63,759 research outputs found
Networks for Nonlinear Diffusion Problems in Imaging
A multitude of imaging and vision tasks have seen recently a major
transformation by deep learning methods and in particular by the application of
convolutional neural networks. These methods achieve impressive results, even
for applications where it is not apparent that convolutions are suited to
capture the underlying physics.
In this work we develop a network architecture based on nonlinear diffusion
processes, named DiffNet. By design, we obtain a nonlinear network architecture
that is well suited for diffusion related problems in imaging. Furthermore, the
performed updates are explicit, by which we obtain better interpretability and
generalisability compared to classical convolutional neural network
architectures. The performance of DiffNet tested on the inverse problem of
nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset.
We obtain competitive results to the established U-Net architecture, with a
fraction of parameters and necessary training data
Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement
The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the isotropic dfffusion equation, has recently resulted in the development of "geometry-driven" dfffusion. Nonlinear and anisotropic diffusion methods, as well as image-driven nonlinear filtering, have provided improved performance relative to the older isotropic and linear diffusion techniques. These techniques, which either explicitly or implicitly make use of kernels whose shape and center are functions of local image structure are too computationally expensive for use in real-time vision applications. In this paper, we show that results which are largely equivalent to those obtained from geometry-driven diffusion can be achieved by a process which is conceptually separated info two very different functions. The first involves the construction of a vector~field of "offsets", defined on a subset of the original image, at which to apply a filter. The offsets are used to displace filters away from boundaries to prevent edge blurring and destruction. The second is the (straightforward) application of the filter itself. The former function is a kind generalized image skeletonization; the latter is conventional image filtering. This formulation leads to results which are qualitatively similar to contemporary nonlinear diffusion methods, but at computation times that are roughly two orders of magnitude faster; allowing applications of this technique to real-time imaging. An additional advantage of this formulation is that it allows existing filter hardware and software implementations to be applied with no modification, since the offset step reduces to an image pixel permutation, or look-up table operation, after application of the filter
Dimension reduction for systems with slow relaxation
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof
Nonlinear Attitude Filtering: A Comparison Study
This paper contains a concise comparison of a number of nonlinear attitude
filtering methods that have attracted attention in the robotics and aviation
literature. With the help of previously published surveys and comparison
studies, the vast literature on the subject is narrowed down to a small pool of
competitive attitude filters. Amongst these filters is a second-order optimal
minimum-energy filter recently proposed by the authors. Easily comparable
discretized unit quaternion implementations of the selected filters are
provided. We conduct a simulation study and compare the transient behaviour and
asymptotic convergence of these filters in two scenarios with different
initialization and measurement errors inspired by applications in unmanned
aerial robotics and space flight. The second-order optimal minimum-energy
filter is shown to have the best performance of all filters, including the
industry standard multiplicative extended Kalman filter (MEKF)
Particle filtering in high-dimensional chaotic systems
We present an efficient particle filtering algorithm for multiscale systems,
that is adapted for simple atmospheric dynamics models which are inherently
chaotic. Particle filters represent the posterior conditional distribution of
the state variables by a collection of particles, which evolves and adapts
recursively as new information becomes available. The difference between the
estimated state and the true state of the system constitutes the error in
specifying or forecasting the state, which is amplified in chaotic systems that
have a number of positive Lyapunov exponents. The purpose of the present paper
is to show that the homogenization method developed in Imkeller et al. (2011),
which is applicable to high dimensional multi-scale filtering problems, along
with important sampling and control methods can be used as a basic and flexible
tool for the construction of the proposal density inherent in particle
filtering. Finally, we apply the general homogenized particle filtering
algorithm developed here to the Lorenz'96 atmospheric model that mimics
mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure
Comparing Kalman Filters and Observers for Power System Dynamic State Estimation with Model Uncertainty and Malicious Cyber Attacks
Kalman filters and observers are two main classes of dynamic state estimation
(DSE) routines. Power system DSE has been implemented by various Kalman
filters, such as the extended Kalman filter (EKF) and the unscented Kalman
filter (UKF). In this paper, we discuss two challenges for an effective power
system DSE: (a) model uncertainty and (b) potential cyber attacks. To address
this, the cubature Kalman filter (CKF) and a nonlinear observer are introduced
and implemented. Various Kalman filters and the observer are then tested on the
16-machine, 68-bus system given realistic scenarios under model uncertainty and
different types of cyber attacks against synchrophasor measurements. It is
shown that CKF and the observer are more robust to model uncertainty and cyber
attacks than their counterparts. Based on the tests, a thorough qualitative
comparison is also performed for Kalman filter routines and observers.Comment: arXiv admin note: text overlap with arXiv:1508.0725
Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter
The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a
draft/preprint of one paper submitted to the IEEE Transaction
Adaptive Filtering Enhances Information Transmission in Visual Cortex
Sensory neuroscience seeks to understand how the brain encodes natural
environments. However, neural coding has largely been studied using simplified
stimuli. In order to assess whether the brain's coding strategy depend on the
stimulus ensemble, we apply a new information-theoretic method that allows
unbiased calculation of neural filters (receptive fields) from responses to
natural scenes or other complex signals with strong multipoint correlations. In
the cat primary visual cortex we compare responses to natural inputs with those
to noise inputs matched for luminance and contrast. We find that neural filters
adaptively change with the input ensemble so as to increase the information
carried by the neural response about the filtered stimulus. Adaptation affects
the spatial frequency composition of the filter, enhancing sensitivity to
under-represented frequencies in agreement with optimal encoding arguments.
Adaptation occurs over 40 s to many minutes, longer than most previously
reported forms of adaptation.Comment: 20 pages, 11 figures, includes supplementary informatio
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