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## ‣ Display Pre-Filtering for Multi-View Video Compression

Fonte: Association for Computing Machinery
Publicador: Association for Computing Machinery

Tipo: Monograph or Book

Português

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Multi-view 3D displays are preferable to other stereoscopic display technologies because they provide autostereoscopic viewing from any viewpoint without special glasses. However, they require a large number of pixels to achieve high image quality. Therefore, data compression is a major issue for this approach. In this paper, we present a framework for efficient compression of multi-view video streams for multi-view 3D displays. Our goal is to optimize image quality without increasing the required data bandwidth. We achieve this by taking into account a precise notion of the multi-dimensional display bandwidth. The display bandwidth implies that scene elements that appear at a given distance from the display become increasingly blurry as the distance grows. Our main contribution is to enhance conventional multi-view compression pipelines with an additional pre-filtering step that bandlimits the multi-view signal to the display bandwidth. This imposes a shallow depth of field on the input images, thereby removing high frequency content. We show that this pre-filtering step leads to increased image quality compared to state-of-the-art multi-view coding at equal bitrate. We present results of an extensive user study that corroborate the benefits of our approach. Our work suggests that display pre-filtering will be a fundamental component in signal processing for 3D displays...

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## ‣ Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/06/2013
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It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and, particularly for applications in the
geosciences, for scalar and vectorial signals defined on the surface of a unit
sphere.; Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics...

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## ‣ Spatiospectral concentration of vector fields on a sphere

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/06/2013
Português

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We construct spherical vector bases that are bandlimited and spatially
concentrated, or, alternatively, spacelimited and spectrally concentrated,
suitable for the analysis and representation of real-valued vector fields on
the surface of the unit sphere, as arises in the natural and biomedical
sciences, and engineering. Building on the original approach of Slepian,
Landau, and Pollak we concentrate the energy of our function bases into
arbitrarily shaped regions of interest on the sphere, and within certain
bandlimits in the vector spherical-harmonic domain. As with the concentration
problem for scalar functions on the sphere, which has been treated in detail
elsewhere, a Slepian vector basis can be constructed by solving a
finite-dimensional algebraic eigenvalue problem. The eigenvalue problem
decouples into separate problems for the radial and tangential components. For
regions with advanced symmetry such as polar caps, the spectral concentration
kernel matrix is very easily calculated and block-diagonal, lending itself to
efficient diagonalization. The number of spatiospectrally well-concentrated
vector fields is well estimated by a Shannon number that only depends on the
area of the target region and the maximal spherical-harmonic degree or
bandwidth. The spherical Slepian vector basis is doubly orthogonal...

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## ‣ Slepian functions and their use in signal estimation and spectral analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/09/2009
Português

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It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and on the surface of a sphere.; Comment: Submitted to the Handbook of Geomathematics...

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## ‣ Construction of M - Band bandlimited wavelets for orthogonal decomposition

Fonte: Rochester Instituto de Tecnologia
Publicador: Rochester Instituto de Tecnologia

Tipo: Tese de Doutorado

Português

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#Bandlimits#Electrical engineering#Wavelet#QA403.3 .T46 2003#Wavelets (Mathematics)#Signal processing--Mathematics

While bandlimited wavelets and associated IIR filters have shown serious potential in
areas of pattern recognition and communications, the dyadic Meyer wavelet is the only
known approach to construct bandlimited orthogonal decomposition. The sine scaling
function and wavelet are a special case of the Meyer. Previous works have proposed a M
- Band extension of the Meyer wavelet without solving the problem. One key
contribution of this thesis is the derivation of the correct bandlimits for the scaling
function and wavelets to guarantee an orthogonal basis. In addition, the actual
construction of the wavelets based upon these bandlimits is developed. A composite
wavelet will be derived based on the M scale relationships from which we will extract the
wavelet functions. A proper solution to this task is proposed which will generate
associated filters with the knowledge of the scaling function and the constraints for Mband
orthogonality.

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