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1 On a Correlation-based Scheme of Digital Watermarking for Images Exploiting 2-D LOT Hiromu KODA and Kyousuke KAMINUSI Abstract In this paper, we propose a correlation based scheme of digital watermarking for images exploiting 2-D LOT (Lapped Orthogonal Transform). First we describe the definition of LOT and measure the level of energy compaction in LOT domain by calculating the coding gain. Next we explain basic procedures for the embedment and detection of watermark information taking the above result into account. Finally we perform the computer simulation for some test images in order to examine the availability of our scheme. The experimental results show that our scheme using LOT provides better performance than the scheme using DCT (Discrete Cosine Transform) and that the property of BER (Bit Error Rate) can be improved by introducing a bipolar model into our scheme. Keywords : Didital watermarking, Lapped orthogonal transform, Coding gain, M-sequence, Bipolar model, Bit error rate [][] [] [] [][] [] YAXA X A A []

2 XNN N PNN Y N N NN GIRL MOON AERIAL COUPLE DCT LOT [] k k [] k [] [] (n)n L() () n p p () pp k E1 N N N N

3 Y u (i)(i N u N B ) N B ( N N ) i un B D1Y u (i) D u (i) E2 Y u (i) Y u (i)(i ssslu N B )Y u (i) Ỹ(j)(j N B l ) D1 Y u (i)d u Ỹ(j) D (j) E3 kw(n) nll E4E1Y u (i) E3 Ŷ(j) NN D1 E1E2D (j)(j N B l) D (j)ŷ(j) D2 LD (n)d (jl) (n)n L E[] [][] E1 N N NN Y u (i)(i N u N B )N B ( N N ) i un B D1Y u (i)d u (i) E2 Y u (i) Y u (i)i ss slu N B u Y u (i)(y u (i)) Ỹ (j)(ỹ (j))j N B l D1Y u (i) Y u (i) D u (i)d u (i)ỹ (j)ỹ (j) D (j)d (j) E3 kw(n) (nll) E4E1Y u (i) E3Ŷ (j)ŷ (j) NN D1 E1E2D (j)d (j) j N B l D (j)ŷ (j)d (j)ŷ (j) D2D (j)d (j) D3LD (n)d (jl) W(n)n L E[D (n)w(n)] L L n D (n)w(n)

4 E[] NN E2 sl [][] [] [] [] [] [][] [][] [][] [] [] (sl) [] [] [] [] []

5 [][] sl []sl[] [] [] [] [] NN [] [] [] () [] () [] [] () [] () [] () [] () [] [] ()

6 SNR[dB] SNR[dB] SNR[dB] SNR[dB]

7 SD SD SD SD

8 P [][] COMPRESSION RATIO COMPRESSION RATIO COMPRESSION RATIO COMPRESSION RATIO P NN Z NN D e NN D o NN J NN JI(NN) Z I T i NN i [] θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 N =8.13π.16π.13π N = P S Z L(NN)[] P P S ZL

9 N N Y(m) Y(m)m N W(n)n LL W (n) Y(j)(j L ) L (N ) kw(n) Y(j) [] Ak [] k N N lal l N N k [] k [] SNR[dB] GAIN theoretical value measured value [db] [db] [db] [%] k k k k

10 k D (j)d (j) D (j) L Ỹ (n) Ỹ (j L)Ỹ (n) Ỹ (j L) W(n)W(j L) D (n) Ỹ (n)ỹ (n) W(n) W(n) E[W(n)] E[W (n)] E[W(n) W(n)] ( ) k

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