7,744 research outputs found
A survey of exemplar-based texture synthesis
Exemplar-based texture synthesis is the process of generating, from an input
sample, new texture images of arbitrary size and which are perceptually
equivalent to the sample. The two main approaches are statistics-based methods
and patch re-arrangement methods. In the first class, a texture is
characterized by a statistical signature; then, a random sampling conditioned
to this signature produces genuinely different texture images. The second class
boils down to a clever "copy-paste" procedure, which stitches together large
regions of the sample. Hybrid methods try to combine ideas from both approaches
to avoid their hurdles. The recent approaches using convolutional neural
networks fit to this classification, some being statistical and others
performing patch re-arrangement in the feature space. They produce impressive
synthesis on various kinds of textures. Nevertheless, we found that most real
textures are organized at multiple scales, with global structures revealed at
coarse scales and highly varying details at finer ones. Thus, when confronted
with large natural images of textures the results of state-of-the-art methods
degrade rapidly, and the problem of modeling them remains wide open.Comment: v2: Added comments and typos fixes. New section added to describe
FRAME. New method presented: CNNMR
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Uncertainty quantification is a critical missing component in radio
interferometric imaging that will only become increasingly important as the
big-data era of radio interferometry emerges. Statistical sampling approaches
to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling,
can in principle recover the full posterior distribution of the image, from
which uncertainties can then be quantified. However, for massive data sizes,
like those anticipated from the Square Kilometre Array (SKA), it will be
difficult if not impossible to apply any MCMC technique due to its inherent
computational cost. We formulate Bayesian inference problems with
sparsity-promoting priors (motivated by compressive sensing), for which we
recover maximum a posteriori (MAP) point estimators of radio interferometric
images by convex optimisation. Exploiting recent developments in the theory of
probability concentration, we quantify uncertainties by post-processing the
recovered MAP estimate. Three strategies to quantify uncertainties are
developed: (i) highest posterior density credible regions; (ii) local credible
intervals (cf. error bars) for individual pixels and superpixels; and (iii)
hypothesis testing of image structure. These forms of uncertainty
quantification provide rich information for analysing radio interferometric
observations in a statistically robust manner. Our MAP-based methods are
approximately times faster computationally than state-of-the-art MCMC
methods and, in addition, support highly distributed and parallelised
algorithmic structures. For the first time, our MAP-based techniques provide a
means of quantifying uncertainties for radio interferometric imaging for
realistic data volumes and practical use, and scale to the emerging big-data
era of radio astronomy.Comment: 13 pages, 10 figures, see companion article in this arXiv listin
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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