3,028 research outputs found
DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. These
networks have mostly been developed for regular Euclidean domains such as those
supporting images, audio, or video. Because of their success, CNN-based methods
are becoming increasingly popular in Cosmology. Cosmological data often comes
as spherical maps, which make the use of the traditional CNNs more complicated.
The commonly used pixelization scheme for spherical maps is the Hierarchical
Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for
analysis of full and partial HEALPix maps, which we call DeepSphere. The
spherical CNN is constructed by representing the sphere as a graph. Graphs are
versatile data structures that can act as a discrete representation of a
continuous manifold. Using the graph-based representation, we define many of
the standard CNN operations, such as convolution and pooling. With filters
restricted to being radial, our convolutions are equivariant to rotation on the
sphere, and DeepSphere can be made invariant or equivariant to rotation. This
way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix
sampling of the sphere. This approach is computationally more efficient than
using spherical harmonics to perform convolutions. We demonstrate the method on
a classification problem of weak lensing mass maps from two cosmological models
and compare the performance of the CNN with that of two baseline classifiers.
The results show that the performance of DeepSphere is always superior or equal
to both of these baselines. For high noise levels and for data covering only a
smaller fraction of the sphere, DeepSphere achieves typically 10% better
classification accuracy than those baselines. Finally, we show how learned
filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other
author
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Edge-enhancing Filters with Negative Weights
In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by
projecting the noisy image to a lower dimensional Krylov subspace of the graph
Laplacian, constructed using nonnegative weights determined by distances
between image data corresponding to image pixels. We~extend the construction of
the graph Laplacian to the case, where some graph weights can be negative.
Removing the positivity constraint provides a more accurate inference of a
graph model behind the data, and thus can improve quality of filters for
graph-based signal processing, e.g., denoising, compared to the standard
construction, without affecting the costs.Comment: 5 pages; 6 figures. Accepted to IEEE GlobalSIP 2015 conferenc
A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer
This investigation is motivated by the problem of optimal design of cooling
elements in modern battery systems. We consider a simple model of
two-dimensional steady-state heat conduction described by elliptic partial
differential equations and involving a one-dimensional cooling element
represented by a contour on which interface boundary conditions are specified.
The problem consists in finding an optimal shape of the cooling element which
will ensure that the solution in a given region is close (in the least squares
sense) to some prescribed target distribution. We formulate this problem as
PDE-constrained optimization and the locally optimal contour shapes are found
using a gradient-based descent algorithm in which the Sobolev shape gradients
are obtained using methods of the shape-differential calculus. The main novelty
of this work is an accurate and efficient approach to the evaluation of the
shape gradients based on a boundary-integral formulation which exploits certain
analytical properties of the solution and does not require grids adapted to the
contour. This approach is thoroughly validated and optimization results
obtained in different test problems exhibit nontrivial shapes of the computed
optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing"
(31 pages, 9 figures
Ptychographic X-ray computed tomography of extended colloidal networks in food emulsions
As a main structural level in colloidal food materials, extended colloidal
networks are important for texture and rheology. By obtaining the 3D
microstructure of the network, macroscopic mechanical properties of the
material can be inferred. However, this approach is hampered by the lack of
suitable non-destructive 3D imaging techniques with submicron resolution.
We present results of quantitative ptychographic X-ray computed tomography
applied to a palm kernel oil based oil-in-water emulsion. The measurements were
carried out at ambient pressure and temperature. The 3D structure of the
extended colloidal network of fat globules was obtained with a resolution of
around 300 nm. Through image analysis of the network structure, the fat globule
size distribution was computed and compared to previous findings. In further
support, the reconstructed electron density values were within 4% of reference
values.Comment: 19 pages, 4 figures, to be published in Food Structur
- …