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A Hybrid SVD and Wavelet based Watermarking

A Hybrid SVD and Wavelet based Watermarking. S. Majumder , M. Mishra, A. D. Singh Dept of Electronics & Communication Engg., NERIST (Deemed University), Arunachal Pradesh, India. DWT (Discrete Wavelet Transform). Single level Discrete Wavelet Transform steps to extract approximate image.

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A Hybrid SVD and Wavelet based Watermarking

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  1. A Hybrid SVD and Wavelet based Watermarking S. Majumder, M. Mishra, A. D. Singh Dept of Electronics & Communication Engg., NERIST (Deemed University), Arunachal Pradesh, India

  2. DWT (Discrete Wavelet Transform) Single level Discrete Wavelet Transform steps to extract approximate image

  3. SVD (Singular Value Decomposition) SVD operation on image I

  4. Embedding the Watermark

  5. Embedding Algorithm: • Take the Image to be Watermarked & undergo 2D DWT to get CA, CH, CV & CD • On each of the 4 coefficient blocks perform the SVD operation to get U, S & V [UCA, SCA , VCA, UCH, SCH , VCH, UCV, SCV , VCV, UCD, SCD & VCD] • Get S'CA=SCA + KEY x (iterated logo); Similarly S'CH , S'CV & S'CD • Perform SVD operation on S'CA , S'CH , S'CV & S'CD to get U1, S1 & V1 [U1CA, S1CA , V1CA, U1CH, S1CH , V1CH, U1CV, S1CV , V1CV, U1CD, S1CD & V1CD] • Now get watermarked coefficients (CAW, CHW, CVW & CDW) by CAW=UCA*S1CA*VCAT • Similarly get the key image coefficients (CAK, CHK, CVK & CDK) by CAK=U1CA*SCA*V1CAT • Finally get Watermarked image by IDWT of (CAW, CHW, CVW & CDW) and Key image by IDWT of (CAK, CHK, CVK & CDK)

  6. Extracting the Watermark

  7. Extracting Algorithm: • On receiving the watermarked Image (which may or may not be corrupted) perform the DWT to get (CAW, CHW, CVW & CDW) • Similarly for the key image stored in the reciever the DWT is performed to get (CAK, CHK, CVK & CDK) • On each of the 4 coefficient blocks of the watermarked image perform the SVD operation to get UW, SW & VW [UCAW, SCAW, VCAW, UCHW, SCHW, VCHW, UCVW, SCVW, VCVW, UCDW, SCDW & VCDW] • On each of the 4 coefficient blocks of the key image perform the SVD operation to get UK, SK & VK [UCAK, SCAK, VCAK, UCHK, SCHK, VCHK, UCVK, SCVK, VCVK, UCDK, SCDK & VCDK] • For each coefficient block get Difference matrix DCA=UKCA*SWCA*VKCAT to get DCA, DCH, DCV and DCD. • Find the difference of each of the Difference matrix with the diagonal matrix of the key image to get the corresponding logo coefficients using get CAL= (1/KEY)x (DCA - SCAK ); Similarly CHL, CVL & CDL and finally doing IDWT get the logo Extracted Image.

  8. Attacks: Various possible simulated attacks like sharpening, histogram equalization, rescaling, cropping, low pass filtering, median filtering etc. were applied on the watermarked image to check the robustness of the watermarking technique. The corrupted watermarked images after attack have been evaluated on basis of peak signal to noise ratio (PSNR) which is one of the most popular methods for quality checking for images. Mean Square Error: For m x n image: Peak Signal to Noise Ratio:

  9. Hybrid SVD and wavelet based watermarks extracted after the different attacks:

  10. Result and Analysis: PSNR values obtained for the three different standard test images (256x256) on embedding of the iterated watermark using the hybrid technique and their respective variations on the application of different attacks with the original image:

  11. Conclusion: The hybrid technique using SVD and wavelet based watermarking system is Robust as even after the different popular attacks that images undergo, we still are able to extract the watermark and it is visibly detectable. Normally the use of iterated logo for watermark normally degrades the PSNR of the watermarked image significantly. But this was overcome by the usage of SVD technique where the logo is actually hidden with the eigen values of the image matrix, which are actually distributed throughout the spatial as well as the frequency domain due to the usage of the DWT technique before SVD implementation and distribution via IDWT after SVD operation. Moreover we see that when the image is scaled the watermark is scaled as well but the legibility of it is at par with that of the image and in cases like image resizing and low pass filtering the logos at the lower right corner disappear but the top left become brighter and an extra vertical logo series comes up to reinforce it to some extent. Images with PSNR as low as 14dB we can still extract a visibly good logo.

  12. Future Scope: Implementation of error control coding on the logo bits, for better detection (even after some bits are corrupted) Checking with some international standard attacks like ‘Chekmark’ Combining the equations of DWT and SVD to form a single equation to reduce the quantization error. Thank You!

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