting the image to a one-dimensional signal in
each color, or more than one color, has been
proposed. By altering the one-dimensional spectrum
of each segment of a cover image at two key
frequencies, embedding becomes barely noticeable.
Availability of a choice of frequencies
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514
(a)
(b)
Figure 1: (a) Original host image, and (b) Image with blue
color carrying 903 bits of 1’s.
(for the key at which the spectrum is modified)
renders a strong key and makes the hidden data
impervious to unauthorized access. Another
advantage of the technique is that the hidden
information is extracted by an oblivious method;
hence, the proposed method is suitable for
transmitting embedded information using any cover
image regardless of its availability at the receiver.
Additionally, the proposed method can be used to
embed authentication information in the picture of
an employee.
Figure 2: 2 Modifying spectrum in red and blue colors.
A key question that arises from the proposed
method is the lack of correlation between audibly
masked frequencies and the JND in each image
frame. Another is the choice of an appropriate
sampling frequency in the conversion so that an
embedded image is indistinguishable from its
original cover image. Since there is no relationship
between the audibility of a masked tone frequency
and the visibility of a masked pixel, the implicit
assumption in going from one-dimensional (audible)
to two-dimensional (visible) domain may not always
result in imperceptible embedding. The simplicity
of the proposed technique, therefore, must be
weighed against these questions.
REFERENCES
Petitcolas, F.A.P., R.J. Anderson and M.G. Kuhn,
Information hiding – a survey,” Proc. IEEE, Vol. 87,
No. 7, pp. 1062-1078, 1999.
Wu, M. and B. Liu, “Data hiding in image and video .I.
Fundamental issues and solutions,” IEEE Transactions
on Image Processing, Vol. 12 , pp. 685 – 695, June
2003.
Gopalan, K., S. Wenndt, S. Adams and D. Haddad,
“Covert Speech Communication Via Cover Speech By
Tone Insertion,” Proc. of the IEEE Aerospace
Conference, Big Sky, MT, Mar. 2003.
Gopalan, K., “A Spectrum Modification Technique for
Embedding Data in Images,” Proc. of the IEEE 38th
Southeastern Symposium on System Theory,
Cookeville, TN, March 2006.
Original
Stego, R & B
Stego, Blue with all 1's
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