GPU-Accelerated Algorithm to Compute Bessel-Fourier Moments

Bessel-Fourier moments have been applied in image pattern reconstruction since their introduction in 2010. In this research, a scalable GPU-based algorithm is proposed to accelerate the computation of Bessel-Fourier moments of high orders while preserving accuracy. To analyze our new algorithm, image reconstructions from Bessel-Fourier moments of orders up to 1000 were tested on two systems. The experimental results prove the correctness and scalability of the algorithm. In addition, by investigating the precision-related performance, both 64-bit and 32-bit precisions were shown to provide the same level of computational accuracy for Bessel-Fourier moments of orders up to 1000. Nevertheless, reconstructions with 64-bit precision are computationally more costly. Furthermore, we applied filtering in Bessel-Fourier moments and Fourier Frequency domains and found that Bessel-Fourier moments share some similarities with the frequencies in Fourier Frequency domain, though more image power is distributed in the Bessel-Fourier moments of lower orders.Master of Science in Applied Computer Scienc

Data Hiding in Digital Video

With the rapid development of digital multimedia technologies, an old method which is called steganography has been sought to be a solution for data hiding applications such as digital watermarking and covert communication. Steganography is the art of secret communication using a cover signal, e.g., video, audio, image etc., whereas the counter-technique, detecting the existence of such as a channel through a statistically trained classifier, is called steganalysis. The state-of-the art data hiding algorithms utilize features; such as Discrete Cosine Transform (DCT) coefficients, pixel values, motion vectors etc., of the cover signal to convey the message to the receiver side. The goal of embedding algorithm is to maximize the number of bits sent to the decoder side (embedding capacity) with maximum robustness against attacks while keeping the perceptual and statistical distortions (security) low. Data Hiding schemes are characterized by these three conflicting requirements: security against steganalysis, robustness against channel associated and/or intentional distortions, and the capacity in terms of the embedded payload. Depending upon the application it is the designer\u27s task to find an optimum solution amongst them. The goal of this thesis is to develop a novel data hiding scheme to establish a covert channel satisfying statistical and perceptual invisibility with moderate rate capacity and robustness to combat steganalysis based detection. The idea behind the proposed method is the alteration of Video Object (VO) trajectory coordinates to convey the message to the receiver side by perturbing the centroid coordinates of the VO. Firstly, the VO is selected by the user and tracked through the frames by using a simple region based search strategy and morphological operations. After the trajectory coordinates are obtained, the perturbation of the coordinates implemented through the usage of a non-linear embedding function, such as a polar quantizer where both the magnitude and phase of the motion is used. However, the perturbations made to the motion magnitude and phase were kept small to preserve the semantic meaning of the object motion trajectory. The proposed method is well suited to the video sequences in which VOs have smooth motion trajectories. Examples of these types could be found in sports videos in which the ball is the focus of attention and exhibits various motion types, e.g., rolling on the ground, flying in the air, being possessed by a player, etc. Different sports video sequences have been tested by using the proposed method. Through the experimental results, it is shown that the proposed method achieved the goal of both statistical and perceptual invisibility with moderate rate embedding capacity under AWGN channel with varying noise variances. This achievement is important as the first step for both active and passive steganalysis is the detection of the existence of covert channel. This work has multiple contributions in the field of data hiding. Firstly, it is the first example of a data hiding method in which the trajectory of a VO is used. Secondly, this work has contributed towards improving steganographic security by providing new features: the coordinate location and semantic meaning of the object

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Probabilistic modeling of wavelet coefficients for processing of image and video signals

Statistical estimation and detection techniques are widely used in signal processing including wavelet-based image and video processing. The probability density function (PDF) of the wavelet coefficients of image and video signals plays a key role in the development of techniques for such a processing. Due to the fixed number of parameters, the conventional PDFs for the estimators and detectors usually ignore higher-order moments. Consequently, estimators and detectors designed using such PDFs do not provide a satisfactory performance. This thesis is concerned with first developing a probabilistic model that is capable of incorporating an appropriate number of parameters that depend on higher-order moments of the wavelet coefficients. This model is then used as the prior to propose certain estimation and detection techniques for denoising and watermarking of image and video signals. Towards developing the probabilistic model, the Gauss-Hermite series expansion is chosen, since the wavelet coefficients have non-compact support and their empirical density function shows a resemblance to the standard Gaussian function. A modification is introduced in the series expansion so that only a finite number of terms can be used for modeling the wavelet coefficients with rendering the resulting PDF to become negative. The parameters of the resulting PDF, called the modified Gauss-Hermite (NIGH) PDF, are evaluated in terms of the higher-order sample-moments. It is shown that the MGH PDF fits the empirical density function better than the existing PDFs that use a limited number of parameters do. The proposed MGH PDF is used as the prior of image and video signals in designing maximum a posteriori and minimum mean squared error-based estimators for denoising of image and video signals and log-likelihood ratio-based detector for watermarking of image signals. The performance of the estimation and detection techniques are then evaluated in terms of the commonly used metrics. It is shown through extensive experimentations that the estimation and detection techniques developed utilizing the proposed MGH PDF perform substantially better than those that utilize the conventional PDFs. These results confirm that the superior fit of the MGH PDF to the empirical density function resulting from the flexibility of the MGH PDF in choosing the number of parameters, which are functions of higher-order moments of data, leads to the better performance. Thus, the proposed MGH PDF should play a significant role in wavelet-based image and video signal processin

Contourlet Domain Image Modeling and its Applications in Watermarking and Denoising

Statistical image modeling in sparse domain has recently attracted a great deal of research interest. Contourlet transform as a two-dimensional transform with multiscale and multi-directional properties is known to effectively capture the smooth contours and geometrical structures in images. The objective of this thesis is to study the statistical properties of the contourlet coefficients of images and develop statistically-based image denoising and watermarking schemes. Through an experimental investigation, it is first established that the distributions of the contourlet subband coefficients of natural images are significantly non-Gaussian with heavy-tails and they can be best described by the heavy-tailed statistical distributions, such as the alpha-stable family of distributions. It is shown that the univariate members of this family are capable of accurately fitting the marginal distributions of the empirical data and that the bivariate members can accurately characterize the inter-scale dependencies of the contourlet coefficients of an image. Based on the modeling results, a new method in image denoising in the contourlet domain is proposed. The Bayesian maximum a posteriori and minimum mean absolute error estimators are developed to determine the noise-free contourlet coefficients of grayscale and color images. Extensive experiments are conducted using a wide variety of images from a number of databases to evaluate the performance of the proposed image denoising scheme and to compare it with that of other existing schemes. It is shown that the proposed denoising scheme based on the alpha-stable distributions outperforms these other methods in terms of the peak signal-to-noise ratio and mean structural similarity index, as well as in terms of visual quality of the denoised images. The alpha-stable model is also used in developing new multiplicative watermark schemes for grayscale and color images. Closed-form expressions are derived for the log-likelihood-based multiplicative watermark detection algorithm for grayscale images using the univariate and bivariate Cauchy members of the alpha-stable family. A multiplicative multichannel watermark detector is also designed for color images using the multivariate Cauchy distribution. Simulation results demonstrate not only the effectiveness of the proposed image watermarking schemes in terms of the invisibility of the watermark, but also the superiority of the watermark detectors in providing detection rates higher than that of the state-of-the-art schemes even for the watermarked images undergone various kinds of attacks

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Robust Logo Watermarking

Digital image watermarking is used to protect the copyright of digital images. In this thesis, a novel blind logo image watermarking technique for RGB images is proposed. The proposed technique exploits the error correction capabilities of the Human Visual System (HVS). It embeds two different watermarks in the wavelet/multiwavelet domains. The two watermarks are embedded in different sub-bands, are orthogonal, and serve different purposes. One is a high capacity multi-bit watermark used to embed the logo, and the other is a 1-bit watermark which is used for the detection and reversal of geometrical attacks. The two watermarks are both embedded using a spread spectrum approach, based on a pseudo-random noise (PN) sequence and a unique secret key. Robustness against geometric attacks such as Rotation, Scaling, and Translation (RST) is achieved by embedding the 1-bit watermark in the Wavelet Transform Modulus Maxima (WTMM) coefficients of the wavelet transform. Unlike normal wavelet coefficients, WTMM coefficients are shift invariant, and this important property is used to facilitate the detection and reversal of RST attacks. The experimental results show that the proposed watermarking technique has better distortion parameter detection capabilities, and compares favourably against existing techniques in terms of robustness against geometrical attacks such as rotation, scaling, and translation

Applications of MATLAB in Science and Engineering

The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest