Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Investigation of the starch gelatinisation phenomena in water-glycerol systems: application of modulated temperature differential scanning calorimetry

The use of modulated temperature differential scanning calorimetry (MTDSC) has provided further insight into the gelatinisation process since it allows the detection of glass transition during gelatinisation process. It was found in this work that the glass transition overlapped with the gelatinisation peak temperature for all maize starch formulations studied. Systematic investigation on maize starch gelatinisation over a range of water-glycerol concentrations with MTDSC revealed that the addition of glycerol increased the gelatinisation onset temperature with an extent that depended on the water content in the system. Furthermore, the addition of glycerol promoted starch gelatinisation at low water content (0.4 g water/g dry starch) and the enthalpy of gelatinisation varied with glycerol concentration (0.73-19.61 J/g dry starch) depending on the water content and starch type. The validities of published gelatinisation models were explored. These models failed to explain the glass transition phenomena observed during the course of gelatinisation and failed to describe the gelatinisation behaviour observed over the water-glycerol concentrations range investigated. A hypothesis for the mechanisms involved during gelatinisation was proposed based on the side chain liquid crystalline polymer model for starch structure and the concept that the order-disorder transition in starch requires that the hydrogen bonds (the major structural element in the granule packing) to be broken before the collapse of order (helix-coil transition) can take place. (C) 2004 Elsevier Ltd. All rights reserved.

Testing the 'photoinhibition' model of coral bleaching using chemical inhibitors

Explants of the hard coral Seriatopora hystrix were exposed to sublethal concentrations of the herbicide diuron DCMU (N'-(3,4-dichlorophenyl,-N,N-dimethylurea)) and the heavy metal copper. Pulse amplitude modulated (PAM) chlorophyll fluorescence techniques were used to assess the effects on the photosynthetic efficiency of the algal symbionts in the tissue (in Symbio), and chlorophyll fluorescence and counts of symbiotic algae (normalised to surface area) were used to assess the extent of coral bleaching. At 30 mug DCMU l(-1), there was a reduction in both the maximum effective quantum yield (DeltaF/F-m') and maximum potential quantum yield (F-v/F-m) of the algal symbionts in symbio. Corals subsequently lost their algal symbionts and discoloured (bleached), especially on their upper sunlight-exposed surfaces. At the same DCMU concentration but under low light (5% of growth irradiance), there was a marked reduction in DeltaF/F-m' but only a slight reduction in F-v/F-m and slight loss of algae. Loss of algal symbionts was also noted after a 7 d exposure to concentrations as low as 10 mug DCMU l(-1) under normal growth irradiance, and after 14 d exposure to 10 mug DCMU l(-1) under reduced irradiance. Collectively the results indicate that DCMU-induced bleaching is caused by a light-dependent photoinactivation of algal symbionts, and that bleaching occurs when F-v/F-n, (measured 2 h after sunset) is reduced to a value of less than or equal to 0.6. Elevated copper concentrations (60 mug Cu l(-1) for 10 h) also induced a rapid bleaching in S. hystrix but without affecting the quantum yield of the algae in symbio. Tests with isolated algae indicated that substantially higher concentrations (300 mug Cu l(-1) for 8 h) were needed to significantly reduce the quantum yield. Thus, copper-induced bleaching occurs without affecting the algal photosynthesis and may be related to effects on the host (animal). It is argued that warm-water bleaching of corals resembles both types of chemically induced bleaching, suggesting the need for an integrated model of coral bleaching involving the effect of temperature on both host (coral) and algal symbionts.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

A scatterometer neural network sensor model with input noise

The ERS-1 satellite carries a scatterometer which measures the amount of radiation scattered back toward the satellite by the ocean's surface. These measurements can be used to infer wind vectors. The implementation of a neural network based forward model which maps wind vectors to radar backscatter is addressed. Input noise cannot be neglected. To account for this noise, a Bayesian framework is adopted. However, Markov Chain Monte Carlo sampling is too computationally expensive. Instead, gradient information is used with a non-linear optimisation algorithm to find the maximum em a posteriori probability values of the unknown variables. The resulting models are shown to compare well with the current operational model when visualised in the target space.

Time delay estimation with hidden Markov models

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.

A generative probabilistic oriented wavelet model for texture segmentation

This Letter addresses image segmentation via a generative model approach. A Bayesian network (BNT) in the space of dyadic wavelet transform coefficients is introduced to model texture images. The model is similar to a Hidden Markov model (HMM), but with non-stationary transitive conditional probability distributions. It is composed of discrete hidden variables and observable Gaussian outputs for wavelet coefficients. In particular, the Gabor wavelet transform is considered. The introduced model is compared with the simplest joint Gaussian probabilistic model for Gabor wavelet coefficients for several textures from the Brodatz album [1]. The comparison is based on cross-validation and includes probabilistic model ensembles instead of single models. In addition, the robustness of the models to cope with additive Gaussian noise is investigated. We further study the feasibility of the introduced generative model for image segmentation in the novelty detection framework [2]. Two examples are considered: (i) sea surface pollution detection from intensity images and (ii) image segmentation of the still images with varying illumination across the scene.

A generative model for separating illumination and reflectance from images

It is well known that even slight changes in nonuniform illumination lead to a large image variability and are crucial for many visual tasks. This paper presents a new ICA related probabilistic model where the number of sources exceeds the number of sensors to perform an image segmentation and illumination removal, simultaneously. We model illumination and reflectance in log space by a generalized autoregressive process and Hidden Gaussian Markov random field, respectively. The model ability to deal with segmentation of illuminated images is compared with a Canny edge detector and homomorphic filtering. We apply the model to two problems: synthetic image segmentation and sea surface pollution detection from intensity images.

A scatterometer neural network sensor model with input noise

The ERS-1 satellite carries a scatterometer which measures the amount of radiation scattered back toward the satellite by the ocean's surface. These measurements can be used to infer wind vectors. The implementation of a neural network based forward model which maps wind vectors to radar backscatter is addressed. Input noise cannot be neglected. To account for this noise, a Bayesian framework is adopted. However, Markov Chain Monte Carlo sampling is too computationally expensive. Instead, gradient information is used with a non-linear optimisation algorithm to find the maximum em a posteriori probability values of the unknown variables. The resulting models are shown to compare well with the current operational model when visualised in the target space.

Volatility changes caused by the trading system:a Markov switching application

An expanding literature exists to suggest that the trading mechanism can influence the volatility of security returns. This study adds to this literature by examining the impact that the introduction of SETS, on the London Stock Exchange, had on the volatility of security returns. Using a Markov switching regime change model security volatility is categorized as being in a regime of either high or low volatility. It is shown that prior to the introduction of SETS securities tended to be in a low volatility regime. At the time SETS was introduced securities moved to a high volatility regime. This suggests that volatility increased when SETS was introduced.

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

An accurate and scalable analytical model for IEEE 802.15.4 slotted CSMA/CA networks

In this paper a Markov chain based analytical model is proposed to evaluate the slotted CSMA/CA algorithm specified in the MAC layer of IEEE 802.15.4 standard. The analytical model consists of two two-dimensional Markov chains, used to model the state transition of an 802.15.4 device, during the periods of a transmission and between two consecutive frame transmissions, respectively. By introducing the two Markov chains a small number of Markov states are required and the scalability of the analytical model is improved. The analytical model is used to investigate the impact of the CSMA/CA parameters, the number of contending devices, and the data frame size on the network performance in terms of throughput and energy efficiency. It is shown by simulations that the proposed analytical model can accurately predict the performance of slotted CSMA/CA algorithm for uplink, downlink and bi-direction traffic, with both acknowledgement and non-acknowledgement modes.