A new robust watermarking approach was proposed in 2D continuous wavelet domain （CWT）. The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima （WTMM） of the hos...A new robust watermarking approach was proposed in 2D continuous wavelet domain （CWT）. The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima （WTMM） of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.展开更多
Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DN...Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.展开更多
基金The National Natural Science Foundation of China (No.60703048)the Natural Science Foundation of Hubei Province (No.2007ABA303)
文摘A new robust watermarking approach was proposed in 2D continuous wavelet domain （CWT）. The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima （WTMM） of the host image. After possible attacks, the watermark is then detected and extracted by correlation analysis. Compared with other wavelet domain watermarking approaches, the WTMM approach can endow the image with beth rotation and shift invariant properties. On the other hand, scale invariance is achieved with the geometric normalization during watermark detection. Case studies involve various attacks such as shifting, lossy compression, scaling, rotation and median filtering on the watermarked image, and the result shows that the approach is robust to these attacks.
基金Project supported by the Science and Technology Commission of Shanghai Municipality (Grant No. 05DZ19747)the National Basic Research Program of China (Grant No. 2006CB504509)
文摘Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.
