69,996 research outputs found
Spatial variation of total column ozone on a global scale
The spatial dependence of total column ozone varies strongly with latitude,
so that homogeneous models (invariant to all rotations) are clearly unsuitable.
However, an assumption of axial symmetry, which means that the process model is
invariant to rotations about the Earth's axis, is much more plausible and
considerably simplifies the modeling. Using TOMS (Total Ozone Mapping
Spectrometer) measurements of total column ozone over a six-day period, this
work investigates the modeling of axially symmetric processes on the sphere
using expansions in spherical harmonics. It turns out that one can capture many
of the large scale features of the spatial covariance structure using a
relatively small number of terms in such an expansion, but the resulting fitted
model provides a horrible fit to the data when evaluated via its likelihood
because of its inability to describe accurately the process's local behavior.
Thus, there remains the challenge of developing computationally tractable
models that capture both the large and small scale structure of these data.Comment: Published at http://dx.doi.org/10.1214/07-AOAS106 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Salient Local 3D Features for 3D Shape Retrieval
In this paper we describe a new formulation for the 3D salient local features
based on the voxel grid inspired by the Scale Invariant Feature Transform
(SIFT). We use it to identify the salient keypoints (invariant points) on a 3D
voxelized model and calculate invariant 3D local feature descriptors at these
keypoints. We then use the bag of words approach on the 3D local features to
represent the 3D models for shape retrieval. The advantages of the method are
that it can be applied to rigid as well as to articulated and deformable 3D
models. Finally, this approach is applied for 3D Shape Retrieval on the McGill
articulated shape benchmark and then the retrieval results are presented and
compared to other methods.Comment: Three-Dimensional Imaging, Interaction, and Measurement. Edited by
Beraldin, J. Angelo; Cheok, Geraldine S.; McCarthy, Michael B.;
Neuschaefer-Rube, Ulrich; Baskurt, Atilla M.; McDowall, Ian E.; Dolinsky,
Margaret. Proceedings of the SPIE, Volume 7864, pp. 78640S-78640S-8 (2011).
Conference Location: San Francisco Airport, California, USA ISBN:
9780819484017 Date: 10 March 201
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
Graph-Based Classification of Omnidirectional Images
Omnidirectional cameras are widely used in such areas as robotics and virtual
reality as they provide a wide field of view. Their images are often processed
with classical methods, which might unfortunately lead to non-optimal solutions
as these methods are designed for planar images that have different geometrical
properties than omnidirectional ones. In this paper we study image
classification task by taking into account the specific geometry of
omnidirectional cameras with graph-based representations. In particular, we
extend deep learning architectures to data on graphs; we propose a principled
way of graph construction such that convolutional filters respond similarly for
the same pattern on different positions of the image regardless of lens
distortions. Our experiments show that the proposed method outperforms current
techniques for the omnidirectional image classification problem
From 3D Point Clouds to Pose-Normalised Depth Maps
We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)
Learning SO(3) Equivariant Representations with Spherical CNNs
We address the problem of 3D rotation equivariance in convolutional neural
networks. 3D rotations have been a challenging nuisance in 3D classification
tasks requiring higher capacity and extended data augmentation in order to
tackle it. We model 3D data with multi-valued spherical functions and we
propose a novel spherical convolutional network that implements exact
convolutions on the sphere by realizing them in the spherical harmonic domain.
Resulting filters have local symmetry and are localized by enforcing smooth
spectra. We apply a novel pooling on the spectral domain and our operations are
independent of the underlying spherical resolution throughout the network. We
show that networks with much lower capacity and without requiring data
augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio
Quantum Anti-de Sitter space and sphere at roots of unity
An algebra of functions on q-deformed Anti-de Sitter space AdS_q^D is defined
which is covariant under U_q(so(2,D-1)), for q a root of unity. The
star-structure is studied in detail. The scalar fields have an intrinsic
high-energy cutoff, and arise most naturally as fields on orbifolds AdS_q^D
\times S^D/G if D is odd, and AdS_q^D \times S_{\chi}^{2D-1}/G if D is even.
Here G is a finite abelian group, and S_{\chi} is a certain ``chiral sector''
of the classical sphere. Hilbert spaces of square integrable functions are
discussed. Analogous results are found for the q-deformed sphere S_q^D.Comment: 45 pages, LaTeX, 2 figures using epsf. Slight change in notation
allows to obtain AdS^2, AdS^3 as special cases of the general schem
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