30,544 research outputs found
A brief introduction to cosmic topology
Whether we live in a spatially finite universe, and what its shape and size
may be, are among the fundamental long-standing questions in cosmology. These
questions of topological nature have become particularly topical, given the
wealth of increasingly accurate astro-cosmological observations, especially the
recent observations of the cosmic microwave background radiation. An overview
of the basic context of cosmic topology, the detectability constraints from
recent observations, as well as the main methods for its detection and some
recent results are briefly presented.Comment: 14 pages, 5 figures. Short review of the topics addressed with
details in the lectures. To appear in the proc. of the XIth Brazilian School
of Cosmology and Gravitation, eds. M.Novelo and S.E. Perez Bergliaffa,
American Institute of Physics Conference Proceedings (2005
Memory vectors for similarity search in high-dimensional spaces
We study an indexing architecture to store and search in a database of
high-dimensional vectors from the perspective of statistical signal processing
and decision theory. This architecture is composed of several memory units,
each of which summarizes a fraction of the database by a single representative
vector. The potential similarity of the query to one of the vectors stored in
the memory unit is gauged by a simple correlation with the memory unit's
representative vector. This representative optimizes the test of the following
hypothesis: the query is independent from any vector in the memory unit vs. the
query is a simple perturbation of one of the stored vectors.
Compared to exhaustive search, our approach finds the most similar database
vectors significantly faster without a noticeable reduction in search quality.
Interestingly, the reduction of complexity is provably better in
high-dimensional spaces. We empirically demonstrate its practical interest in a
large-scale image search scenario with off-the-shelf state-of-the-art
descriptors.Comment: Accepted to IEEE Transactions on Big Dat
Evaluation of Hashing Methods Performance on Binary Feature Descriptors
In this paper we evaluate performance of data-dependent hashing methods on
binary data. The goal is to find a hashing method that can effectively produce
lower dimensional binary representation of 512-bit FREAK descriptors. A
representative sample of recent unsupervised, semi-supervised and supervised
hashing methods was experimentally evaluated on large datasets of labelled
binary FREAK feature descriptors
View subspaces for indexing and retrieval of 3D models
View-based indexing schemes for 3D object retrieval are gaining popularity
since they provide good retrieval results. These schemes are coherent with the
theory that humans recognize objects based on their 2D appearances. The
viewbased techniques also allow users to search with various queries such as
binary images, range images and even 2D sketches. The previous view-based
techniques use classical 2D shape descriptors such as Fourier invariants,
Zernike moments, Scale Invariant Feature Transform-based local features and 2D
Digital Fourier Transform coefficients. These methods describe each object
independent of others. In this work, we explore data driven subspace models,
such as Principal Component Analysis, Independent Component Analysis and
Nonnegative Matrix Factorization to describe the shape information of the
views. We treat the depth images obtained from various points of the view
sphere as 2D intensity images and train a subspace to extract the inherent
structure of the views within a database. We also show the benefit of
categorizing shapes according to their eigenvalue spread. Both the shape
categorization and data-driven feature set conjectures are tested on the PSB
database and compared with the competitor view-based 3D shape retrieval
algorithmsComment: Three-Dimensional Image Processing (3DIP) and Applications
(Proceedings Volume) Proceedings of SPIE Volume: 7526 Editor(s): Atilla M.
Baskurt ISBN: 9780819479198 Date: 2 February 201
Cosmic microwave background constraints on multi-connected spherical spaces
This article describes the Cosmic Microwave Background anisotropies expected
in a closed universe with the topology of a lens space L(p,q) and with density
parameter Omega_0 close to 1. It provides the first simulated maps for such
spaces along with their corresponding power spectra. In spite of our initial
expectations that increasing p (and thus decreasing the size of the fundamental
domain) should suppress the quadrupole, we found just the opposite: increasing
p elevates the relative power of the low multipoles, for reasons that have
since become clear. For Omega_0 = 1.02, an informal ``by eye'' examination of
the simulated power spectra suggests that must be less than 15 for
consistency with WMAP's data, while geometric considerations imply that
matching circles will exist (potentially revealing the multi-connected
topology) only if p > 7. These bounds become less stringent for values of
Omega_0 closer to 1.Comment: 4 pages, 9 figures, to appear in PR
Simulating Cosmic Microwave Background maps in multi-connected spaces
This article describes the computation of cosmic microwave background
anisotropies in a universe with multi-connected spatial sections and focuses on
the implementation of the topology in standard CMB computer codes. The key
ingredient is the computation of the eigenmodes of the Laplacian with boundary
conditions compatible with multi-connected space topology. The correlators of
the coefficients of the decomposition of the temperature fluctuation in
spherical harmonics are computed and examples are given for spatially flat
spaces and one family of spherical spaces, namely the lens spaces. Under the
hypothesis of Gaussian initial conditions, these correlators encode all the
topological information of the CMB and suffice to simulate CMB maps.Comment: 33 pages, 55 figures, submitted to PRD. Higher resolution figures
available on deman
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