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The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex LCT. In this paper, we normalize the Bargmann transform such that it can be bounded near infinity. We derive the relationships of the normalized Bargmann transform to Gabor transform, Hermite-Gaussian functions, gyrator transform, and 2D nonseparable LCT. Several kinds of fast and accurate computational methods of the normalized Bargmann transform and its inverse are proposed based on these relationships.

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As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D CM), and 2D affine transformations. However, 2D affine transformations will introduce interpolation error. In this paper, we propose a new decomposition called CM-CC-CM-CC decomposition, which decomposes the 2D NsLCT into two 2D CMs and two 2D chirp convolutions. No 2D affine transforms are involved. Simulation results show that the proposed methods have higher accuracy, lower computational complexity, and smaller error in the additivity property compared with the previous works. Plus, the proposed methods have a perfect reversibility property, meaning that one can reconstruct the input signal/image losslessly from the output.

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Objective image quality assessment (IQA) plays an important role in the development of multimedia applications. Prediction of IQA metric should be consistent with human perception. The release of the newest IQA database (TID2013) challenges most of the widely used quality metrics (e.g., peak-to-noise-ratio and structure similarity index). We propose a new methodology to build the metric model using a regression approach. The new IQA score is set to be the nonlinear combination of features extracted from several difference of Gaussian (DOG) frequency bands, which mimics the human visual system (HVS). Experimental results show that the random forest regression model trained by the proposed DOG feature is highly correspondent to the HVS and is also robust when tested by available databases.

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In this paper, we propose a novel algorithm for high-definition displays to enlarge low-resolution images while maintaining perceptual constancy (i.e., the same field-of-view, perceptual blur radius, and the retinal image size in viewer's eyes). We model the relationship between a viewer and a display by considering two main aspects of visual perception, i.e., scaling factor and perceptual blur radius. As long as we enlarge an image while adjust its image blur levels on the display, we can maintain viewer's perceptual constancy. We show that the scaling factor should be set in proportion to the viewing distance and the blur levels on the display should be adjusted according to the focal length of a viewer. Toward this, we first refer to edge directions to interpolate a low-resolution image with the increasing of viewing distance and the scaling factor. After images are interpolated, we utilize a local contrast to estimate the spatially varying image blur levels of the interpolated image. We then further adjust the image blur levels using a parametric deblurring method, which combines L1 as well as L2 reconstruction errors, and Tikhonov with total variation regularization terms. By taking these factors into account, high-resolution images adaptive to viewing distance on a display can be generated. Experimental results on both natural image metric and user subjective studies across image scales demonstrate that the proposed super-resolution algorithm for high-definition displays performs favorably against the state-of-the-art methods.

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The linear canonical transform (LCT) with a, b, c, d parameter plays an important role in quantum mechanics, optics, and signal processing. The eigenfunctions of the LCT are also important because they describe the self-imaging phenomenon in optical systems. However, the existing solutions for the eigenfunctions of the LCT are divided into many cases and they lack a systematic way to solve these eigenfunctions. In this paper, we find a linear, second-order, self-adjoint differential commuting operator that commutes with the LCT operator. Hence, the commuting operator and the LCT share the same eigenfunctions with different eigenvalues. The commuting operator is very general and simple when it is compared to the existing multiple-parameter differential equations. Then, the eigenfunctions can be derived systematically. The eigenvalues of the commuting operator have closed-form relationships with the eigenvalues of the LCT. We also simplify the eigenfunctions for |a+d|>2 and a+d=±2, b≠0 into the more compact closed form instead of the integral form. For |a+d|>2, the eigenfunctions are related to the parabolic cylinder functions.

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In the conventional JPEG algorithm, an image is divided into eight by eight blocks and then the 2-D DCT is applied to encode each block. In this paper, we find that, in addition to rectangular blocks, the 2-D DCT is also orthogonal in the trapezoid and triangular blocks. Therefore, instead of eight by eight blocks, we can generalize the JPEG algorithm and divide an image into trapezoid and triangular blocks according to the shapes of objects and achieve higher compression ratio. Compared with the existing shape adaptive compression algorithms, as we do not try to match the shape of each object exactly, the number of bytes used for encoding the edges can be less and the error caused from the high frequency component at the boundary can be avoided. The simulations show that, when the bit rate is fixed, our proposed algorithm can achieve higher PSNR than the JPEG algorithm and other shape adaptive algorithms. Furthermore, in addition to the 2-D DCT, we can also use our proposed method to generate the 2-D complete and orthogonal sine basis, Hartley basis, Walsh basis, and discrete polynomial basis in a trapezoid or a triangular block.

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Analytic signal and Hilbert transform associated with linear canonical transform (LCT) have been developed [Opt. Commun.281, 1468 (2008)]. However, the aforementioned paper has some drawbacks; for example, this kind of analytic signal cannot preserve the positive frequency bands of the original signal under LCT operations. In this paper, these drawbacks are pointed out, and a better definition for analytic signal associated with LCT is proposed. In addition, a discrete implementation for the analytic signal associated with discrete LCT is also provided. Several numerical examples, shown with both time and Wigner time-frequency domains, are demonstrated to illustrate the efficiency and accuracy of the proposed LCT analytic signal.

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In this paper, a robust illuminant estimation algorithm for color constancy is proposed. Considering the drawback of the well-known max-RGB algorithm, which regards only pixels with the maximum image intensities, we explore the representative pixels from an image for illuminant estimation: The representative pixels are determined via the intensity bounds corresponding to a certain percentage value in the normalized accumulative histograms. To achieve the suitable percentage, an iterative algorithm is presented by simultaneously neutralizing the chromaticity distribution and preventing overcorrection. The experimental results on the benchmark databases provided by Simon Fraser University and Microsoft Research Cambridge, as well as several web images, demonstrate the effectiveness of our approach.

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The two-dimensional nonseparable linear canonical transform (2D NSLCT), which is a generalization of the fractional Fourier transform and the linear canonical transform, is useful for analyzing optical systems. However, since the 2D NSLCT has 16 parameters and is very complicated, it is a great challenge to implement it in an efficient way. In this paper, we improved the previous work and propose an efficient way to implement the 2D NSLCT. The proposed algorithm can minimize the numerical error arising from interpolation operations and requires fewer chirp multiplications. The simulation results show that, compared with the existing algorithm, the proposed algorithms can implement the 2D NSLCT more accurately and the required computation time is also less.

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Privacy has received considerable attention but is still largely ignored in the multimedia community. Consider a cloud computing scenario where the server is resource-abundant, and is capable of finishing the designated tasks. It is envisioned that secure media applications with privacy preservation will be treated seriously. In view of the fact that scale-invariant feature transform (SIFT) has been widely adopted in various fields, this paper is the first to target the importance of privacy-preserving SIFT (PPSIFT) and to address the problem of secure SIFT feature extraction and representation in the encrypted domain. As all of the operations in SIFT must be moved to the encrypted domain, we propose a privacy-preserving realization of the SIFT method based on homomorphic encryption. We show through the security analysis based on the discrete logarithm problem and RSA that PPSIFT is secure against ciphertext only attack and known plaintext attack. Experimental results obtained from different case studies demonstrate that the proposed homomorphic encryption-based privacy-preserving SIFT performs comparably to the original SIFT and that our method is useful in SIFT-based privacy-preserving applications.

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Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

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Video halftoning is a key technology for use in electronic paper (e-paper) or smart paper, which is an emerging display device that has received considerable attention recently. In this paper, a temporal frequency of flickering-distortion optimized video halftoning method is proposed. We first uncover three visual defects that conventional neighboring frame referencing-based video halftoning methods, due to their sequential changes of reference frames, will encounter. To deal with the problem, we then propose a reference frame update per GOP-based error diffusion video halftoning method based on a flickering sensitivity-based human visual model. To efficiently compromise between average temporal frequency of flickering (ATFoF) and visual quality, temporal frequency of flickering-distortion (TFoFD) is presented as a metric for video halftoning performance evaluation. Based on the proposed probability model of video halftoning, the TFoFD curve can be accurately estimated to optimize the tradeoff between quality and ATFoF before the video is halftoned. Our temporal frequency of flickering-distortion optimization strategy can also be applied to other video halftoning schemes for performance improvement. Experimental results and comparisons with known methods demonstrate the effectiveness of our video halftoning method.

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In this correspondence, we introduce a systematic algorithm that can convert any 3 x 3 color transform into a reversible integer-to-integer transform. We also discuss the ways to improve accuracy and reduce implementation complexity. We derive the integer RGB-to-KLA, IV1 V2, YCbCr, DCT, YUV, and YIQ transforms that are optimal in accuracy.

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This work presents a color enhancement scheme to virtually restore ancient Chinese paintings in electronic form. Two degradations result in color contrast loss in ancient Chinese paintings: paper aging and pigment fading. The proposed enhancement scheme comprises two subsequent methods: background adjustment and saturation enhancement. The former method, based on the Von Kries color conversion in the CIE xyY color space, retrieves the original color of the paint paper by modifying colors based on their similarity to the background color. The proposed saturation enhancement method makes colors more vivid and bright, and also improves the image contrast.

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The process of limited-color image compression usually involves color quantization followed by palette re-indexing. Palette re-indexing could improve the compression of color-indexed images, but it is still complicated and consumes extra time. Making use of the topology-preserving property of self-organizing Kohonen feature map, we can generate a fairly good color index table to achieve both high image quality and high compression, without re-indexing. Promising experiment results will be presented.

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In this paper, a high-capacity data hiding is proposed for embedding a large amount of information into halftone images. The embedded watermark can be distributed into several error-diffused images with the proposed minimal-error bit-searching technique (MEBS). The method can also be generalized to self-decoding mode with dot diffusion or color halftone images. From the experiments, the embedded capacity from 33% up to 50% and good quality results are achieved. Furthermore, the proposed MEBS method is also extended for robust watermarking against the degradation from printing-and-scanning and several kinds of distortions. Finally, a least-mean square-based halftoning is developed to produce an edge-enhanced halftone image, and the technique also cooperates with MEBS for all the applications described above, including high-capacity data hiding with secret sharing or self-decoding mode, as well as robust watermarking. The results prove much sharper than the error diffusion or dot diffusion methods.

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Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

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This work presents a novel algorithm using color contrast enhancement and lacuna texture synthesis is proposed for the virtual restoration of ancient Chinese paintings. Color contrast enhancement based on saturation and de-saturation is performed in the u'v'Y color space, to change the saturation value in the chromaticity diagram, and adaptive histogram equalization then is adopted to adjust the luminance component. Additionally, this work presents a new patching method using the Markov Random Field (MRF) model of texture synthesis. Eliminating undesirable aged painting patterns, such as stains, crevices, and artifacts, and then filling the lacuna regions with the appropriate textures is simple and efficient. The synthesization procedure integrates three key approaches, weighted mask, annular scan and auxiliary, with neighborhood searching. These approaches can maintain a complete shape and prevent edge disconnection in the final results. Moreover, the boundary between original and synthesized paintings is seamless, and unable to distinguish in which the undesirable pattern appears.

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The offset Fourier transform (offset FT), offset fractional Fourier transform (offset FRFT), and offset linear canonical transform (offset LCT) are the space-shifted and frequency-modulated versions of the original transforms. They are more general and flexible than the original ones. We derive the eigenfunctions and the eigenvalues of the offset FT, FRFT, and LCT. We can use their eigenfunctions to analyze the self-imaging phenomena of the optical system with free spaces and the media with the transfer function exp[j(h2x2 + h1x + h0)] (such as lenses and shifted lenses). Their eigenfunctions are also useful for resonance phenomena analysis, fractal theory development, and phase retrieval.