2. » Copying images is easy » Distributing images is easy » But what if we want to protect our rights to an image?

3. » Embedding data into an image » Format may change » Data must be stored in the actual pixels

4. » Visible watermark » Invisible watermark

5. » Copyright identification » Fingerprinting » Authenticity determination » Monitoring » Data hiding

6. » Often a weighted sum of two images

9. » Doesn’t reduce usability » Store the watermark in imperceptible data » Image is slightly changed, but appears unchanged

10. » Examine the contribution of each bit » For PGM images each pixel is an eight bit value » A bit plane is a binary image representing each bit

12. » Lower bits (LSB’s) contain noise » We don’t perceive them » Idea-Hide data in LSB’s of the image

14. » Can hide a whole image in another » 4 LSB’s changed

15. » What happens if we use lossy jpeg compression? » LSB’s are changed! Retrieved Watermark

16. » Lossy compression » Geometric transformations » Intensity transformations » Rewatermarking

17. » Imperceptible » Undeletable » Robust to attacks » Undetectable - even with multiple images watermarked by the same author

18. » Take the discrete cosine transform » DCT compacts energy » Store data in the most important frequency components

19. » Step 1: Take the 2D DCT

20. » Step 2: Locate the K largest coefficients by magnitude » Step 3: Create a watermark by generating a K- element pseudo-random numbers ω 1, ω 2,…, ω K » Use mean μ=0 and standard deviation σ=1 for random numbers

22. » Change in image is very small (1) Original (2) Watermarked (3) Difference scaled up

26. Lossy JPEG Compression with an rms error of 7 intensity levels Lossy JPEG Compression with an rms error of 10 intensity levels Smoothing by spatial filtering

27. Gaussian noise Histogram EqualizationRotation