Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces

Image analysis using visual saliency with applications in hazmat sign detection and recognition

Visual saliency is the perceptual process that makes attractive objects stand out from their surroundings in the low-level human visual system. Visual saliency has been modeled as a preprocessing step of the human visual system for selecting the important visual information from a scene. We investigate bottom-up visual saliency using spectral analysis approaches. We present separate and composite model families that generalize existing frequency domain visual saliency models. We propose several frequency domain visual saliency models to generate saliency maps using new spectrum processing methods and an entropy-based saliency map selection approach. A group of saliency map candidates are then obtained by inverse transform. A final saliency map is selected among the candidates by minimizing the entropy of the saliency map candidates. The proposed models based on the separate and composite model families are also extended to various color spaces. We develop an evaluation tool for benchmarking visual saliency models. Experimental results show that the proposed models are more accurate and efficient than most state-of-the-art visual saliency models in predicting eye fixation.^ We use the above visual saliency models to detect the location of hazardous material (hazmat) signs in complex scenes. We develop a hazmat sign location detection and content recognition system using visual saliency. Saliency maps are employed to extract salient regions that are likely to contain hazmat sign candidates and then use a Fourier descriptor based contour matching method to locate the border of hazmat signs in these regions. This visual saliency based approach is able to increase the accuracy of sign location detection, reduce the number of false positive objects, and speed up the overall image analysis process. We also propose a color recognition method to interpret the color inside the detected hazmat sign. Experimental results show that our proposed hazmat sign location detection method is capable of detecting and recognizing projective distorted, blurred, and shaded hazmat signs at various distances.^ In other work we investigate error concealment for scalable video coding (SVC). When video compressed with SVC is transmitted over loss-prone networks, the decompressed video can suffer severe visual degradation across multiple frames. In order to enhance the visual quality, we propose an inter-layer error concealment method using motion vector averaging and slice interleaving to deal with burst packet losses and error propagation. Experimental results show that the proposed error concealment methods outperform two existing methods

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

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Multimodal Computational Attention for Scene Understanding

Robotic systems have limited computational capacities. Hence, computational attention models are important to focus on specific stimuli and allow for complex cognitive processing. For this purpose, we developed auditory and visual attention models that enable robotic platforms to efficiently explore and analyze natural scenes. To allow for attention guidance in human-robot interaction, we use machine learning to integrate the influence of verbal and non-verbal social signals into our models

Forensic research on detecting seam carving in digital images

Digital images have been playing an important role in our daily life for the last several decades. Naturally, image editing technologies have been tremendously developed due to the increasing demands. As a result, digital images can be easily manipulated on a personal computer or even a cellphone for many purposes nowadays, so that the authenticity of digital images becomes an important issue. In this dissertation research, four machine learning based forensic methods are presented to detect one of the popular image editing techniques, called ‘seam carving’. To reveal seam carving applied to uncompressed images from the perspective of energy distribution change, an energy based statistical model is proposed as the first work in this dissertation. Features measured global energy of images, remaining optimal seams, and noise level are extracted from four local derivative pattern (LDP) domains instead of from the original pixel domain to heighten the energy change caused by seam carving. A support vector machine (SVM) based classifier is employed to determine whether an image has been seam carved or not. In the second work, an advanced feature model is presented for seam carving detection by investigating the statistical variation among neighboring pixels. Comprised with three types of statistical features, i.e., LDP features, Markov features, and SPAM features, the powerful feature model significantly improved the state-of-the-art accuracy in detecting low carving rate seam carving. After the feature selection by utilizing SVM based recursive feature elimination (SVM-RFE), with a small amount of features selected from the proposed model the overall performance is further improved. Combining above mentioned two works, a hybrid feature model is then proposed as the third work to further boost the accuracy in detecting seam carving at low carving rate. The proposed model consists of two sets of features, which capture energy change and neighboring relationship variation respectively, achieves remarkable performance on revealing seam carving, especially low carving rate seam carving, in digital images. Besides these three hand crafted feature models, a deep convolutional neural network is designed for seam carving detection. It is the first work that successfully utilizes deep learning technology to solve this forensic problem. The experimental works demonstrate their much more improved performance in the cases where the amount of seam carving is not serious. Although these four pieces of work move the seam carving detection ahead substantially, future research works with more advanced statistical model or deep neural network along this line are expected

Comparative Analysis of Techniques Used to Detect Copy-Move Tampering for Real-World Electronic Images

Evolution of high computational powerful computers, easy availability of several innovative editing software package and high-definition quality-based image capturing tools follows to effortless result in producing image forgery. Though, threats for security and misinterpretation of digital images and scenes have been observed to be happened since a long period and also a lot of research has been established in developing diverse techniques to authenticate the digital images. On the contrary, the research in this region is not limited to checking the validity of digital photos but also to exploring the specific signs of distortion or forgery. This analysis would not require additional prior information of intrinsic content of corresponding digital image or prior embedding of watermarks. In this paper, recent growth in the area of digital image tampering identification have been discussed along with benchmarking study has been shown with qualitative and quantitative results. With variety of methodologies and concepts, different applications of forgery detection have been discussed with corresponding outcomes especially using machine and deep learning methods in order to develop efficient automated forgery detection system. The future applications and development of advanced soft-computing based techniques in digital image forgery tampering has been discussed