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A quantum color image encryption algorithm based on geometric transformation and intensity channel diffusion was designed. Firstly, a plaintext image was transformed into a quantum state form using the quantum image representation based on HSI color space (QIRHSI) representation as a carrier. Next, a pseudo-random sequence was generated using the generalized logistic map, and the pixel positions permuted multiple two-point swap operations. Immediately afterward, the intensity values were changed by an intensity bit-plane cross-swap and XOR, XNOR operations. Finally, the intensity channel of the above image was diffused in combination with the pseudo-confusion sequence as produced by the quantum logistic map to perform a diffusion operation on the intensity bit-plane to obtain the ciphertext image. Numerical simulations and analyses show that the designed algorithm is implementable and robust, especially in terms of outstanding performance and less computational complexity than classical algorithms in terms of security perspective.

As the invariant function for some of the transform has non-denatured, this paper made a research on the watermarking algorithm robust to geometric transformations for geo-spatial vector data. Firstly, the conception and characteristic of invariant function were presented. Secondly, an invariant function robust to rotation, scaling and translation was proposed and proved, then based on the obtained invariant function, by embedding watermark into the geometric invariant, a watermarking algorithm for geo-spatial vector data was proposed. Finally, experiments on the proposed watermarking algorithm were made. The experiments conducted in this paper showed that the proposed algorithm had good robust and could resist attacks such as compressing, adding, deleting, clipping, translating, rotating, scaling and complex attacks composited of above attacks.

Most conventional gaze-tracking systems require that users look at many points during the initial calibration stage, which is inconvenient for them. To avoid this requirement, we propose a new gaze-tracking method with four important characteristics. First, our gaze-tracking system uses a large screen located at a distance from the user, who wears a lightweight device. Second, our system requires that users look at only four calibration points during the initial calibration stage, during which four pupil centers are noted. Third, five additional points (virtual pupil centers) are generated with a multilayer perceptron using the four actual points (detected pupil centers) as inputs. Fourth, when a user gazes at a large screen, the shape defined by the positions of the four pupil centers is a distorted quadrangle because of the nonlinear movement of the human eyeball. The gaze-detection accuracy is reduced if we map the pupil movement area onto the screen area using a single transform function. We overcame this problem by calculating the gaze position based on multi-geometric transforms using the five virtual points and the four actual points. Experiment results show that the accuracy of the proposed method is better than that of other methods.

Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. The present paper develops and studies two conceptually new ways to define convolution products for such transforms. As a by-product, convolution theorems are obtained that will enable the development and fast implementation of new filters for quaternionic signals and systems, as well as for their higher dimensional counterparts.

The feature-based image registration method has a better performance in terms of robustness to the intensity variance, but its accuracy of the feature-based image registration still could be improved. This paper utilizes the low-rank factorization and maximum rank resolving to improve the accuracy of image registration. In detail, the proposed method extracts coarse geometrical transform parameters based on the feature point pairs between images, then constructs low-rank model to optimize the geometrical transform parameters and estimate the inliers. Finally, an iterative optimization strategy is introduced to acquire the optimized transform parameters by maximum rank resolving. Experimental results illustrate that the proposed approach presents a good performance in terms with the root residual mean squares error and the entropy of image difference.

A novel digital watermarking scheme featuring centroid-based sectoring is proposed in this paper. To get higher robustness against geometric attacks, such as rotation, scaling, and translation （RST）, a delicate synchronization mechanism was developed and incorporated into the proposed approach. During the process of watermark embedding, the original image was partitioned into sectors based on the image centroid. Synchronization information as well as the message bits is then embedded into these sectors. With the help of the centroid-based sectoring and synchronization information, the proposed approach is capable of restoring the cor- rect sectoring even if it has experienced severe geometric distortion. This attribute ensures the correct recovery of embedded watermarks and contributes to the robustness of the proposed scheme. A series of experiments have been conducted to verify the feasibility and effectiveness of the proposed approach. Experimental results show that the proposed scheme possesses good robustness against RST attacks and considerable robustness against other common image processing attacks.

Geometrical attacks can destroy most watermarking systems at present. So how to efficiently resist such kind of attacks remains a challenging direction in watermarking research. In this paper, a novel sequence watermarking scheme, which exploits a geometrical invariant, i.e. average AC energy (AAE) to combat arbitrary geometrical attacks, is presented. The scheme also uses some other measures, such as synchronization and optimal whitening filter to resist other attacks and improve detection performance. The experimental results show that the scheme can efficiently improve the visual quality of the watermarked video and achieve good robustness against random geometrical attacks. The scheme also has good robustness against other attacks, such as low-pass filtering along time axis and frame removal.

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this present paper we consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain We also study in detail the mother body problem associated to To construct the mother body measure, we define a quadratic differential Following previous works of Bleher & Kuijlaars and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials. Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of the associated

The linear canonical transform is a widely utilized integral transform in the field of signal analysis, characterized by three independent parameters. It not only facilitates rotation of the time-frequency plane but also enables expansion and contraction of the frequency domain, thereby playing a crucial role in handling non-stationary signals. In recent years, the linear canonical transform has been extended to octonion domains, which possess a more generalized form and offer greater research potential. This extension effectively harnesses the processing capabilities of the linear canonical transform for non-stationary signals in high-dimensional spaces. In this paper, we explore the definition and the conjugacy of the left side octonion linear canonical transform. Moreover, we thoroughly examine the differential properties of octonion linear canonical transform. The study of these properties is helpful for understanding the characteristics and applications of geometric transformations as well as expanding the scope of mathematical theory and practical applications.

The authors study algebras of singular integral operators on \\mathbb R^n and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on L^p for 1 \\lt p \\lt \\infty . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.