## 1 Introduction
Their research showed that DWT decomposed an image or video frame into a lower level approximation component and three detail components. However, the major drawbacks of frequency domain schemes lie in the computational complexity and the vulnerability to potential attacks (e.g., geometric attack) [8]. Theoretical performance analysis of watermarking schemes has also been conducted based on correlation detection. Correlation and spectral properties of the watermark sequences generated by the piecewise-linear Markov maps were easily adjusted. The family of chaotic maps was used to verify theoretical analysis. Skew tent chaotic sequences have been compared with widely used pseudorandom sequences, indicating superiority of the former in watermarking applications. The audio data experiments verified theoretical analysis results [9]. Chaotic parameter modulation was used to modulate copyright information into the bifurcating parameter of a chaotic system. The system output was a wideband signal acting as a watermark to be inserted into the host image. The scheme, based on the ergodic property of chaotic sequence, was applied in order to demodulate the embedded copyright information. The technique effectively removed interference from the host image that improved detection performance dramatically. It was effective for image watermarking with the presence of noises, attacks, and payloads. This approach has been shown to be superior to conventional holographic transform domain method and spread spectrum-watermarking schemes due to its simple design and short computation time [10]. A novel authentication scheme has been proposed based on chaotic semi-fragile watermarking. The timing information of video frames was modulated into parameters of a chaotic system. The noise-like system output was applied as the watermark to be embedded into the block-based discrete cosine transform domain. The embedded information can be demodulated using maximum likelihood estimation. Temporal tampering was detected by the mismatch of timing information. Spatial tampering was detected by the deviation of the extracted watermark. The scheme satisfied particular requirements to authenticate a digital video surveillance system [11]. Fractional order analysis of chaotic systems has also been conducted. Qualitative analysis of fractional orders on chaotic system characteristics was made which provided a solid basis for applying fractional order control to either generate or suppress chaotic behaviors [12]. The goal of image watermarking is to embed hidden data into the host image. A new watermarking scheme for embedding watermark bits has been based on Chaotic Fractal Coding. The chaotic signal was deterministic, pseudo periodic, and sensitive to initial conditions. Integration of the chaotic system and Fractal Coding plays an important role in the security, invisibility, and capacity of the scheme. The idea now, is to come up with a set of selective blocks for steady embedding. Chaos-Fractal Coding has shown confidential capacity [13]. Dual chaotic watermarking in the spatial domain has been proposed in the context in order to protect intellectual property, where the chaotic logistic map generated watermarking and the subsequent dual chaotic watermarked images possess sensitivity variations of high probability, which has extensive applicability for authentication systems by inserting a controlled amount of distortion to the host images. To evaluate variations after watermarking, two additional tests of NPCR (Number of Pixel Change Rate) and UACI (Unified Average Changing Intensity) will be provided as case studies in the spatial domain. The role of the chaotic driving parameter on computation time and information security is also discussed in terms of the testing data. Two additional security tests based on the discrete entropy and relative entropy will also be implemented in the frequency domain.