Fig 4. Haar DWT based logo extraction with Rotational attacks.

1. Introduction

With the rapid growth of multimedia and internet technologies the enforcement of copyright protection becomes an important issue. Cryptographic tools can only protect digital assets during transmission but once the encrypted content is decrypted it does not stop its illegal distribution. Watermarking is ’security by obscurity’. Digital watermarking is a technique for embedding information into multimedia data such that it is imperceptible and irremovable. Watermarking is integrated into content itself, so that no additional storage space is required. Image watermarking is increasing becoming popular as a possible solution for the protection of intellectual property rights.

Spatial domain watermarking methods are easy to implement but often fail under image processing attacks. Also the fidelity of the original image data can be severely degraded since the watermark logo is directly applied on the pixel value. Frequency domain logo watermarking methods provide more protection under most of the image processing attacks, that is, they are more robust than the spatial counterpart. The frequency domain of the image is viewed as a communication channel, and watermark is viewed as a signal that is transmitted through it. Attacks and unintentional signal distortions are thus treated as noise that the immersed signal must be immune to. The success of watermark for intellectual property rights management depends on how easily it is adopted with common policy and how effectively infringement cases are addressed. In general, all the watermarking schemes consist of three parts namely, Watermark, Encoder and Decoder. Digital Logo Watermarking is viewed as an effective way to determining content users from illegal distributing, that is, it is the process by which an image is coded with an owner’s logo and can be done using frequency domain methods. The most important features watermarking techniques should exhibit are unobtrusiveness and robustness i.e. it is required that a logo is accurately hidden into the image data in such a way that it is very difficult to be perceived and removed. Another important characteristic is blindness i.e. the watermark decoder must not require the original non watermarked image for extracting the embedded logo. Discrete Fourier transform, Discrete Cosine Transform, Fourier Mellin transform, Fractal transform and other transforms are used for image and video coding but recent researchers give more attention on wavelets as they are capable of providing time and frequency localization simultaneously. Hence we have used wavelet transforms for implementing our proposed scheme for digital logo watermarking in images.

2. Human Visual System

Today it is widely accepted that robust image watermarking technique should largely exploit the characteristics of Human Visual System. The recent research in the field of watermarking states that wavelet transform is more suitable to model the HVS behavior. The proposed Watermarking scheme embeds and extracts the watermark in Discrete Wavelet Transform (DWT) domain which addresses robustness against an optimistic number of image attacks while maintaining perceptual transparency of the watermarked image.

Maar’s theory states that Image Processing in the HVS has a complicated hierarchal structure that involves several layers of processing. At each processing level, the retinal system provides a visual representation that scales progressively in a geometrical manner. In order to embed the watermark into images we have to consider how the eye perceives disturbances.

The HVS has the following properties

1.Brightness Sensitivity – It refers to the sensitivity of the human eye to perceive a watermark in the presence of backgrounds of different intensity. The eye has high sensitivity at low intensity levels and greatly reduced sensitivity at high intensity levels.

2. Frequency Sensitivity - Psycho visual studies have shown that the HVS has a general band pass characteristic with peak sensitivity between 3 and 4 cycles per degree and reduced sensitivity at higher and lower spatial frequencies.

3. Texture Sensitivity - The visibility of distortion depends on the background texture. The distortion visibility is low when the background has a strong texture. In a highly textured image block, energy tends to be more evenly distributed among the different coefficients. In a flat-featured portion of the image the energy is concentrated in the low frequency components of the spectrum.

The watermark should not be placed in perceptually insignificant regions of the image or its spectrum since many common signals and geometric processes attack these components. e.g.- a watermark placed in the high frequency process that directly or indirectly performs low pass filtering. The problem then becomes how to insert a watermark into the most perceptually significant regions of spectrum without such alternations becoming noticeable. Clearly, any spectral coefficient may be altered, provided such modification is small. However, very small changes are very susceptible to noise.

The DWT is very appropriate to identify the image areas where a disturbance can more easily be hidden. The sophisticated mechanism derived from DWT coding studies is introduced to take into account several HVS phenomena, such as gray level sensibility, isofrequency and non isofrequency masking and noise sensibility around edges. If a DWT coefficient is modified only the region of the image where the particular frequency corresponding to that coefficient is present will be modified, in contrast to DFT/DCT watermarking.

3. Wavelet Transforms

A wavelet is a small wave that oscillates and decays in the time domain. Wavelets can have infinite varieties that are fundamentally different from each other. The wavelets that have strictly finite extent in the time domain are called discrete wavelets and other wavelets are called continuous wavelets.

Wavelet transforms can be used to separate the spectral content of an image from the spatial information. It provides the equivalence of a musical score for an image, revealing not only what notes (frequency) to play but also when to play them. Wavelet based encoding schemes also known as subband coding contains approximate subband (LL) and detailed subbands ( LH, HL, HH). Wavelet Transform understands the Human Visual System more closely than DCT also visual artifacts are much less than the DCT. It is a mathematical transform with its own strong benefits such as outlook, multi scale outlook, cooperation between scales and time scales analysis. It demonstrates that sine and cosine are not only useful function and other bases made strange functions serve to look at new foreign signals, as strong as most fractal or some transient signals.

In FFT, sine function is employed as a base function. A sine function is an infinitive smooth function, therefore, the information obtained by the FFT does not include the local information such as the place and frequency where and which frequency the original signals have. Wavelet based analysis of signals is an interesting tool similar to Fourier analysis. Wavelet analysis is based on a decomposition of a signal using an orthonormal family of basis functions. Unlike sine wave, a wavelet has its energy concentrated in time. Sinusoids are useful in analyzing periodic and time invariant phenomena, while wavelets are well suited for the analysis of transient and time varying signals.

The Morlet-Grossman definition for wavelet transform is all square integral function.

where w(a,b) are wavelet coefficients of the function f(t), ?(t) is the analyzing wavelet and * is the complex conjugate. i.e. the function f(t) is decomposed into a linear combination of a set of bases functions ?_a,b(t)$ which are called wavelets. The variables a,b are scale and translation, the new dimensions after the wavelet transform.

The inverse Wavelet Transforms is represented by

The basic set of wavelets are generated from the mother or basic wavelet which is defined as

where a reflects the scale of a particular function such that its large value gives low frequency and small value gives high frequency and b specifies translation along x-axis in time. Having very short basis function we can isolate signal discontinuities and having very long basis functions we can obtain detailed frequency analysis.

3.1. Discrete Wavelet Transforms

It can decompose a signal into several components in different octave or frequency bands. DWT offers more useful properties such as adaptive time-frequency windows, inherent scalability, efficient computational complexity and perfect reconstruction. The DWT can be written as

The Inverse DWT is

Let

then the above equation becomes

if j = 0,

i.e. the function f₀(x) is transformed into wavelet coefficients g_-1(x), g_-2(x) , g_-3(x) …

The following wavelets are used in our work for embedding and extracting the logo as watermark in images.

1. Haar Wavelets- It has compact support i.e.it vanishes outside of a finite interval. It employs straightforward addition and subtraction of two members at a time. It is a more sophisticated wavelet using weighted averages and differences involving more than two members of the data sets. It is conceptually simple and fast. It is memory efficient because it does not require temporary array to store intermediate results. A Haar wavelet function H(t) is a simple piecewise constant function defined as

whose dilations and translations generate an orthonormal basis of L²(R).

2. Meyer Wavelets - A Meyer wavelet is a frequency band limited function whose Fourier Transform is smooth;, the smoothness provides a much faster asymptotic decay in time. These wavelets are constructed with conjugate mirror filters ?(w) that are cⁿ and satisfy

3. Mexican Hat Wavelets are equal to the second derivative of a gaussian. They are used to detect mutliscale edges. The normalized Mexican hat wavelet is

4. Daubechies wavelets are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. A vanishing moment refers to the wavelet’s ability to represent polynomial behaviour or information in a signal. Daubechies wavelets are widely used in solving a broad range of problems, e.g. self-similarity properties of a signal or fractal problem, signal discontinuities, etc. Daubechies orthogonal wavelets D2-D20 are commonly used.

with N=2A, p having real coefficients, p(1)=1 and degree(p)=A-1, one can write the orthogonality condition as

(12)

4. Proposed Algorithm for logo watermarking

The following is an algorithm for embedding and extracting the logo into images. The second level LL subband is chosen for embedding the logo for our work.

Embedding scheme

1. Get the host image to be watermark, logo

Image and key.

2. Encode and hash the logo with the key

3. Divide the host image into 8 x 8 blocks

and apply DWT transforms

4. V¹_ij = V_ij + W(i,j) * ? where V¹_ij is the ij^th

watermark embedded coefficients. V_ij is the ij^th DWT coefficient of V and ? is the embedding factor.

5. Take IDWT transform of each block.

Extraction scheme

1. Get the original, watermarked image and

the key

2. Divide both host and watermarked image

into 8×8 blocks and apply DWT transforms to each block

3. Subtract corresponding image blocks.

4. W’(i,j) = (V¹_ij – V_ij )/ ?

5. Compare the extracted logo with the

original logo to make a decision whether the image is authentic or not.

5. Sample Results

The following are the sample images implemented using wavelets. In all these cases, the original image is 128 x 128 and the watermark logo image is 32 x 32.The figures show how the logo is embedded and extracted in host images. From the experience with our images the proposed method works better in general and it is not affecting the quality of the image and maintains some degree of robustness. Also some of the attacked images are shown here to prove the tamper resistance and authenticity.

Fig 1. – Haar DWT based logo watermarking

Fig 2. DFT, DCT and DWT based extracted marks

Fig 3. Haar DWT based logo extraction with various Noises

Fig 4. Haar DWT based logo extraction with Rotational attacks.

Fig 5. Logo extraction from Cropped Image.

6. Conclusion and Further Research

In this paper we have proposed a scheme, which embed and extract the logo watermark in images using wavelets. The scheme embeds the logo by modifying the LL subband DWT coefficients. The extraction scheme detects the hidden logo in an effective way to prove the authenticity. The wavelet based logo watermarking, when compared to the DFT and DCT counterparts, is more robust and also preserves the characteristics of human visual system. In future the scheme will be extended for handling video data and also to address more attacks.

References

[1] Milan Sonka, Vachav Hlavac and Roger Boyle - Image Processing Analysis and Machine Vision

[2] Khalid Sayood – Introduction to Data Compression, Harcourt India Pvt. Ltd., 2^nd Edition 1996, 2000 by Academic press.

[3] Mallat A. – Theory for Multi resolution signal decomposition and wavelet representation – IEEE Transaction on pattern Analysis and Machine Intelligence.

[4] Deepa Kundur – Toward Robust Logo Watermarking Using Mutliresolution Image Fusion Principles – IEEE Transactions on Multimedia – Feb.2001.

[5] Haiping Lu, Alec C. Kot and Jun Cheng – Secure Data Hiding in Binary Decument images for Authentication IEEE Transactions – Mar. 2003.

[6] Houng-jyh Mike Wang, Po-Chyi Su and C-C Jay Kuo - Wavelet-based Digital image watermarking – Optic Express ‘98

[7] C-H. Lee, Y-K. Lee – An adaptive digital image watermarking technique for copyright protection, 1999

[8] Haiping Lu, Alex C. Kot, Rahardja Susanto - Binary image watermarking through biased binarization, ICM 2003.

[9] Raval Mehul S., Rege Priti. P., - Discrete Wavelet Transform based multiple watermarking scheme, IEEE 2003.

[10] Performance Analysis of image compression using wavelets, Sonja Grgic, Mislav Grgic and Branka Zovko_Cihar,member IEEE transactions on Industrial Electronics Vol.48, N0.3, June 2001.

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