1. Outline Carrier design Embedding and extraction for single tile and Multi-tiles (improving the robustness) Parameter α selection and invisibility Moment Normalization Rotation/Scale Detection

2. Carrier Implementation 1 Carrier is implemented in frequency domain Carrier has random phase The amplitude of Carrier is high pass in order to make it invisible in spatial domain Carrier should be symmetric in frequency domain in order to make its imaginary part to 0 in spatial domain

3. Carrier Implementation 2 High-pass vs. All-pass

4. Carrier Implementation 3 Auto correlation of Carrier function should approximate delta function The average of Carrier should be 0

5. Carrier Implementation 4 if Carrier is not symmetric in frequency domain

6. Embedded Message * Convolution is implemented by multiplication of Fourier transform in frequency domain Zero padding must be performed before FFT

7. Tiling Improves the Robustness

8. After 8 by 8 tiling, the summation of tiles is shown at right The amplitude of the input image will be averaged to flatten after summation of 64 tiles The watermark information is amplified

9. Parameter α = 0.1 α = 0.05 α = 0.1 α = 0.3 α = 0.5 α = 0.7

10. Similarity vs. α Similarity is measured by cross correlation between original and extracted log 64 tiles were used in embedding The α controls the visibility of the watermark logo in the watermarked image The α also depends on the number of tiles

11. Attacked by low pass filter The watermarked image is blurred The extracted logo is equivalent to original log convolve with a low pass filter

12. Moment Normalization Preprocessing to remove the high amplitude, low frequency noise At flat area, v’ is replaced by random number with variance of σ d

13. Rotation/Scale Detection Threshold and image Dilation

14. Rotation/Scale Detection Image rotation