Proceedings of the 38th Southeastern Symposium on System Theory Tennessee Technological University Cookeville, TN, USA, March 5-7, 2006
MB5.3
A Spectrum Modification Technique for Embedding Data in Images Kaliappan Gopalan, Senior Member, IEEE
Abstract — We propose a method of embedding data in images for secure communication of covert or sensitive information. The method employs an extension of the recent technique of imperceptible embedding in audio signals by inserting tones at perceptually masked frequencies. Instead of detecting visually masked frequencies in two-dimensions, a simpler approach was used by converting an image to a onedimensional signal. Using the well-established audio frequency masking procedure, audibly masked frequencies at a chosen sampling frequency were determined for each segment or block. Embedding of given data was carried out by modifying the spectral power at a pair of commonly occurring masked frequencies. Preliminary results of embedding 1024 bits of random data in a 256x256 pixel black-and-white image show that the spectrum modification technique is viable and simple to process. The technique is useful for hiding a small amount of information on identification card images, credit card logos, etc. Payload can be increased at the cost of an acceptable level of image degradation.
I. INTRODUCTION
D
ATA
embedding employing a host image is a useful
means for storing information with increased storage capacity and for covert transmission or steganography. Information is hidden in a cover image in such a way that the embedded image (the stego) is indiscernible from the unembedded host, or cover image. An imperceptible embedding technique that can also recover the hidden information accurately and without requiring the cover image, i.e., by an oblivious method, can be used in secure communication [1]. Another key application area is in embedding vital medical and biometric information of employees in their pictures for secure identification and/or data retrieval [2, 3]. By concealing information imperceptibly and using a strong key, attempts at illegal recovery and use of sensitive data are foiled. Use of an oblivious data recovery technique enables deploying any innocuous cover image for carrying battlefield information in covert or secure communication. With the additional requirements of large capacity and robustness of hidden information, development of efficient embedding techniques is highly useful in other areas such as authentication of employees, travelers, security personnel, etc., from their picture identification cards that carry unique security K. Gopalan is with the Electrical and Computer Engineering Department, Purdue University Calumet, Hammond, IN 46323, USA. (Phone: 219 989 2685; e-mail:
[email protected]).
0-7803-9457-7/06/$20.00 ©2006 IEEE.
information. In addition, watermarking of images and video can be used for compliance of digital rights management applications. In this paper we present a method of embedding of data in an image that requires a strong key for retrieval using spectral domain modification. This method is proposed as an extension to prior work on spectral domain audio embedding by tone addition [4-6]. II. SPECTRAL DOMAIN EMBEDDING Based on the results of secure embedding in the spectral domain of audio signals, the proposed technique for image embedding relies on the masking property of the human visual system. In the case of audio embedding at psychoacoustically masked audio frequencies, a two step procedure is used [4]. In the first step, a set of auditorily masked spectral points for each segment (frame) of a given cover audio signal is determined. These frequencies for each short segment of speech depend on the just noticeable difference (JND) in hearing and a global masking threshold based on a set of critical band filters. A pair of masked frequencies that occurs in most segments of the cover speech signal is obtained using a common minimum threshold of sound pressure level (SPL) relative to the global masking threshold of each segment. Since the two frequencies in each segment have SPL below the hearing (global) threshold, an increase in SPL up to the global threshold level (or decrease from its current level) cannot alter hearing perception. Based on this premise, SPL at the two frequencies can be set to a known ratio for each bit value of data. 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 in accordance with the bit value to be embedded in the frame. The pair of frequencies and the power ratio of the two masked spectral components form the key for embedding and retrieval of data. In the case of audio embedding, average power levels set to one-tenth and one-hundredth of the segment power at masked frequencies have been observed to result in inaudible and robust hiding of information [4]. Since the modification to the two spectral points are at relatively low power levels, and the addition is carried out in the spectral domain, the modification is spread across all audio samples in a segment, thereby rendering the embedded (stego) audio indistinguishable from the original (cover) audio.
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Additionally, spreading of embedding makes detection by steganalysis difficult to accomplish. Extension of spectrum modification at masked frequencies for image embedding and its implementation are described in the following sections.
To embed a 1:
X ' (f1)=α .eiθ1 X ' (f2)=β .eiθ2
(1a)
To embed a 0: III. IMAGE SPECTRUM MODIFICATION ALGORITHM
X ' (f2)=α .eiθ2
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 [7]. 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 treating each block of 8x8 image, say, as a frame (by conversion to one-dimensional data) of audio at a suitable sampling frequency; alternatively, the two-dimensional data of a black-and-white image may be converted to onedimensional signal by appending all the rows (or columns) sequentially. With well-established audio masking detection, a pair of most masked frequencies can then be obtained using a ‘sampling frequency,’ and their spectral power levels can be set by a known ratio for embedding. An advantage of this dimensional reduction and spectral modification is that it entails less computational complexity and faster detection of embedding points compared to a DCT-based procedure. Since there is no relationship between the audibility of a masked tone and the visibility of a masked pixel, there is no guarantee that an audibly masked frequency will result in a visibly masked two-dimensional frequency pair, or a masked pixel. To test if modification of some audibly masked frequencies will result in an imperceptibly modified image, extension to the two-step audio embedding is carried out as follows.
X ' (f1)=β .eiθ1
Audibly masked frequencies in the converted onedimensional signal of an image are obtained first using segments of 64 samples, corresponding to 8x8 image blocks, or from row-by-row conversion, and a pair of most commonly occurring masked frequencies f1 and f2, are selected for modification. The two frequencies, f1 and f2, form the key for embedding and retrieval of data. In the second step, 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 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 at low levels in each segment as follows.
where
(1b)
X ' (f1) and X ' (f2) are the modified spectral
components at frequencies f1 and f2, and
θ1 and θ 2
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 by a factor of five or more 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 of the audio signal and large enough to be not lost in quantization after spectrum modification. The values for α and β are, in general, set empirically for a given cover image.
Since the two frequencies f1 and f2 for the embeddable frame are in its masked region, adding or subtracting spectra at these frequencies ensures that the modification results in minimal change in ‘audibility.’ Also, by retaining the same phase as that in the original spectrum at f1 and f2, no phaserelated distortion is introduced by the modification. Spectrum-modified (data-embedded) segment (block) is transformed to time domain, quantized to the same number of levels as the cover image, and converted back to twodimensional image. Data Retrieval: 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 (image block) is given by
⎧ ⎫ X r (f1) > b1 ⎪ ⎪1, if X r (f2) ⎪ ⎪ ⎪ ⎪ X (f2) ⎪ ⎪ rb = ⎨0, if r > b0 ⎬ , X r (f1) ⎪ ⎪ ⎪ −1 (no data ), else ⎪ ⎪ ⎪ ⎪⎩ ⎪⎭
(2)
where Xr(f) is the spectral component of the data-embedded frame (block) at frequency f, and b1 and b2 are set empirically.
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The key for embedding and retrieval consist of the indices of the embedded frames (image blocks), if only a selected frames are used to carry hidden data, and the corresponding frequency pair used to modify spectrum. This key, clearly, depends on the cover (host) image. Additionally, a given cover image may have more than one pair of embeddable (masked) frequencies. Both the variability and the presence of many masked points make it harder for illegal retrieval and/or tampering of data by exhaustive search of possible embedded frequencies.
Original Image
IV. IMPLEMENTATION OF THE ALGORITHM AND RESULTS The two-step image embedding algorithm was implemented using the cameraman image available in Matlab. This black-and-white image of 256x256 pixels was converted to a one-dimensional signal (a) by appending all the rows of pixel values together, or (b) by segmenting into 8x8 blocks and appending the 64 pixel values of the blocks into an array. Using an arbitrary sampling frequency of 16000 Hz, the masked frequencies for each case were obtained. Although many low frequencies were available in the masked set with a majority of frames, spectrum modification at a pair of frequencies below 5000 Hz using Eq. (1) caused noticeable distortion in the image. Instead, a choice of high frequencies at 6250 Hz and 7500 Hz, which were in the masking set of only 10 to 20 segments, resulted in minimal distortion of embedded image using row-wise conversion to one-dimensional signal. The data-embedded image with spectrum modification is shown in Fig. 1 along with the original cover image. With one bit of random value in each frame, a total of 1024 bits were embedded in Fig. 1b with the constants α and β set at a ratio of 1E5 from the average power of each segment. Using a log spectral ratio of b1 = b2 = 1 in Eq. (2), which was determined empirically from spectrum modification for the cases of all 0’s and all 1’s, all the embedded bits were retrieved correctly from the modified and quantized image. (We note that all the available segments of the image were used for embedding; hence, no data of -1, corresponding to an unembedded segment, can result.) Many other pairs of frequencies above 5000 Hz also produced barely noticeable embedding and correct data recovery. We notice a slight visibility of embedding in the background of the image in Fig. 1a, which may appear to render the algorithm unsuitable for steganography or covert communication employing commonly available images. Use of unknown images, however, can mitigate this limitation. Additionally, perceptibility of embedding may not be significant in applications such as hiding a small amount of identification information on the picture of an authorized employee, for example. Modification of spectrum after conversion to onedimensional signal from 8x8 blocks, however, caused
(a) Stego Image, 1024 bits (random)
(b) Fig. 1 (a) Original cover image, and (b) embedded image with 1024 bits significant distortion in the image regardless of the frequency pair used. Although data retrieval resulted in a bit error rate of fewer than 8 out of 1024, changes in the image quality were highly noticeable. A possible reason for this is that spectral change in a small image block is more visible than a similar change in a row of pixels. Fig. 2 shows a case of embedding 1024 bits of random data. From the resulting image and the low bit error rate of 8 out of 1024, it is possible to determine the distorted image blocks and exclude them from spectrum modification. While this may reduce payload, it can improve security of embedded data as imperceptibility is increased; that is, unauthorized retrieval of data is foiled by the lack of embedding in all image blocks.
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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. Still, the simplicity of the proposed technique is useful for hiding a small set of data, such as concealed identifying information, in a driver’s license or other picture where imperceptibility or degradation of the image quality may not be a problem. Robustness of hidden data to noise arising from scanning an embedded image is another question to be considered. Work on this and on extending the technique to color image embedding is in progress.
Stego Image, 1024 bits
REFERENCES [1] [2]
[3]
Fig. 2 Embedded image using 8x8 blocks for spectrum modification
[4]
V. CONCLUSION A method of embedding data in an image by converting the image to a one-dimensional signal has been proposed. By altering the one-dimensional spectrum of each segment of a cover image at two key frequencies, embedding becomes barely noticeable and an oblivious method is used to recover the hidden data. The key used to embed and recover data consists of the two frequencies at which the spectrum is modified; these frequencies are obtained from the psychoacoustically masked spectral points of the onedimensional signal. Availability of a number of frequencies for the key renders the hidden data impervious to unauthorized access. Visibility of embedding, particularly in the background of an image, makes the method suitable for applications (a) that use unfamiliar cover images for steganography, or (b) where the difference in image quality is tolerable. Embedding in blocks of images converted to one-dimension caused more noticeable image distortion and significant bit errors in data retrieval.
[5]
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Embedded data can be made resistant to illegal access by using a different frequency pair for each block. Additionally, payload or hidden data capacity can possibly be doubled by using four frequencies to modify the spectrum. One of the questions that arise from the proposed method is due to 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
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