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

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

» Visible watermark » Invisible watermark

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

» Often a weighted sum of two images

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

» 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

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

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

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

» Lossy compression » Geometric transformations » Intensity transformations » Rewatermarking

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

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

» Step 1: Take the 2D DCT

» 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

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

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

Gaussian noise Histogram EqualizationRotation