Blur Invariants for Image Recognition

Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified theory of blur invariants. Unlike all previous attempts, the new theory does not require any prior knowledge of the blur type. The invariants are constructed in the Fourier domain by means of orthogonal projection operators and moment expansion is used for efficient and stable computation. It is shown that all blur invariants published earlier are just particular cases of this approach. Experimental comparison to concurrent approaches shows the advantages of the proposed theory.Comment: 15 page

Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Visualization and analysis of diffusion tensor fields

technical reportThe power of medical imaging modalities to measure and characterize biological tissue is amplified by visualization and analysis methods that help researchers to see and understand the structures within their data. Diffusion tensor magnetic resonance imaging can measure microstructural properties of biological tissue, such as the coherent linear organization of white matter of the central nervous system, or the fibrous texture of muscle tissue. This dissertation describes new methods for visualizing and analyzing the salient structure of diffusion tensor datasets. Glyphs from superquadric surfaces and textures from reactiondiffusion systems facilitate inspection of data properties and trends. Fiber tractography based on vector-tensor multiplication allows major white matter pathways to be visualized. The generalization of direct volume rendering to tensor data allows large-scale structures to be shaded and rendered. Finally, a mathematical framework for analyzing the derivatives of tensor values, in terms of shape and orientation change, enables analytical shading in volume renderings, and a method of feature detection important for feature-preserving filtering of tensor fields. Together, the combination of methods enhances the ability of diffusion tensor imaging to provide insight into the local and global structure of biological tissue

Surface theorem for the Chern-Simons axion coupling

The Chern-Simons axion coupling of a bulk insulator is only defined modulo a quantum of e^2/h. The quantized part of the coupling is uniquely defined for a bounded insulating sample, but it depends on the specific surface termination. Working in a slab geometry and representing the valence bands in terms of hybrid Wannier functions, we show how to determine that quantized part from the excess Chern number of the hybrid Wannier sheets located near the surface of the slab. The procedure is illustrated for a tight-binding model consisting of coupled quantum anomalous Hall layers. By slowly modulating the model parameters, it is possible to transfer one unit of Chern number from the bottom to the top surface over the course of a cyclic evolution of the bulk Hamiltonian. When the evolution of the surface Hamiltonian is also cyclic, the Chern pumping is obstructed by chiral touchings between valence and conduction surface bands.Comment: 15 page

Image understanding and feature extraction for applications in industry and mapping

Bibliography: p. 212-220.The aim of digital photogrammetry is the automated extraction and classification of the three dimensional information of a scene from a number of images. Existing photogrammetric systems are semi-automatic requiring manual editing and control, and have very limited domains of application so that image understanding capabilities are left to the user. Among the most important steps in a fully integrated system are the extraction of features suitable for matching, the establishment of the correspondence between matching points and object classification. The following study attempts to explore the applicability of pattern recognition concepts in conjunction with existing area-based methods, feature-based techniques and other approaches used in computer vision in order to increase the level of automation and as a general alternative and addition to existing methods. As an illustration of the pattern recognition approach examples of industrial applications are given. The underlying method is then extended to the identification of objects in aerial images of urban scenes and to the location of targets in close-range photogrammetric applications. Various moment-based techniques are considered as pattern classifiers including geometric invariant moments, Legendre moments, Zernike moments and pseudo-Zernike moments. Two-dimensional Fourier transforms are also considered as pattern classifiers. The suitability of these techniques is assessed. These are then applied as object locators and as feature extractors or interest operators. Additionally the use of fractal dimension to segment natural scenes for regional classification in order to limit the search space for particular objects is considered. The pattern recognition techniques require considerable preprocessing of images. The various image processing techniques required are explained where needed. Extracted feature points are matched using relaxation based techniques in conjunction with area-based methods to 'obtain subpixel accuracy. A subpixel pattern recognition based method is also proposed and an investigation into improved area-based subpixel matching methods is undertaken. An algorithm for determining relative orientation parameters incorporating the epipolar line constraint is investigated and compared with a standard relative orientation algorithm. In conclusion a basic system that can be automated based on some novel techniques in conjunction with existing methods is described and implemented in a mapping application. This system could be largely automated with suitably powerful computers

In-Plane Orbital Texture Switch at the Dirac Point in the Topological Insulator Bi2Se3

Topological insulators are novel macroscopic quantum-mechanical phase of matter, which hold promise for realizing some of the most exotic particles in physics as well as application towards spintronics and quantum computation. In all the known topological insulators, strong spin-orbit coupling is critical for the generation of the protected massless surface states. Consequently, a complete description of the Dirac state should include both the spin and orbital (spatial) parts of the wavefunction. For the family of materials with a single Dirac cone, theories and experiments agree qualitatively, showing the topological state has a chiral spin texture that changes handedness across the Dirac point (DP), but they differ quantitatively on how the spin is polarized. Limited existing theoretical ideas predict chiral local orbital angular momentum on the two sides of the DP. However, there have been neither direct measurements nor calculations identifying the global symmetry of the spatial wavefunction. Here we present the first results from angle-resolved photoemission experiment and first-principles calculation that both show, counter to current predictions, the in-plane orbital wavefunctions for the surface states of Bi2Se3 are asymmetric relative to the DP, switching from being tangential to the k-space constant energy surfaces above DP, to being radial to them below the DP. Because the orbital texture switch occurs exactly at the DP this effect should be intrinsic to the topological physics, constituting an essential yet missing aspect in the description of the topological Dirac state. Our results also indicate that the spin texture may be more complex than previously reported, helping to reconcile earlier conflicting spin resolved measurements

Ice Crystal Classification Using Two Dimensional Light Scattering Patterns

An investigation is presented into methods of characterising cirrus ice crystals from in-situ light scattering data. A database of scattering patterns from modelled crystals was created using the Ray Tracing with Diffraction on Facets (RTDF) model from the University of Hertfordshire, to which experimental and modelled data was fitted. Experimental data was gathered in the form of scattering patterns from ice analogue crystals with similar optical properties and hexagonal symmetry to ice, yet stable at room temperature. A laboratory rig is described which images scattering patterns from single particles while allowing precise control over the orientation of the particle with respect to the incident beam. Images of scattering patterns were captured and compared to patterns from modelled crystals with similar geometry. Methods for introducing particles en-masse and individually to the Small Ice Detector (SID) instruments are discussed, with particular emphasis on the calibration of the gain of the SID-2 instrument. The variation in gain between detector elements is found to be significant, variable over the life of the detector, and different for different detectors. Fitting was performed by comparison of test scattering patterns (either modelled or experimental) to the reference database. Representation of the two dimensional scattering patterns by asymmetry factor, moment invariants, azimuthal intensity patterns (AIP) and the Fourier transform of the AIP are compared for fitting accuracy. Direct comparison of the AIP is found to be the most accurate method. Increased resolution of the AIP is shown to improve the fitting substantially. Case studies are presented for the fitting of two ice analogue crystals to the modelled database. Fitting accuracy is found to be negatively influenced by small amounts of surface roughness and detail not currently considered by the RTDF model. Fitting of in-situ data gathered by the SID-3 instrument during the HALO 02 campaign at the AIDA cloud chamber in Germany is presented and discussed. Saturation of detector pixels is shown to affect pattern fitting. In-flight operation of the instrument involves the variation of gain of the whole detector (as opposed to individual elements) in order to obtain unsaturated images of both large and small particles