The Study of Properties of n-D Analytic Signals and Their Spectra in Complex and Hypercomplex Domains

In the paper, two various representations of a n-dimensional (n-D) real signal u(x1,x2,…,xn) are investigated. The first one is the n-D complex analytic signal with a single-orthant spectrum defined by Hahn in 1992 as the extension of the 1-D Gabor’s analytic signal. It is compared with two hypercomplex approaches: the known n-D Clifford analytic signal and the Cayley-Dickson analytic signal defined by the Author in 2009. The signal-domain and frequency-domain definitions of these signals are presented and compared in 2-D and 3-D. Some new relations between the spectra in 2-D and 3-D hypercomplex domains are presented. The paper is illustrated with the example of a 2-D separable Cauchy pulse

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

Spatial and Temporal Image Prediction with Magnitude and Phase Representations

In this dissertation, I develop the theory and techniques for spatial and temporal image prediction with the magnitude and phase representation of the Complex Wavelet Transform (CWT) or the over-complete DCT to solve the problems of image inpainting and motion compensated inter-picture prediction. First, I develop the theory and algorithms of image reconstruction from the analytic magnitude or phase of the CWT. I prove the conditions under which a signal is uniquely specified by its analytic magnitude or phase, propose iterative algorithms for the reconstruction of a signal from its analytic CWT magnitude or phase, and analyze the convergence of the proposed algorithms. Image reconstruction from the magnitude and pseudo-phase of the over-complete DCT is also discussed and demonstrated. Second, I propose simple geometrical models of the CWT magnitude and phase to describe edges and structured textures and develop a spatial image prediction (inpainting) algorithm based on those models and the iterative image reconstruction mentioned above. Piecewise smooth signals, structured textures and their mixtures can be predicted successfully with the proposed algorithm. Simulation results show that the proposed algorithm achieves appealing visual quality with low computational complexity. Finally, I propose a novel temporal (inter-picture) image predictor for hybrid video coding. The proposed predictor enables successful predictive coding during fades, blended scenes, temporally decorrelated noise, and many other temporal evolutions that are beyond the capability of the traditional motion compensated prediction methods. The proposed predictor estimates the transform magnitude and phase of the desired motion compensated prediction by exploiting the temporal and spatial correlations of the transform coefficients. For the case of implementation in standard hybrid video coders, the over-complete DCT is chosen over the CWT. Better coding performance is achieved with the state-of-the-art H.264/AVC video encoder equipped with the proposed predictor. The proposed predictor is also successfully applied to image registration

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

Computational Modeling of Human Dorsal Pathway for Motion Processing

Reliable motion estimation in videos is of crucial importance for background iden- tification, object tracking, action recognition, event analysis, self-navigation, etc. Re- constructing the motion field in the 2D image plane is very challenging, due to variations in image quality, scene geometry, lighting condition, and most importantly, camera jit- tering. Traditional optical flow models assume consistent image brightness and smooth motion field, which are violated by unstable illumination and motion discontinuities that are common in real world videos. To recognize observer (or camera) motion robustly in complex, realistic scenarios, we propose a biologically-inspired motion estimation system to overcome issues posed by real world videos. The bottom-up model is inspired from the infrastructure as well as functionalities of human dorsal pathway, and the hierarchical processing stream can be divided into three stages: 1) spatio-temporal processing for local motion, 2) recogni- tion for global motion patterns (camera motion), and 3) preemptive estimation of object motion. To extract effective and meaningful motion features, we apply a series of steer- able, spatio-temporal filters to detect local motion at different speeds and directions, in a way that\u27s selective of motion velocity. The intermediate response maps are cal- ibrated and combined to estimate dense motion fields in local regions, and then, local motions along two orthogonal axes are aggregated for recognizing planar, radial and circular patterns of global motion. We evaluate the model with an extensive, realistic video database that collected by hand with a mobile device (iPad) and the video content varies in scene geometry, lighting condition, view perspective and depth. We achieved high quality result and demonstrated that this bottom-up model is capable of extracting high-level semantic knowledge regarding self motion in realistic scenes. Once the global motion is known, we segment objects from moving backgrounds by compensating for camera motion. For videos captured with non-stationary cam- eras, we consider global motion as a combination of camera motion (background) and object motion (foreground). To estimate foreground motion, we exploit corollary dis- charge mechanism of biological systems and estimate motion preemptively. Since back- ground motions for each pixel are collectively introduced by camera movements, we apply spatial-temporal averaging to estimate the background motion at pixel level, and the initial estimation of foreground motion is derived by comparing global motion and background motion at multiple spatial levels. The real frame signals are compared with those derived by forward predictions, refining estimations for object motion. This mo- tion detection system is applied to detect objects with cluttered, moving backgrounds and is proved to be efficient in locating independently moving, non-rigid regions. The core contribution of this thesis is the invention of a robust motion estimation system for complicated real world videos, with challenges by real sensor noise, complex natural scenes, variations in illumination and depth, and motion discontinuities. The overall system demonstrates biological plausibility and holds great potential for other applications, such as camera motion removal, heading estimation, obstacle avoidance, route planning, and vision-based navigational assistance, etc

CORDIC-ТЕХНИКА ДЛЯ ФИКСИРОВАННОГО УГЛА ВРАЩЕНИЯ В ОПЕРАЦИИ УМНОЖЕНИЯ КВАТЕРНИОНОВ

The article contains a number of solutions for the key element of paraunitary filter banks based on quaternionic algebra (Q-PUBF) – the multiplier of quaternions with usage of CORDIC (Coordinate Rotation Digital Computer) techniques for the fixed angle of rotation where, unlike known solutions, 4D rotation control parameters are represented by nonlinear function of shifts number of input operands of the microrotation operation. Suggested approach of the multiplier designing on a quaternion-constant allows reaching the maximum performance of the multiplier scheme with low use of resources, for example, of FPGA.Предлагается ряд решений ключевого элемента параунитарного банка фильтров на основе алгебры кватернионов – умножителя кватернионов с использованием CORDIC (Coordinate Rotation Digital Computer)-техники для фиксированного угла вращения, в которых в отличие от известных решений параметры управления 4D-вращением представляются нелинейной функцией числа сдвигов входных операндов операции микровращения. Предложенный подход проектирования умножителя на кватернион-константу позволяет достигать максимальной производительности схемы умножителя при скромном использовании ресурсов, например FPGA