RESUMEN
Digital watermarking of images is an essential method for copyright protection and image security. This paper presents an innovative, robust watermarking system for color images based on moment and wavelet transformations, algebraic decompositions, and chaotic systems. First, we extended classical Charlier moments to quaternary Charlier moments (QCM) using quaternion algebra. This approach eliminates the need to decompose color images before applying the discrete wavelet transform (DWT), reducing the computational load. Next, we decompose the resulting DWT matrix using QR and singular value decomposition (SVD). To enhance the system's security and robustness, we introduce a modified version of Henon's 2D chaotic map. Finally, we integrate the arithmetic optimization algorithm to ensure dynamic and adaptive watermark insertion. Our experimental results demonstrate that our approach outperforms current color image watermarking methods in security, storage capacity, and resistance to various attacks, while maintaining a high level of invisibility.
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Transform-domain audio watermarking systems are more robust than time-domain systems. However, the main weakness of these systems is their high computational cost, especially for long-duration audio signals. Therefore, they are not desirable for real-time security applications where speed is a critical factor. In this paper, we propose a fast watermarking system for audio signals operating in the hybrid transform domain formed by the fractional Charlier transform (FrCT) and the dual-tree complex wavelet transform (DTCWT). The central idea of the proposed algorithm is to parallelize the intensive and repetitive steps in the audio watermarking system and then implement them simultaneously on the available physical cores on an embedded systems cluster. In order to have a low power consumption and a low-cost cluster with a large number of physical cores, four Raspberry Pis 4B are used where the communication between them is ensured using the Message Passing Interface (MPI). The adopted Raspberry Pi cluster is also characterized by its portability and mobility, which are required in watermarking-based smart city applications. In addition to its resistance to any possible manipulation (intentional or unintentional), high payload capacity, and high imperceptibility, the proposed parallel system presents a temporal improvement of about 70%, 80%, and 90% using 4, 8, and 16 physical cores of the adopted cluster, respectively.
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In this paper, we present an efficient and optimal method for optimization of Hahn parameters a and b using the Artificial Bee Colony algorithm (ABC) in order to improve the quality of reconstruction and the compression of bio-signals and 2D / 3D color images of large sizes. The proposed methods are essentially based on two concepts: the development of a recursive calculation of the initial terms of Hahn polynomials in order to avoid the problems of instability of polynomial values and the use of ABC algorithm to optimize the values of the parameters a and b of the discrete orthogonal Hahn polynomials (HPs) during the reconstruction and the compression of bio-signals and 2D / 3D color images. The simulation results performed on bio-signals and on large size 2D /3D color images clearly show the efficiency and superiority of the proposed methods over conventional methods in terms of reconstruction of signals and images.
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In this paper, we initially provide significant improvements on the computational aspects of dual Hahn moment invariants (DHMIs) in both 2D and 3D domains. These improvements ensure the numerical stability of DHMIs for large-size images. Then, we propose an efficient method for optimizing the local parameters of dual Hahn polynomials (DHPs) when computing DHMIs using the Sine-Cosine Algorithm (SCA). DHMIs optimized via SCA are used to propose new and robust zero-watermarking scheme applied to both 2D and 3D images. On one hand, the simulation results confirm the efficiency of the proposed computation of 2D and 3D DHMIs regarding the numerical stability and invariability. Indeed, the proposed computation method of 2D DHMIs allows to reach a relative error (RE) of the order ≈10-10 for images of size 1024 × 1024 with an execution time improvement ratio exceeds 70% ( ETIR ≥ 70%), which validates the efficiently of the proposed computation method. On the other hand, the simulation and comparison outcomes clearly demonstrate the robustness of the proposed zero-watermarking scheme against various geometric attacks (translation, rotation, scaling and combined transformations), as well as against other common 2D and 3D image processing attacks (compression, filtering, noise addition, etc.).
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This article presents, on the one hand, new algorithms for the fast and stable computation of discrete orthogonal Hahn polynomials of high order (HPs) based on the elimination of all gamma and factorial functions that cause the numerical fluctuations of HPs, and based on the use of appropriate stability conditions. On the other hand, a new method for the fast and numerically stable computation of Hahn moment invariants (HMIs) is also proposed. This method is mainly based on the use of new recursive relations of HPs and of matrix multiplications when calculating HMIs. To validate the efficiency of the algorithms proposed for the calculation of HPs, several signals and large images (≥4000 × 4000) are reconstructed by Hahn moments (HMs) up to the last order with a reconstruction error tending towards zero (MSE ≃ 10-10). The efficiency of the proposed method for calculating HMIs is demonstrated on large medical images (2048 × 2048) with a very low relative error (RE ≃ 10-10). Finally, comparisons with some recent work in the literature are provided.
RESUMEN
The discrete orthogonal moments are powerful descriptors for image analysis and pattern recognition. However, the computation of these moments is a time consuming procedure. To solve this problem, a new approach that permits the fast computation of Hahn's discrete orthogonal moments is presented in this paper. The proposed method is based, on the one hand, on the computation of Hahn's discrete orthogonal polynomials using the recurrence relation with respect to the variable x instead of the order n and the symmetry property of Hahn's polynomials and, on the other hand, on the application of an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. The paper also proposes a new set of Hahn's invariant moments under the translation, the scaling, and the rotation of the image. This set of invariant moments is computed as a linear combination of invariant geometric moments from a finite number of image intensity slices. Several experiments are performed to validate the effectiveness of our descriptors in terms of the acceleration of time computation, the reconstruction of the image, the invariability, and the classification. The performance of Hahn's moment invariants used as pattern features for a pattern classification application is compared with Hu [IRE Trans. Inform. Theory 8, 179 (1962)] and Krawchouk [IEEE Trans. Image Process.12, 1367 (2003)] moment invariants.