Enhancing change detection in low-quality surveillance footage using markov random fields

Urban surveillance footage can be of poor quality, partly due to the low quality of the camera and partly due to harsh lighting and heavily reflective scenes. For some computer surveillance tasks very simple change detection is adequate, but sometimes a more detailed change detection mask is desirable, eg, for accurately tracking identity when faced with multiple interacting individuals and in pose-based behaviour recognition. We present a novel technique for enhancing a low-quality change detection into a better segmentation using an image combing estimator in an MRF based model.

Land-cover classification from airborne LIDAR data fused with aerial optical images

Airborne LIght Detection And Ranging (LIDAR) provides accurate height information for objects on the earth, which makes LIDAR become more and more popular in terrain and land surveying. In particular, LIDAR data offer vital and significant features for land-cover classification which is an important task in many application domains. In this paper, an unsupervised approach based on an improved fuzzy Markov random field (FMRF) model is developed, by which the LIDAR data, its co-registered images acquired by optical sensors, i.e. aerial color image and near infrared image, and other derived features are fused effectively to improve the ability of the LIDAR system for the accurate land-cover classification. In the proposed FMRF model-based approach, the spatial contextual information is applied by modeling the image as a Markov random field (MRF), with which the fuzzy logic is introduced simultaneously to reduce the errors caused by the hard classification. Moreover, a Lagrange-Multiplier (LM) algorithm is employed to calculate a maximum A posteriori (MAP) estimate for the classification. The experimental results have proved that fusing the height data and optical images is particularly suited for the land-cover classification. The proposed approach works very well for the classification from airborne LIDAR data fused with its coregistered optical images and the average accuracy is improved to 88.9%.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Optimization algorithms in FMRF model-based segmentation for LIDAR data and co-registered bands

In this paper, a fuzzy Markov random field (FMRF) model is used to segment land-objects into free, grass, building, and road regions by fusing remotely, sensed LIDAR data and co-registered color bands, i.e. scanned aerial color (RGB) photo and near infra-red (NIR) photo. An FMRF model is defined as a Markov random field (MRF) model in a fuzzy domain. Three optimization algorithms in the FMRF model, i.e. Lagrange multiplier (LM), iterated conditional mode (ICM), and simulated annealing (SA), are compared with respect to the computational cost and segmentation accuracy. The results have shown that the FMRF model-based ICM algorithm balances the computational cost and segmentation accuracy in land-cover segmentation from LIDAR data and co-registered bands.

An effective approach for land-cover classification from airborne lidar fused with co-registered data

Airborne lidar provides accurate height information of objects on the earth and has been recognized as a reliable and accurate surveying tool in many applications. In particular, lidar data offer vital and significant features for urban land-cover classification, which is an important task in urban land-use studies. In this article, we present an effective approach in which lidar data fused with its co-registered images (i.e. aerial colour images containing red, green and blue (RGB) bands and near-infrared (NIR) images) and other derived features are used effectively for accurate urban land-cover classification. The proposed approach begins with an initial classification performed by the Dempster–Shafer theory of evidence with a specifically designed basic probability assignment function. It outputs two results, i.e. the initial classification and pseudo-training samples, which are selected automatically according to the combined probability masses. Second, a support vector machine (SVM)-based probability estimator is adopted to compute the class conditional probability (CCP) for each pixel from the pseudo-training samples. Finally, a Markov random field (MRF) model is established to combine spatial contextual information into the classification. In this stage, the initial classification result and the CCP are exploited. An efficient belief propagation (EBP) algorithm is developed to search for the global minimum-energy solution for the maximum a posteriori (MAP)-MRF framework in which three techniques are developed to speed up the standard belief propagation (BP) algorithm. Lidar and its co-registered data acquired by Toposys Falcon II are used in performance tests. The experimental results prove that fusing the height data and optical images is particularly suited for urban land-cover classification. There is no training sample needed in the proposed approach, and the computational cost is relatively low. An average classification accuracy of 93.63% is achieved.

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

Induced random fields in the LiHoxY1-xF4 quantum ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bxx̂ perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x̂ direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising ẑ direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.

Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Memory and burstiness in dynamic networks

A discrete-time random process is described, which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time t is given by a fixed probability x, is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding t. For small values of x the interevent time distribution follows a power law with exponent −2−x. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of x for each node depends on the fitness distribution, \rho(x), from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data, such as online social communications and fMRI scans.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Multiple, discrete arcs on sunward convecting field lines in the 14-15 MLT region

Ionospheric plasma flow measurements and simultaneous observations of thin (∼0.2° invariant latitude (ILAT)), multiple, longitudinally extended auroral arcs of transient nature within 74°-76° ILAT and 1030-1130 UT (∼14-15 MLT) on January 12, 1989, are reported. The auroral structures appeared within the luminous belt of strong 630.0-nm emissions located predominantly on sunward convecting field lines equatorward of the convection reversal boundary as identified by the European Incoherent Scatter UHF radar. The events occurred during a period of several hours quasi-steady solar wind speed (∼ 700 km s−1) and a radially orientated interplanetary magnetic field (IMF) with a weak northward tilt (IMF Bz>0). These typical dayside auroral features are related to previous studies of auroral activity related to the upward region 1 current in the postnoon sector. The discrete auroral events presented here may result from magnetosheath plasma injections into the low-latitude boundary layer (LLBL) and an associated dynamo mechanism. An alternative explanation invokes kinetic Alfvén waves, triggered either by Kelvin-Helmholtz instability at the inner (or outer) edge of the LLBL or by pressure pulse induced magnetopause surface waves.