869 research outputs found
A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
We investigate the suitability and properties of a quasi-Kinnersley tetrad
and a geometrically motivated coordinate system as tools for quantifying both
strong-field and wave-zone effects in numerical relativity (NR) simulations. We
fix the radial and latitudinal coordinate degrees of freedom of the metric,
using the Coulomb potential associated with the quasi-Kinnersley transverse
frame. These coordinates are invariants of the spacetime and can be used to
unambiguously fix the outstanding spin-boost freedom associated with the
quasi-Kinnersley frame (resulting in a preferred quasi-Kinnersley tetrad
(QKT)). In the limit of small perturbations about a Kerr spacetime, these
coordinates and QKT reduce to Boyer-Lindquist coordinates and the Kinnersley
tetrad, irrespective of the simulation gauge choice. We explore the properties
of this construction both analytically and numerically, and we gain insights
regarding the propagation of radiation described by a super-Poynting vector. We
also quantify in detail the peeling properties of the chosen tetrad and gauge.
We argue that these choices are particularly well suited for a rapidly
converging wave-extraction algorithm as the extraction location approaches
infinity, and we explore numerically the extent to which this property remains
applicable on the interior of a computational domain. Using a number of
additional tests, we verify that the prescription behaves as required in the
appropriate limits regardless of simulation gauge. We explore the behavior of
the geometrically motivated coordinate system in dynamical binary-black-hole NR
mergers, and find them useful for visualizing features in NR simulations such
as the spurious "junk" radiation. Finally, we carefully scrutinize the head-on
collision of two black holes and, for example, the way in which the extracted
waveform changes as it moves through the computational domain.Comment: 30 pages, 17 figures, 2 table
Subjective geometry and geometric psychology
AbstractâSubjective geometryâ is a term coined by Weintraub and Krantz to describe the distortion imposed upon geometric patterns by the visual system itselfâso-called optical illusions. The latter are widely regarded as being generated by misplaced âconstancyâ effects, i.e., they are regarded as stemming from the invariance of an object's appearance under wide variations in viewing conditions, such as obliquity, rotations, etc. The invariances represented by these constanciesâshape constancy, size constancy, etc.âare spatiotemporal invariants of certain Lie subgroups of P4(R) â CO(1, 3) â GL(4, R) that govern Euclidean and non-Euclidean geometry. Tha Euclidean subgroups describe a Cyclopean visual world; the non-Euclidean, a binocular (bipolar) world of hyperbolic nature, according to the work of Luneburg, Blank, Indow, and others. The visual field of view is itself a geometric object involvingnot only âfigureâ and âgroundâ but also visual contours (orbits of the Lie groups involved), linear perspective, interposition, and contact and symplectic structures. The retina and âcortical retinaâ are both covered by a family of âcircular-surroundâ cellular response fields (of a âMexican hatâ nature) which constitute an atlas for the visual manifold S. Upon this manifold are defined certain equivariant vector bundles that account for constancy phenomena and certain jet bundles, arising out of the vector bundles by prolongation, that generate the differential invariants characterizing higher form perception. The resultant theory of perceptual-cognitive processing has been termed âgeometric psychology,â in analogy to MacLane's âgeometrical mechanicsâ and BrockettâHermannâMayne's âgeometry of systems,â the mathematical structure being very similar in all three instances. Functorial maps from the category GvFB(S) of equivariant fibre bundles to the simplicial category and the category of simplicial objects complete the theory by extending the perceptual system to cognitive phenomena and information-processing psychology
Shape description and matching using integral invariants on eccentricity transformed images
Matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision. To keep track of changes inside the breast, for example, it is important for a computer aided detection system to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants (II) and with geodesic distance, yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants describe the boundaries of planar shapes. However, they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure. Conversely, eccentricity transforms (Ecc) can match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines the boundary signature of a shape obtained from II and structural information from the Ecc to yield results that improve on them separately
Geometric and photometric affine invariant image registration
This thesis aims to present a solution to the correspondence problem for the registration
of wide-baseline images taken from uncalibrated cameras. We propose an affine
invariant descriptor that combines the geometry and photometry of the scene to find
correspondences between both views. The geometric affine invariant component of the
descriptor is based on the affine arc-length metric, whereas the photometry is analysed
by invariant colour moments. A graph structure represents the spatial distribution of the
primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs
represent connectivities by extracted contours. After matching, we refine the search for
correspondences by using a maximum likelihood robust algorithm. We have evaluated
the system over synthetic and real data. The method is endemic to propagation of errors
introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System
Distortion Robust Biometric Recognition
abstract: Information forensics and security have come a long way in just a few years thanks to the recent advances in biometric recognition. The main challenge remains a proper design of a biometric modality that can be resilient to unconstrained conditions, such as quality distortions. This work presents a solution to face and ear recognition under unconstrained visual variations, with a main focus on recognition in the presence of blur, occlusion and additive noise distortions.
First, the dissertation addresses the problem of scene variations in the presence of blur, occlusion and additive noise distortions resulting from capture, processing and transmission. Despite their excellent performance, âdeepâ methods are susceptible to visual distortions, which significantly reduce their performance. Sparse representations, on the other hand, have shown huge potential capabilities in handling problems, such as occlusion and corruption. In this work, an augmented SRC (ASRC) framework is presented to improve the performance of the Spare Representation Classifier (SRC) in the presence of blur, additive noise and block occlusion, while preserving its robustness to scene dependent variations. Different feature types are considered in the performance evaluation including image raw pixels, HoG and deep learning VGG-Face. The proposed ASRC framework is shown to outperform the conventional SRC in terms of recognition accuracy, in addition to other existing sparse-based methods and blur invariant methods at medium to high levels of distortion, when particularly used with discriminative features.
In order to assess the quality of features in improving both the sparsity of the representation and the classification accuracy, a feature sparse coding and classification index (FSCCI) is proposed and used for feature ranking and selection within both the SRC and ASRC frameworks.
The second part of the dissertation presents a method for unconstrained ear recognition using deep learning features. The unconstrained ear recognition is performed using transfer learning with deep neural networks (DNNs) as a feature extractor followed by a shallow classifier. Data augmentation is used to improve the recognition performance by augmenting the training dataset with image transformations. The recognition performance of the feature extraction models is compared with an ensemble of fine-tuned networks. The results show that, in the case where long training time is not desirable or a large amount of data is not available, the features from pre-trained DNNs can be used with a shallow classifier to give a comparable recognition accuracy to the fine-tuned networks.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201
Object recognition using multi-view imaging
Single view imaging data has been used in most previous research in computer vision and
image understanding and lots of techniques have been developed. Recently with the fast
development and dropping cost of multiple cameras, it has become possible to have many
more views to achieve image processing tasks. This thesis will consider how to use the
obtained multiple images in the application of target object recognition.
In this context, we present two algorithms for object recognition based on scale-
invariant feature points. The first is single view object recognition method (SOR), which
operates on single images and uses a chirality constraint to reduce the recognition errors
that arise when only a small number of feature points are matched. The procedure is
extended in the second multi-view object recognition algorithm (MOR) which operates on
a multi-view image sequence and, by tracking feature points using a dynamic programming
method in the plenoptic domain subject to the epipolar constraint, is able to fuse feature
point matches from all the available images, resulting in more robust recognition.
We evaluated these algorithms using a number of data sets of real images capturing
both indoor and outdoor scenes. We demonstrate that MOR is better than SOR particularly for noisy and low resolution images, and it is also able to recognize objects that are
partially occluded by combining it with some segmentation techniques
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