814 research outputs found
Multiscale estimation of GPS velocity fields
We present a spherical wavelet-based multiscale approach for estimating a spatial velocity field
on the sphere from a set of irregularly spaced geodetic displacement observations. Because
the adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities
such as dilatation rate, strain rate and rotation rate can be directly computed using the same
coefficients. In a series of synthetic and real examples,we illustrate the benefit of themultiscale
approach, in particular, the inherent ability of the method to localize a given deformation field
in space and scale as well as to detect outliers in the set of observations. This approach has
the added benefit of being able to locally match the smallest resolved process to the local
spatial density of observations, thereby both maximizing the amount of derived information
while also allowing the comparison of derived quantities at the same scale but in different
regions.We also consider the vertical component of the velocity field in our synthetic and real
examples, showing that in some cases the spatial gradients of the vertical velocity field may
constitute a significant part of the deformation. This formulation may be easily applied either
regionally or globally and is ideally suited as the spatial parametrization used in any automatic
time-dependent geodetic transient detector
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Multiscale estimation of GPS velocity fields
We present a spherical wavelet-based multiscale approach for estimating a spatial velocity field on the sphere from a set of irregularly spaced geodetic displacement observations. Because the adopted spherical wavelets are analytically differentiable, spatial gradient tensor quantities such as dilatation rate, strain rate and rotation rate can be directly computed using the same coefficients. In a series of synthetic and real examples,we illustrate the benefit of themultiscale approach, in particular, the inherent ability of the method to localize a given deformation field in space and scale as well as to detect outliers in the set of observations. This approach has the added benefit of being able to locally match the smallest resolved process to the local spatial density of observations, thereby both maximizing the amount of derived information while also allowing the comparison of derived quantities at the same scale but in different regions.We also consider the vertical component of the velocity field in our synthetic and real examples, showing that in some cases the spatial gradients of the vertical velocity field may constitute a significant part of the deformation. This formulation may be easily applied either regionally or globally and is ideally suited as the spatial parametrization used in any automatic time-dependent geodetic transient detector. Key words : Wavelet transform, Satellite geodesy, Seismic cycle, Transient deformation, Kinematics of crustal and mantle deformation.nbsp
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Voxel-based Modeling with Multi-resolution Wavelet Transform for Layered Manufacturing
A voxel-based modeling system with multi-resolution for layered manufacturing is presented in
this paper. When dealing with discretized data input, voxel-based modeling shows its clear
advantages over the conventional geometric modeling methods. To increase the efficiency of
voxel data due to its large storage space requirement, multi-resolution method with wavelet
transform technique is implemented. Combining with iso-surface generation and lossless
polygon reduction, this voxel-based modeling method can easily work with layered
manufacturing. To demonstrate these concepts, components with different resolutions are built
using Layered Manufacturing and presented in the paper.Mechanical Engineerin
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
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