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It is still a challenging work to design a robust image watermarking scheme to resist geometrical transformations. In this paper, we analyze the geometric invariant properties of radial harmonic Fourier moments (RHFMs), and propose a new geometrically resilient digital image watermarking scheme based on RHFMs magnitudes. Firstly, the binary watermark image is encrypted by Arnold transform, and the RHFMs of the host image are computed. Then, the accurate and robust RHFMs are selected according to the moment magnitude distribution. Finally, the encrypted watermark is embedded by quantizing the magnitudes of the selected RHFMs, and the watermarked image is obtained by adding the compensation image to the original host image. Experimental results show that the proposed RHFMs based image watermarking scheme outperforms other moments based watermarking methods, and is robust to a wide range of attacks, e.g., median filtering, random noise addition, JPEG compression, rotation, and scaling, etc. [ABSTRACT FROM AUTHOR]

Denoising of images is one of the most basic tasks of image processing. It is a challenging work to design a edge/texture-preserving image denoising scheme. Nonsubsampled shearlet transform (NSST) is an effective multi-scale and multi-direction analysis method, it not only can exactly compute the shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. Based on NSST, a new edge/texture-preserving image denoising using twin support vector machines (TSVMs) is proposed in this paper. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using the NSST. Secondly, the feature vector for a pixel in a noisy image is formed by the spatial geometric regularity in NSST domain, and the TSVMs model is obtained by training. Then the NSST detail coefficients are divided into information-related coefficients and noise-related ones by TSVMs training model. Finally, the detail subbands of NSST coefficients are denoised by using the adaptive threshold. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges and textures very well while removing noise. [ABSTRACT FROM AUTHOR]

Most of the existing color image watermarking schemes was designed to mark grayscale images or use the color components, which ignore the significant correlation between different color channels. Recently, several approaches were developed to process the color channels intrinsically, but they always cannot counterattack geometric distortions. It is a challenging work to design a robust color image watermarking scheme against geometrical distortions. In this paper, we propose a geometric correction based robust color image watermarking approach using quaternion Exponent moments (QEMs). The novelty of our approach is that (1) the QEMs are derived to deal with the color images in a holistic manner, and (2) the QEMs are exploited for estimating the geometric distortions parameters in order to permit watermark extraction. Experimental results confirm the validity of our approach and its higher robustness against geometrical distortions compared to alternative watermarking methods in the literature. [ABSTRACT FROM AUTHOR]

Moments and moment invariants have become a powerful tool in image processing owing to their image description capability and invariance property. But, conventional methods are mainly introduced to deal with the binary or gray-scale images, and the only approaches for color image always have poor color image description capability. Based on radial harmonic Fourier moments (RHFMs) and quaternion, we introduced the quaternion radial harmonic Fourier moments (QRHFMs) for representing color images in this paper, which can be seen as the generalization of RHFMs for gray-level images. It is shown that the QRHFMs can be obtained from the RHFMs of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QRHFMs. We also discussed the problem of color image retrieval using invariant QRHFMs. Experimental results are provided to illustrate the efficiency of the proposed color image representation. [ABSTRACT FROM AUTHOR]