Introduction
Watermarking by the method of moments
Adaptive watermarking
Proposed methodology
Watermark embedding
Watermark extraction
Fuzzy inference system (FIS): design principles
Genetic optimization
Experimental study
Experiments configuration
Parameter | Value |
---|---|
Population size | 100 |
Maximum generations | 100 |
Crossover probability | 0.8 |
Mutation probability | 0.01 |
Selection method | Stochastic universal approximation (SUS) |
Crossover points | 2 points |
Tchebichef moments (TMs) | Krawtchouk moments (KMs) | |
---|---|---|
Kernel form | Kernel\(_{pq} \left( {x,y} \right) =t_{p} \left( x \right) \times t_{q} \left( x \right) \)
| Kernel\(_{pq} \left( {x,y} \right) =K_{p} \left( {x;p_{1} ,N} \right) \times K_{q} \left( {y;p_{2} ,N} \right) \)
|
Polynomial form |
\(t_{n} \left( x \right) =\sum \limits _{k=0}^n {\left( {-1} \right) ^{n-k}\left( {{\begin{array}{c} {N-1-k} \\ {n-k} \\ \end{array} }} \right) } \left( {{\begin{array}{c} {n+k} \\ n \\ \end{array} }} \right) \left( {{\begin{array}{c} x \\ k \\ \end{array} }} \right) \)
|
\(\begin{array}{l} K_{n} \left( {x;p,N} \right) ={ }_{2}F_{1} \left( {-n,-x;-N;\frac{1}{p}} \right) \\ \quad =\sum \limits _{k=0}^N {a_{k,n,p_{1} } x}^{k} \\ \end{array}\)
|
Normalization factor (NF) |
\(\begin{array}{l} F\left( {p,N} \right) \times F\left( {q,N} \right) \\ \mathrm{where} \\ F(k,N)=\frac{N^{-2k}}{\left( {2k} \right) !\left( {{\begin{array}{l} {N+k} \\ {2n+1} \\ \end{array} }} \right) }, k=p,q \\ \end{array}\)
| 1 |
Simulations
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Lena (KMs) | ||||||
\(\Delta \)
| 117.5 | Var | 65 | Var | 50 | Var |
PSNR (dB) | 40.060 | 39.998 | 40.010 | 39.998 | 39.949 | 39.999 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.440 | 0.410 | 0.447 | 0.450 | 0.480 | 0.476 |
Median 4 \(\times \) 4 | 0.410 | 0.370 | 0.467 | 0.430 | 0.500 | 0.484 |
Median 6 \(\times \) 6 | 0.530 | 0.400 | 0.557 | 0.533 | 0.504 | 0.508 |
Median 8 \(\times \) 8 | 0.500 | 0.430 | 0.463 | 0.480 | 0.530 | 0.518 |
Mean − median | 0.470 | 0.403 | 0.483 | 0.473 | 0.504 | 0.497 |
AWGN 5 % | 0.180 | 0.200 | 0.133 | 0.113 | 0.126 | 0.124 |
AWGN 10 % | 0.140 | 0.120 | 0.117 | 0.130 | 0.172 | 0.170 |
AWGN 15 % | 0.100 | 0.060 | 0.167 | 0.137 | 0.258 | 0.254 |
AWGN 20 % | 0.130 | 0.100 | 0.257 | 0.240 | 0.328 | 0.316 |
Mean − AWGN | 0.138 | 0.120 | 0.168 | 0.155 | 0.221 | 0.216 |
JPEG \(Q=5\) % | 0.520 | 0.330 | 0.510 | 0.417 | 0.506 | 0.462 |
JPEG \(Q=10\) % | 0.100 | 0.130 | 0.350 | 0.310 | 0.436 | 0.396 |
JPEG \(Q=15\) % | 0.010 | 0.020 | 0.200 | 0.147 | 0.298 | 0.278 |
JPEG \(Q=20\) % | 0.000 | 0.010 | 0.080 | 0.087 | 0.222 | 0.178 |
JPEG \(Q=40\) % | 0.000 | 0.000 | 0.000 | 0.000 | 0.006 | 0.008 |
Mean − JPEG | 0.126 | 0.098 | 0.228 | 0.192 | 0.294 | 0.264 |
Total mean | 0.235 | 0.198 | 0.288 | 0.267 | 0.336 | 0.321 |
RF (%) | 15.686 | 7.297 | 4.443 |
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Bicycle (KMs) | ||||||
\(\Delta \)
| 116 | Var | 65 | Var | 49 | Var |
PSNR (dB) | 40.077 | 40.007 | 40.067 | 39.999 | 39.917 | 39.948 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.350 | 0.250 | 0.480 | 0.503 | 0.484 | 0.470 |
Median 4 \(\times \) 4 | 0.390 | 0.360 | 0.503 | 0.513 | 0.518 | 0.464 |
Median 6 \(\times \) 6 | 0.510 | 0.400 | 0.443 | 0.503 | 0.452 | 0.476 |
Median 8 \(\times \) 8 | 0.490 | 0.430 | 0.453 | 0.433 | 0.486 | 0.474 |
Mean − median | 0.435 | 0.360 | 0.470 | 0.488 | 0.485 | 0.471 |
AWGN 5 % | 0.180 | 0.230 | 0.133 | 0.157 | 0.128 | 0.116 |
AWGN 10 % | 0.160 | 0.090 | 0.117 | 0.110 | 0.184 | 0.180 |
AWGN 15 % | 0.090 | 0.120 | 0.167 | 0.143 | 0.260 | 0.256 |
AWGN 20 % | 0.130 | 0.110 | 0.257 | 0.200 | 0.332 | 0.320 |
Mean − AWGN | 0.140 | 0.138 | 0.168 | 0.153 | 0.226 | 0.218 |
JPEG \(Q=5\) % | 0.410 | 0.280 | 0.460 | 0.343 | 0.496 | 0.406 |
JPEG \(Q=10\) % | 0.150 | 0.050 | 0.370 | 0.257 | 0.494 | 0.432 |
JPEG \(Q=15\) % | 0.050 | 0.010 | 0.193 | 0.153 | 0.314 | 0.288 |
JPEG \(Q=20\) % | 0.000 | 0.010 | 0.107 | 0.057 | 0.232 | 0.166 |
JPEG \(Q=40\) % | 0.000 | 0.000 | 0.000 | 0.003 | 0.008 | 0.012 |
Mean − JPEG | 0.122 | 0.070 | 0.226 | 0.163 | 0.309 | 0.261 |
Total mean | 0.224 | 0.180 | 0.283 | 0.260 | 0.338 | 0.312 |
RF (%) | 19.588 | 8.329 | 7.475 |
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Lighthouse (KMs) | ||||||
\(\Delta \)
| 114 | Var | 65 | Var | 50.5 | Var |
PSNR (dB) | 40.037 | 40.000 | 39.991 | 40.003 | 40.046 | 40.001 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.240 | 0.210 | 0.443 | 0.440 | 0.514 | 0.512 |
Median 4 \(\times \) 4 | 0.320 | 0.220 | 0.503 | 0.493 | 0.528 | 0.490 |
Median 6 \(\times \) 6 | 0.410 | 0.360 | 0.467 | 0.473 | 0.512 | 0.484 |
Median 8 \(\times \) 8 | 0.480 | 0.420 | 0.483 | 0.417 | 0.502 | 0.498 |
Mean − median | 0.363 | 0.303 | 0.474 | 0.456 | 0.514 | 0.496 |
AWGN 5 % | 0.170 | 0.160 | 0.133 | 0.150 | 0.126 | 0.150 |
AWGN 10 % | 0.140 | 0.110 | 0.117 | 0.100 | 0.168 | 0.154 |
AWGN 15 % | 0.090 | 0.110 | 0.167 | 0.147 | 0.258 | 0.228 |
AWGN 20 % | 0.120 | 0.100 | 0.257 | 0.233 | 0.324 | 0.312 |
Mean − AWGN | 0.130 | 0.120 | 0.168 | 0.158 | 0.219 | 0.211 |
JPEG \(Q=5\) % | 0.480 | 0.300 | 0.443 | 0.427 | 0.516 | 0.468 |
JPEG \(Q=10\) % | 0.170 | 0.110 | 0.383 | 0.300 | 0.416 | 0.406 |
JPEG \(Q=15\) % | 0.010 | 0.010 | 0.193 | 0.163 | 0.272 | 0.284 |
JPEG \(Q=20\) % | 0.000 | 0.000 | 0.090 | 0.053 | 0.182 | 0.148 |
JPEG \(Q=40\) % | 0.000 | 0.000 | 0.000 | 0.000 | 0.010 | 0.002 |
Mean − JPEG | 0.132 | 0.084 | 0.222 | 0.189 | 0.279 | 0.262 |
Total mean | 0.202 | 0.162 | 0.283 | 0.261 | 0.333 | 0.318 |
RF (%) | 19.772 | 7.699 | 4.436 |
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Lena (TMs) | ||||||
\(\Delta \)
| 4.00 | Var | 3.8 | Var | 3.7 | Var |
PSNR (dB) | 40.239 | 40.000 | 40.252 | 39.966 | 40.433 | 39.988 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.520 | 0.420 | 0.560 | 0.450 | 0.528 | 0.440 |
Median 4 \(\times \) 4 | 0.480 | 0.420 | 0.510 | 0.473 | 0.502 | 0.444 |
Median 6 \(\times \) 6 | 0.510 | 0.500 | 0.490 | 0.447 | 0.484 | 0.514 |
Median 8 \(\times \) 8 | 0.590 | 0.460 | 0.507 | 0.493 | 0.526 | 0.512 |
Mean − median | 0.525 | 0.450 | 0.517 | 0.466 | 0.510 | 0.478 |
AWGN 5 % | 0.020 | 0.010 | 0.137 | 0.073 | 0.214 | 0.100 |
AWGN 10 % | 0.060 | 0.010 | 0.253 | 0.197 | 0.350 | 0.232 |
AWGN 15 % | 0.160 | 0.030 | 0.327 | 0.283 | 0.374 | 0.330 |
AWGN 20 % | 0.210 | 0.050 | 0.397 | 0.320 | 0.428 | 0.326 |
Mean − AWGN | 0.113 | 0.025 | 0.278 | 0.218 | 0.342 | 0.247 |
JPEG \(Q=5\) % | 0.430 | 0.320 | 0.510 | 0.440 | 0.494 | 0.470 |
JPEG \(Q=10\) % | 0.400 | 0.150 | 0.480 | 0.360 | 0.466 | 0.418 |
JPEG \(Q=15\) % | 0.230 | 0.080 | 0.407 | 0.277 | 0.420 | 0.356 |
JPEG \(Q=20\) % | 0.200 | 0.020 | 0.320 | 0.193 | 0.370 | 0.282 |
JPEG \(Q=40\) % | 0.020 | 0.000 | 0.157 | 0.067 | 0.256 | 0.110 |
Mean − JPEG | 0.256 | 0.114 | 0.375 | 0.267 | 0.401 | 0.327 |
Total mean | 0.295 | 0.190 | 0.389 | 0.313 | 0.416 | 0.349 |
RF (%) | 35.509 | 19.396 | 16.223 |
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Bicycle (TMs) | ||||||
\(\Delta \)
| 4.4 | Var | 4.2 | Var | 4 | Var |
PSNR (dB) | 40.048 | 40.005 | 40.347 | 40.000 | 40.045 | 39.997 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.490 | 0.370 | 0.473 | 0.457 | 0.506 | 0.498 |
Median 4 \(\times \) 4 | 0.490 | 0.400 | 0.507 | 0.490 | 0.500 | 0.484 |
Median 6 \(\times \) 6 | 0.540 | 0.450 | 0.537 | 0.537 | 0.522 | 0.470 |
Median 8 \(\times \) 8 | 0.510 | 0.420 | 0.520 | 0.473 | 0.526 | 0.510 |
Mean − median | 0.508 | 0.410 | 0.509 | 0.489 | 0.514 | 0.491 |
AWGN 5 % | 0.020 | 0.050 | 0.110 | 0.063 | 0.198 | 0.086 |
AWGN 10 % | 0.050 | 0.030 | 0.217 | 0.150 | 0.314 | 0.190 |
AWGN 15 % | 0.110 | 0.100 | 0.317 | 0.253 | 0.384 | 0.304 |
AWGN 20 % | 0.150 | 0.070 | 0.360 | 0.277 | 0.398 | 0.306 |
Mean \(- \) AWGN | 0.083 | 0.063 | 0.251 | 0.186 | 0.324 | 0.222 |
JPEG \(Q=5\) % | 0.390 | 0.320 | 0.483 | 0.437 | 0.472 | |
JPEG \(Q=10\) % | 0.310 | 0.230 | 0.417 | 0.320 | 0.436 | 0.434 |
JPEG \(Q=15\) % | 0.260 | 0.120 | 0.383 | 0.273 | 0.412 | 0.392 |
JPEG \(Q=20\) % | 0.120 | 0.040 | 0.270 | 0.210 | 0.398 | 0.336 |
JPEG \(Q=40\) % | 0.030 | 0.040 | 0.150 | 0.057 | 0.244 | 0.260 |
Mean − JPEG | 0.222 | 0.150 | 0.341 | 0.259 | 0.392 | 0.100 |
Total mean | 0.267 | 0.203 | 0.365 | 0.307 | 0.408 | 0.356 |
RF (%) | 23.919 | 15.742 | 12.884 |
Msg. length | 100 bit | 300 bit | 500 bit | |||
---|---|---|---|---|---|---|
ST | PR | ST | PR | ST | PR | |
Image—Lighthouse (TMs) | ||||||
\(\Delta \)
| 3.95 | Var | 3.39 | Var | 3.37 | Var |
PSNR (dB) | 40.033 | 40.003 | 40.021 | 39.995 | 40.028 | 40.004 |
Attack type
| ||||||
Median 2 \(\times \) 2 | 0.520 | 0.360 | 0.517 | 0.487 | 0.506 | 0.492 |
Median 4 \(\times \) 4 | 0.550 | 0.450 | 0.513 | 0.443 | 0.526 | 0.478 |
Median 6 \(\times \) 6 | 0.460 | 0.490 | 0.523 | 0.470 | 0.500 | 0.496 |
Median 8 \(\times \) 8 | 0.600 | 0.400 | 0.537 | 0.497 | 0.504 | 0.512 |
Mean − median | 0.533 | 0.425 | 0.523 | 0.474 | 0.509 | 0.495 |
AWGN 5 % | 0.020 | 0.000 | 0.170 | 0.047 | 0.260 | 0.074 |
AWGN 10 % | 0.060 | 0.020 | 0.310 | 0.123 | 0.388 | 0.192 |
AWGN 15 % | 0.170 | 0.060 | 0.337 | 0.197 | 0.398 | 0.316 |
AWGN 20 % | 0.220 | 0.050 | 0.397 | 0.253 | 0.424 | 0.304 |
Mean − AWGN | 0.118 | 0.033 | 0.303 | 0.155 | 0.368 | 0.222 |
JPEG \(Q=5\) % | 0.530 | 0.310 | 0.477 | 0.430 | 0.522 | 0.462 |
JPEG \(Q=10\) % | 0.320 | 0.170 | 0.493 | 0.370 | 0.468 | 0.402 |
JPEG \(Q=15\) % | 0.290 | 0.100 | 0.427 | 0.277 | 0.476 | 0.360 |
JPEG \(Q=20\) % | 0.200 | 0.070 | 0.357 | 0.203 | 0.382 | 0.266 |
JPEG \(Q=40\) % | 0.020 | 0.010 | 0.160 | 0.033 | 0.284 | 0.110 |
Mean − JPEG | 0.272 | 0.132 | 0.383 | 0.263 | 0.426 | 0.320 |
Total mean | 0.305 | 0.192 | 0.401 | 0.295 | 0.434 | 0.343 |
RF (%) | 37.121 | 26.583 | 20.823 |