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

 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)

(1a)

To embed a 0:

'( 1)

'( 2)

(1b)

where

X'(f1) and X'(f2) are the modified spectral

components at frequencies f1 and f2, and

and

are the phase angles of the original spectrum at f1

and f2. The constants

and

are adapted based

on the average power of each segment. Typically,

is larger than

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

and

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)

0, if 2

(1)

⎧⎫

⎪⎪

⎨⎬

⎪⎪

⎩⎭

(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

and

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

ICINCO 2006 - ROBOTICS AND AUTOMATION

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

A TECHNIQUE FOR IMPERCEPTIBLE EMBEDDING OF DATA IN A COLOR IMAGE

515