Signal Modeling for Two-Dimensional Image Structures and Scale-Space Based Image Analysis

Model based image representation plays an important role in many computer vision tasks. Consequently, it is of high significance to model image structures with more powerful representation capabilities. In the literature, there exist bulk of researches for intensity based modeling. However, most of them suffer from the illumination variation. On the other hand, phase information, which carries most essential structural information of the original signal, has the advantage of being invariant to the brightness change. Therefore, phase based image analysis is advantageous when compared to purely intensity based approaches. This thesis aims to propose novel image representations for 2D image structures, from which useful local features can be extracted, which are useful for phase based image analysis. The first approach presents a 2D rotationally invariant quadrature filter. This model is able to handle superimposed intrinsically two-dimensional (i2D) patterns with flexible angles of intersection. Hence, it can be regarded as an extension of the structure multivector. The second approach is the monogenic curvature tensor. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, we can design a general model for 2D structures as the monogenic extension of a curvature tensor. Based on it, local representations for the intrinsically one-dimensional (i1D) and i2D structures are derived as the monogenic signal and the generalized monogenic curvature signal, respectively. From them, independent features of local amplitude, phase and orientation are simultaneously extracted. Besides, a generalized monogenic curvature scale-space can be built by applying a Poisson kernel to the monogenic curvature tensor. Compared with other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures in a multi-scale framework, which delivers access to phase-based processing in many computer vision tasks. To demonstrate the efficiency and power of the theoretic framework, some computer vision applications are presented, which include the phase based image reconstruction, detecting i2D image structures using local phase and monogenic curvature tensor for optical flow estimation

08291 Abstracts Collection -- Statistical and Geometrical Approaches to Visual Motion Analysis

From 13.07.2008 to 18.07.2008, the Dagstuhl Seminar 08291 ``Statistical and Geometrical Approaches to Visual Motion Analysis\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general

Algebraic Representation and Geometric Interpretation of Hilbert Transformed Signals

This thesis covers a fundamental problem of local phase based signal processing: the isotropic generalization of the classical one dimensional analytic signal (D. Gabor) to higher dimensional signal domains. The classical analytic signal extends a real valued one dimensional signal to a complex valued signal by means of the classical 1D Hilbert transform. This signal extension enables the complete analysis of local phase and local amplitude information for each frequency component in the sense of Fourier analysis. In case of two dimensional signal domains, e.g. for images, additional geometric information is required to characterize higher dimensional signals locally. The local geometric information is called orientation, which consists of the main orientation and apex angle for two superimposed one dimensional signals. The problem of two dimensional signal analysis is the fact that in general those signals could consist of an unlimited number of superimposed one dimensional signals with individual orientations. Local phase, amplitude and additional orientation information can be extracted by the monogenic signal (M. Felsberg and G. Sommer) which is always restricted to the subclass of intrinsically one dimensional signals, i.e. the class of signals which only make use of one degree of freedom within the embedding signal domain. In case of 2D images the monogenic signal enables the rotationally invariant analysis of lines and edges. In contrast to the 1D analytic signal the monogenic signal extends all real valued signals of dimension n to a (n+1) - dimensional vector valued monogenic signal by means of the generalized first order Hilbert transform, which is also known as the Riesz transform. The analytic signal and the monogenic signal show that a direct relation between analytical signals and their algebraic representation exists. This fact has motivated the work and the results of this thesis, namely the extension of the 2D monogenic signal to more general 2D analytic signals, their algebraic representation, and their most geometric embedding. In case of more general 2D signals the geometric algebra will be shown to be a natural representation, and the conformal space as the geometric embedding for the signal interpretation. In this thesis we present 2D analytic signals as generalizations of the 2D monogenic signal which now extend the original 2D signal to a multi-vector valued signal in homogeneous conformal space by means of higher order Hilbert transforms, and by means of a so called hybrid matrix geometric algebra representation. The 2D analytic signal and the more general multi-vector signal will be interpreted in conformal space which delivers a descriptive geometric interpretation and algebraic embedding of signals. In case of 2D image signals the 2D analytic signal and the multi-vector signal enable the rotationally invariant analysis of lines, edges, corners and junctions in one unified framework. Furthermore, additional local curvature can be determined by first order generalized Hilbert transforms without the need of derivatives. This so called conformal monogenic signal can be defined for any signal domain

STRUCTURE DETECTION WITH SECOND ORDER RIESZ TRANSFORMS

A frequently applied indicator of tubular structures is based on the eigenvalues of the Hessian matrix of the original image convolved with a Gaussian, whose standard derivation depends on the size of the tubes. Hence the tube size must either be known in advance or a whole scale of standard deviations has to be tested resulting in higher computational costs – a serious obstacle for data with varying tube thickness. In this paper, we propose to modify the structure indicator by replacing the derivatives of the Gaussian smoothed function by the Riesz transform. We show by various numerical examples that the resulting structure indicator is scale independent. Smoothing with a Gaussian is just necessary to cope with the noise in the image, but is not related to the size of the tubular structures. We apply the novel structure indicator for the fiber orientation analysis of fibrous materials and for the segmentation of leather. The latter one was a special challenging application since all scales are present in the microstructure of leather

Towards spatial and temporal analysis of facial expressions in 3D data

Facial expressions are one of the most important means for communication of emotions and meaning. They are used to clarify and give emphasis, to express intentions, and form a crucial part of any human interaction. The ability to automatically recognise and analyse expressions could therefore prove to be vital in human behaviour understanding, which has applications in a number of areas such as psychology, medicine and security. 3D and 4D (3D+time) facial expression analysis is an expanding field, providing the ability to deal with problems inherent to 2D images, such as out-of-plane motion, head pose, and lighting and illumination issues. Analysis of data of this kind requires extending successful approaches applied to the 2D problem, as well as the development of new techniques. The introduction of recent new databases containing appropriate expression data, recorded in 3D or 4D, has allowed research into this exciting area for the first time. This thesis develops a number of techniques, both in 2D and 3D, that build towards a complete system for analysis of 4D expressions. Suitable feature types, designed by employing binary pattern methods, are developed for analysis of 3D facial geometry data. The full dynamics of 4D expressions are modelled, through a system reliant on motion-based features, to demonstrate how the different components of the expression (neutral-onset-apex-offset) can be distinguished and harnessed. Further, the spatial structure of expressions is harnessed to improve expression component intensity estimation in 2D videos. Finally, it is discussed how this latter step could be extended to 3D facial expression analysis, and also combined with temporal analysis. Thus, it is demonstrated that both spatial and temporal information, when combined with appropriate 3D features, is critical in analysis of 4D expression data.Open Acces

Analysis of motion in scale space

This work includes some new aspects of motion estimation by the optic flow method in scale spaces. The usual techniques for motion estimation are limited to the application of coarse to fine strategies. The coarse to fine strategies can be successful only if there is enough information in every scale. In this work we investigate the motion estimation in the scale space more basically. The wavelet choice for scale space decomposition of image sequences is discussed in the first part of this work. We make use of the continuous wavelet transform with rotationally symmetric wavelets. Bandpass decomposed sequences allow the replacement of the structure tensor by the phase invariant energy operator. The structure tensor is computationally more expensive because of its spatial or spatio-temporal averaging. The energy operator needs in general no further averaging. The numerical accuracy of the motion estimation with the energy operator is compared to the results of usual techniques, based on the structure tensor. The comparison tests are performed on synthetic and real life sequences. Another practical contribution is the accuracy measurement for motion estimation by adaptive smoothed tensor fields. The adaptive smoothing relies on nonlinear anisotropic diffusion with discontinuity and curvature preservation. We reached an accuracy gain under properly chosen parameters for the diffusion filter. A theoretical contribution from mathematical point of view is a new discontinuity and curvature preserving regularization for motion estimation. The convergence of solutions for the isotropic case of the nonlocal partial differential equation is shown. For large displacements between two consecutive frames the optic flow method is systematically corrupted because of the violence of the sampling theorem. We developed a new method for motion analysis by scale decomposition, which allows to circumvent the systematic corruption without using the coarse to fine strategy. The underlying assumption is, that in a certain neighborhood the grey value undergoes the same displacement. If this is fulfilled, then the same optic flow should be measured in all scales. If there arise inconsistencies in a pixel across the scale space, so they can be detected and the scales containing this inconsistencies are not taken into account

Robust Modular Feature-Based Terrain-Aided Visual Navigation and Mapping

The visual feature-based Terrain-Aided Navigation (TAN) system presented in this thesis addresses the problem of constraining inertial drift introduced into the location estimate of Unmanned Aerial Vehicles (UAVs) in GPS-denied environment. The presented TAN system utilises salient visual features representing semantic or human-interpretable objects (roads, forest and water boundaries) from onboard aerial imagery and associates them to a database of reference features created a-priori, through application of the same feature detection algorithms to satellite imagery. Correlation of the detected features with the reference features via a series of the robust data association steps allows a localisation solution to be achieved with a finite absolute bound precision defined by the certainty of the reference dataset. The feature-based Visual Navigation System (VNS) presented in this thesis was originally developed for a navigation application using simulated multi-year satellite image datasets. The extension of the system application into the mapping domain, in turn, has been based on the real (not simulated) flight data and imagery. In the mapping study the full potential of the system, being a versatile tool for enhancing the accuracy of the information derived from the aerial imagery has been demonstrated. Not only have the visual features, such as road networks, shorelines and water bodies, been used to obtain a position ’fix’, they have also been used in reverse for accurate mapping of vehicles detected on the roads into an inertial space with improved precision. Combined correction of the geo-coding errors and improved aircraft localisation formed a robust solution to the defense mapping application. A system of the proposed design will provide a complete independent navigation solution to an autonomous UAV and additionally give it object tracking capability

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. 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

Object Recognition

Vision-based object recognition tasks are very familiar in our everyday activities, such as driving our car in the correct lane. We do these tasks effortlessly in real-time. In the last decades, with the advancement of computer technology, researchers and application developers are trying to mimic the human's capability of visually recognising. Such capability will allow machine to free human from boring or dangerous jobs