1,849 research outputs found
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space
In paper I of this series we discuss how magnification bias distorts the 3D
correlation function by enhancing the observed correlation in the line-of-sight
(LOS) orientation, especially on large scales. This lensing anisotropy is
distinctive, making it possible to separately measure the galaxy-galaxy,
galaxy-magnification {\it and} magnification-magnification correlations. Here
we extend the discussion to the power spectrum and also to redshift space. In
real space, pairs oriented close to the LOS direction are not protected against
nonlinearity even if the pair separation is large; this is because nonlinear
fluctuations can enter through gravitational lensing at a small transverse
separation (or i.e. impact parameter). The situation in Fourier space is
different: by focusing on a small wavenumber , as is usually done, linearity
is guaranteed because both the LOS and transverse wavenumbers must be small.
This is why magnification distortion of the galaxy correlation appears less
severe in Fourier space. Nonetheless, the effect is non-negligible, especially
for the transverse Fourier modes, and should be taken into account in
interpreting precision measurements of the galaxy power spectrum, for instance
those that focus on the baryon oscillations. The lensing induced anisotropy of
the power spectrum has a shape that is distinct from the more well known
redshift space anisotropies due to peculiar motions and the Alcock-Paczynski
effect. The lensing anisotropy is highly localized in Fourier space while
redshift space distortions are more spread out. This means that one could
separate the magnification bias component in real observations, implying that
potentially it is possible to perform a gravitational lensing measurement
without measuring galaxy shapes.Comment: 14 pages, minor revisions, as accepted for publication in Physical
Review
Correcting artifacts from finite image size in Differential Dynamic Microscopy
Differential Dynamic Microscopy (DDM) analyzes traditional real-space
microscope images to extract information on sample dynamics in a way akin to
light scattering, by decomposing each image in a sequence into Fourier modes,
and evaluating their time correlation properties. DDM has been applied in a
number of soft-matter and colloidal systems. However, objects observed to move
out of the microscope's captured field of view, intersecting the edges of the
acquired images, can introduce spurious but significant errors in the
subsequent analysis. Here we show that application of a spatial windowing
filter to images in a sequence before they enter the standard DDM analysis can
reduce these artifacts substantially. Moreover, windowing can increase
significantly the accessible range of wave vectors probed by DDM, and may
further yield unexpected information, such as the size polydispersity of a
colloidal suspension
Kinetic-scale magnetic turbulence and finite Larmor radius effects at Mercury
We use a nonstationary generalization of the higher-order structure function
technique to investigate statistical properties of the magnetic field
fluctuations recorded by MESSENGER spacecraft during its first flyby
(01/14/2008) through the near Mercury's space environment, with the emphasis on
key boundary regions participating in the solar wind -- magnetosphere
interaction. Our analysis shows, for the first time, that kinetic-scale
fluctuations play a significant role in the Mercury's magnetosphere up to the
largest resolvable time scale ~20 s imposed by the signal nonstationarity,
suggesting that turbulence at this planet is largely controlled by finite
Larmor radius effects. In particular, we report the presence of a highly
turbulent and extended foreshock system filled with packets of ULF
oscillations, broad-band intermittent fluctuations in the magnetosheath,
ion-kinetic turbulence in the central plasma sheet of Mercury's magnetotail,
and kinetic-scale fluctuations in the inner current sheet encountered at the
outbound (dawn-side) magnetopause. Overall, our measurements indicate that the
Hermean magnetosphere, as well as the surrounding region, are strongly affected
by non-MHD effects introduced by finite sizes of cyclotron orbits of the
constituting ion species. Physical mechanisms of these effects and their
potentially critical impact on the structure and dynamics of Mercury's magnetic
field remain to be understood.Comment: 46 pages, 5 figures, 2 table
Air-coupled, focused ultrasonic dispersion spectrum reconstruction in plates
This paper presents and demonstrates a noncontact method for measuring the Lamb wave dispersion spectrum of a plate. Noncontact air-coupled source and receive transducers are used with line-focus mirrors and 50–700 kHz broadband apparatus for simultaneous measurement over a broad spectrum of refractive angles and multiple guided modes. Broadband, wide-angle wave forms are measured as a function of position. The Fourier transform of these wave forms from the t – x domain to the v – k domain gives an approximate spectrum of the dispersion relation. We measure the dispersion spectra of Lucite™, aluminum, balsa wood, and a carbon fiber epoxy laminate, and show that the measured spectra agree well with the dispersion relation calculated from Lamb wave theory
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