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Watermark transparency is required mainly for copyright protection. Based on the characteristics of human visual system, the just noticeable distortion (JND) can be used to verify the transparency requirement. More specifically, any watermarks whose intensities are less than the JND values of an image can be added without degrading the visual quality. It takes extensive experimentations for an appropriate JND model. Motivated by the texture masking effect and the spatial masking effect, which are key factors of JND, Chou and Li (1995) proposed the well-known full-band JND model for the transparent watermark applications. In this paper, we propose a novel JND model based on discrete wavelet transform. Experimental results show that the performance of the proposed JND model is comparable to that of the full-band JND model. However, it has the advantage of saving a lot of computation time; the speed is about 6 times faster than that of the full-band JND model.

Watermarking is a process that hides information into a host image for the purpose of copyright protection, integrity checking, or captioning [

Perceptual redundancies refer to the details of an image that are not perceivable by human eyes and therefore can be discarded without affecting the visual quality. As noted, human visual perception is sensitive to the contrast of luminance rather than their individual values [

Wavelet transform provides an efficient multiresolution representation with various desirable properties such as subband decompositions with orientation selectivity and joint space-spatial frequency localization. In wavelet domain, the higher detailed information of a signal is projected onto the shorter basis function with higher spatial resolution; the lower detailed information is projected onto the larger basis function with higher spectral resolution. This matches the characteristics of HVS. Many wavelet-transform-based algorithms were proposed for various applications [

In this paper, we propose a wavelet-transform-based JND model for the watermark applications. It has the advantage of saving a lot of computation time. The remainder of the paper proceeds as follows. In Section

The full-band JND model [

Low-pass filter used in (

A set of high-pass filters used in (

In this section, we propose a novel JND model based on discrete wavelet transform. It has the advantage of reducing computational complexity significantly.

Discrete wavelet transform (DWT) provides an efficient multiresolution analysis for signals, Specifically, any finite energy signal

For image applications, 2D DWT can be obtained by using the tensor product of 1D DWT. Among wavelets, Haar wavelet [

The row decomposition using Haar wavelet (

The column decomposition using Haar wavelet (

1-level 2D DWT using Haar wavelet (

The

As mentioned in Section

In this section, we introduce an adjustable parameter to modify the DWT-based JND model such that the computation time can be reduced significantly while the performance is comparable to that of the benchmark full-band JND model. The test images, namely, Lena, Cameraman, Baboon, Board, and Peppers are shown in the first row of Figure

Figure

PSNR comparisons of the benchmark full-band JND model, the proposed DWT-based JND model, and the modified DWT-based JND model.

JND model | Lena | Cameraman | Baboon | Board | Peppers |
---|---|---|---|---|---|

Full-band JND | 32.7041 | 29.9122 | 34.0845 | 25.3486 | 30.3052 |

DWT-based JND | 34.3301 | 31.7556 | 35.8156 | 30.8003 | 32.1375 |

The modified DWT-based JND | 33.7117 | 30.9614 | 34.0931 | 25.7192 | 31.7148 |

Distortion-tolerant evaluation model for the proposed JND model.

Based on (

The MSE values due to the dominant mask (case 1), the spatial mask (case 2), and the texture mask (case 3) using the full-band JND model, the DWT-based JND model, and the modified DWT-based JND model.

JND model | Case | Lena | Cameraman | Baboon | Board | Peppers |
---|---|---|---|---|---|---|

Full-band JND | 1 | 34.8876 | 66.3534 | 25.3878 | 189.7653 | 60.6121 |

2 | 28.5202 | 53.0297 | 19.6219 | 41.7222 | 52.5825 | |

3 | 10.9574 | 18.4772 | 12.373 | 165.6492 | 12.583 | |

DWT-based JND | 1 | 23.9924 | 43.4027 | 17.0419 | 54.0822 | 39.7492 |

2 | 23.9269 | 43.0406 | 16.942 | 38.4702 | 39.642 | |

3 | 0.972 | 2.1076 | 1.4603 | 24.4885 | 1.1393 | |

The modified DWT-based JND | 1 | 27.6254 | 52.1122 | 25.3378 | 174.244 | 43.8131 |

2 | 23.9269 | 43.0406 | 16.942 | 38.4702 | 39.642 | |

3 | 6.9379 | 13.7233 | 14.7008 | 153.4052 | 7.8595 |

MSE values obtained by modifying the DWT-based texture mask using (

MSE values obtained by modifying the DWT-based texture mask using (

MSE values obtained by modifying the DWT-based texture mask using (

MSE values obtained by modifying the DWT-based texture mask using (

MSE values obtained by modifying the DWT-based texture mask using (

(a) The original images, namely, Lena, Cameraman, Baboon, Board, and Peppers; (b), (c), and (d) the noisy images obtained by adding the full-band JND values, the DWT-based JND values, and the modified DWT-based JND values, respectively.

Figure

In the full-band JND model, the computation of

Log plot of numbers of multiplications required for the three JND models versus different image sizes.

In this paper, an efficient DWT-based JND model is presented. It has the advantage of saving a lot of computation time while the performance is comparable to the benchmark full-band JND model. More specifically, the computation complexity of the proposed DWT-based JND model is only one sixth of that of the full-band JND model. As a result, it is suitable for the real-time applications.

The National Science Council of Taiwan, under Grants NSC98-2221-E-216-037 and NSC99-2221-E-239-034, supported this work.