Spatial Neighbours Research Articles

Decentralised moving‐horizon state estimation for a class of networked spatial‐navigation systems with random parametric uncertainties and communication link failures

This study is concerned with the navigational state estimation problem for a class of networked spatial-navigation systems subject to random parametric uncertainties (RPUs) and communication link failures (CLFs). The observations of the novel systems, comprising remote-access neighbours' states and relative measures, are communicated through wireless packets, and thus are exposed to the impacts of RPUs and CLFs. In this study, a decentralised moving-horizon estimation approach is introduced to handle these ill-conditioned issues, and comprises two stages. First, a regional estimation is determined based on cooperative observations of spatial neighbours; and second, a collective estimation is derived through the fusion of regional estimation, local estimation and/or the cooperative estimations from spatial neighbours. Moreover, the resulting min–max problem is solved by a robust recursive scheme, which allows one to determine approximate estimates with a reduced computational condition. The convergence properties of the optimal estimator are also studied. The obtained stability condition implicitly establishes a relationship among the upper bound of estimation error, RPUs, and the CLF probability. Finally, an illustrative example of networked unmanned aerial vehicles (UAVs) is given to demonstrate the main features of the proposed estimator design approach.

Adaptively weighted decision fusion in 30 m land-cover mapping with Landsat and MODIS data

Although the combined use of Landsat and Moderate Resolution Imaging Spectroradiometer (MODIS) time-series data in land-cover classification has been widely adopted, the majority of such use of Landsat and MODIS data is done at the pixel level or feature input level in land-cover classification. We propose in this research a new method to make integrated use of different satellite data by adaptively weighted decision-level fusion. Training and validation samples were collected independently. Training samples were obtained from 329 regions and validation samples from 439 randomly distributed single-point positions. A Support Vector Machine (SVM) classifier was applied to the Landsat 8 data for classification and probability estimation. A Random Forests (RF) classifier was applied to the MODIS time-series data for probability estimation. Weight values were computed based on decision credibility, and reliability values were computed based on data quality. Three decision fusion procedures were performed. In the first procedure, decisions obtained from a Landsat 8 pixel and its corresponding MODIS pixel were fused for improvements (FUSION1). In the second, decisions obtained from the spatial neighbours of the Landsat 8 pixel were added to FUSION1 (FUSION2). In the third, decision fusion only among the Landsat 8 pixel and its spatial neighbours was performed (FUSION3) for comparison. Overall accuracies for the results with Landsat data only, FUSION1, FUSION2, and FUSION3 are 74.0%, 79.3%, 80.6%, and 75.6%, respectively. As a comparison, we also experimented on the use of Landsat and MODIS data by concatenating their features directly. Two classifiers, SVM and RF, were trained and validated on the concatenated features. The overall accuracies were 72.9% and 75.4%, respectively. Results show that the proposed method can utilize information selectively, so that considerable improvements can be obtained and fewer errors introduced. Moreover, it can be easily extended to handle more than two types of data source.

Multivariate Spatial Outlier Detection Using Robust Geographically Weighted Methods

Outlier detection is often a key task in a statistical analysis and helps guard against poor decision-making based on results that have been influenced by anomalous observations. For multivariate data sets, large Mahalanobis distances in raw data space or large Mahalanobis distances in principal components analysis, transformed data space, are routinely used to detect outliers. Detection in principal components analysis space can also utilise goodness of fit distances. For spatial applications, however, these global forms can only detect outliers in a non-spatial manner. This can result in false positive detections, such as when an observation’s spatial neighbours are similar, or false negative detections such as when its spatial neighbours are dissimilar. To avoid mis-classifications, we demonstrate that a local adaptation of various global methods can be used to detect multivariate spatial outliers. In particular, we account for local spatial effects via the use of geographically weighted data with either Mahalanobis distances or principal components analysis. Detection performance is assessed using simulated data as well as freshwater chemistry data collected over all of Great Britain. Results clearly show value in both geographically weighted methods to outlier detection.

Introducing spatial neighbourhood in Evidential C-Means for segmentation of multi-source images: Application to prostate multi-parametric MRI

In this paper we introduce an evidential multi-source segmentation scheme for the extraction of prostate zonal anatomy using multi-parametric MRI. The Evidential C-Means (ECM) classifier was adapted to a segmentation scheme by introducing spatial neighbourhood-based relaxation step in its optimisation process. In order to do so, basic belief assignments on voxels membership were relaxed using distance-weighted combination of belief from spatial neighbours. For the application on prostate tissues, geometric a priori was modelled and used as an additional data source. Our method was first experimented on simulated images to prove the improvement brought to the ECM. A validation study of the segmentation method was then conducted on 31 patients MRI data. In order to take into account inter-observer variability, each MRI was manually segmented by three independent expert radiologists, and an estimated truth was computed using STAPLE algorithm. This validation proved that segmentation obtained with our method is accurate and comparable to expert segmentation. We also show that our segmentation scheme enables to detect and highlight outliers, which could be interpreted by physicians as irregular tissues. The use of belief functions also provides additional information on borders between structures. We do believe these are sources of evidence that could help physicians/algorithms in characterising tissues and structures. The method that is introduced in this paper is a step forward to the use of belief functions theory in the context of multi-source image segmentation. Nevertheless, a full comparison to both baseline (e.g. Gaussian Mixture Models) and recent (e.g. Graph Cut) segmentation methods is needed to assess its performance.

An Effective Graph-Based Hierarchy Image Segmentation

Abstract This paper explores a Minimum Span Tree (MST) based multi-level image segmentation method. We define an edge weight based optimal criterion (merging predicate) which based on statistical learning theory (SLT), a scale control parameter is used to control the segmentation scale. On the other hand, a data structure is designed to keep adjacency of the objects during the MST based segmenting process. This make it is a simple and easy way to realize multi-level hierarchy image segmentation. Experiments based on the natural image and high resolution remote sensing images show the proposed merging predicate can keep the integrity of the objects and do well on preventing over-segmentation; the multi-level segmentation can avoid less segmentation. It also proves its efficiency in segmenting the high resolution remote sensing images. It will provide multilevel spatial neighbours’ information for image interpretation.

Analysis of housing price by means of STAR models with neighbourhood effects: a Bayesian approach

In this paper, we extend the Bayesian methodology introduced by Beamonte et al. (Stat Modelling 8:285–311, 2008) for the estimation and comparison of spatio-temporal autoregressive models (STAR) with neighbourhood effects, providing a more general treatment that uses larger and denser nets for the number of spatial and temporal influential neighbours and continuous distributions for their smoothing weights. This new treatment also reduces the computational time and the RAM necessities of the estimation algorithm in Beamonte et al. (Stat Modelling 8:285–311, 2008). The procedure is illustrated by an application to the Zaragoza (Spain) real estate market, improving the goodness of fit and the outsampling behaviour of the model thanks to a more flexible estimation of the neighbourhood parameters.

Variable selection in STAR models with neighbourhood effects using genetic algorithms

In this paper we deal with the problem of variable selection in spatiotemporal autoregressive (STAR) models with neighbourhood effects. We propose a procedure to carry out the selection process, taking into account the uncertainty associated with estimation of the parameters and the predictive behaviour of the compared models, in order to give more realism to the analysis. We set up a multi-objective programming problem that combines the use of different criteria to measure both these aspects. We use genetic algorithms which are very flexible and suitable for our multicriteria decision problem. In particular, the procedure allows us to estimate the number of spatial and temporal nearest neighbours as well as their relative effects. The methodology is illustrated through an application to the real estate market of Zaragoza. Copyright © 2010 John Wiley & Son, Ltd.

Determinants of backbone packing in globular proteins: an analysis of spatial neighbours.

This study attempts to examine the pattern and variability of backbone packing density in protein structures. A carefully selected non-redundant data set of known protein structures is analyzed in terms of amino-acid composition and the preference of individual amino acids to fall into regions of low, medium or high density depending on the number of observed non-sequence spatial neighbours. The relationship of the backbone packing density to a number of properties such as the hydrophobicity, non-bonded energies and secondary structural features of the amino acids are examined. The correlation between the average percentage composition and the percentage composition in regions corresponding to different levels of packing density of the proteins is evaluated. These studies are extended to the family of globins whose amino-acid sequences have diverged retaining the same three-dimensional structure during evolution. The significance of high-backbone-density regions in this family has become apparent as due to helix/helix packing. Further, the variation in the amino-acid composition in different contact regions of globin proteins follows the same pattern found for the general data set.

Charge transfer in discontinuous thin and cermet films

The influence of distributions of particle sizes and spacings on the electrical properties of discontinuous metal and cermet films is examined. It is shown that a well-defined activation energy will only be observed at high temperatures, or in a highly regular array where charge transfer occurs between nearest spatial neighbours. At lower temperatures it is proposed that the conductivity will be of the form σ ∝ exp{-( A/T n )}, where n is one-third at very low temperatures and one-half in a limited transition region between the high and low ranges. In both these fractional power cases charge transfer is by a hopping process between particles that are not nearest spatial neighbours.

Statistical thermodynamics of random networks

Polymeric networks exhibiting high elasticity consist, typically, of linear chains several hundred bonds in length joined at their ends to ϕ -functional junctions ( ϕ > 2). For random unconstrained chains of this length, the density distribution of chain vectors r is Gaussian in satisfactory approximation. The chains interpenetrate copiously in the network; the domain described by the set of ϕ junctions that are topological neighbours of a given junction encompasses many (20–100) spatial neighbours. A phantom network is expressly defined as a hypothetical one whose chains may move freely through one another; the chains act exclusively by introducing a force that is proportional to the distance between each pair of junctions so connected. The following results of James & Guth are rederived for a Gaussian phantom network using a simplified version of their procedure: (1) the mean values r̄ of the individual chain vectors are linear functions of the tensor λ of the principal extension ratios specifying the macroscopic strain, (2) fluctuations ∆ r ═ r – r̄ about these mean values are Gaussian, and (3) the mean-square fluctuations depend only on the structure of the network and not on the strain. Additionally, we show (4) that the distribution of the average vectors r̄ is Gaussian, and (5) that ≺(∆ r ) 2 ≻ ═ (2/ ϕ ) < r 2 ≻ 0 , a result obtained previously by Graessley. It follows from (1) and (3) that the transformation of chain vectors r of the phantom network is not affine in λ , and hence that junctions exchange neighbours with strain. In real networks, the mutual interpenetration of chains pendent at a given junction must obstruct this process of local rearrangement of junctions; the transformation of chain vectors may therefore be more nearly affine in λ , especially when the network is undiluted. The elastic free energy derived for a phantom network of any functionality and degree of imperfection reduces to ∆ A e1 ═ ½ξ kT ( I 1 – 3), where I 1 ═ trace ( λ T λ ) is the first invariant of the strain and ξ is the cycle rank of the network. If the fluctuations of junctions in a real network are suppressed for the reasons stated, the elastic free energy is ∆ A* e1 = ξ(1 – 2 ϕ ) –1 ½ kT ( I 1 – 3) – (2ξ/ ϕ ) (1 – 2/ϕ) –1 kT In ( V / V 0 ), where V and V 0 are the actual and reference volumes, respectively. The expected trend from ∆ A* e1 to ∆ A e1 with dilution may account, qualitatively at least, for the effect of dilution on the stress–strain relation. A similar trend with extension may explain the familiar departure of the observed tension–elongation relation from theory.