Spatial–spectral ant colony optimization for hyperspectral image classification

Hyperspectral satellite images contain a lot of information in terms of spectral behaviour of objects and this information can be extracted by several mechanisms including image classification. Traditional spectral information-based methods of hyperspectral image classification are generally followed by spatial information-driven post-processing techniques such as relaxation labelling and Markov Random Field. Spectral or spatial information alone may lead to different results depending upon scene captured. An algorithm which can incorporate influence of both spectral and spatial features is needed to address this problem. In this article, an ant colony optimisation-based hyperspectral image classification technique is proposed. This method exploits both spatial and spectral features. Five standard hyperspectral data sets have been used to validate the proposed method and comparisons with other approaches have been carried out. It was observed that the proposed method yielded a significant improvement in classification accuracy. For the instance, nearly 10% increase in accuracy was observed when compared to Support Vector Machine for Indian pines, Botswana, and Salinas images.     

Spatial–spectral locality constrained elastic net hypergraph for hyperspectral image clustering

Hypergraph is an effective method used to represent the contextual correlation within hyperspectral imagery for clustering. Nevertheless, how to discover the closely correlated samples to form hyperedges is the key issue for constructing an informative hypergraph. In this article, a new spatial–spectral locality constrained elastic net hypergraph learning model is proposed for hyperspectral image clustering (i.e. unsupervised classification). In order to utilize the spatial–spectral correlation among the pixels in hyperspectral images, first, we construct a locality-constrained dictionary by selecting K relevant pixels within a spatial neighbourhood, which activates the most correlated atoms and suppresses the uncorrelated ones. Second, each pixel is represented as a linear combination of the atoms in the dictionary under the elastic net regularization. Third, based on the obtained representations, the pixels and their most related pixels are linked as hyperedges, which can effectively capture high–order relationships among the pixels. Finally, a hypergraph Laplacian matrix is built for unsupervised learning. Experiments have been conducted on two widely used hyperspectral images, and the results show that the proposed method can achieve a superior clustering performance when compared to state-of-the-art methods.     

Spatial–Temporal Relation Reasoning for Action Prediction in Videos

International Journal of Computer Vision - Action prediction in videos refers to inferring the action category label by an early observation of a video. Existing studies mainly focus on exploiting...     

Evaluation of linear spectral unmixing and ΔNBR for predicting post‐fire recovery in a North American ponderosa pine forest

The Differenced Normalized Burn Ratio (ΔNBR) is widely used to map post‐fire effects in North America from multispectral satellite imagery, but has not been rigorously validated across the great diversity in vegetation types. The importance of these maps to fire rehabilitation crews highlights the need for continued assessment of alternative remote sensing approaches. To meet this need, this study presents a first preliminary comparison of immediate post‐fire char (black ash) fraction, as measured by linear spectral unmixing, and ΔNBR, with two quantitative one‐year post‐fire field measures indicative of canopy and sub‐canopy conditions: % live tree and dry organic litter weight (gm^?2). Image analysis was applied to Landsat 7 Enhanced Thematic Mapper (ETM+) imagery acquired both before and immediately following the 2000 Jasper Fire, South Dakota. Post‐fire field analysis was conducted one‐year post‐fire. Although the immediate post‐fire char fraction (r ² = 0.56, SE = 28.03) and ΔNBR (r ² = 0.55, SE = 29.69) measures produced similarly good predictions of the % live tree, the standard error in the prediction of litter weight with the char fraction method (r ² = 0.55, SE = 4.78) was considerably lower than with ΔNBR (r ² = 0.52, SE = 8.01). Although further research is clearly warranted to evaluate more field measures, in more fires, and across more fire regimes, the char fraction may be a viable approach to predict longer‐term indicators of ecosystem recovery and may potentially act as a surrogate retrospective measure of the fire intensity.     

Space–time spectral collocation method for one-dimensional PDE constrained optimisation

This paper solves an optimal control problem governed by a parabolic PDE. Using Lagrangian multipliers, necessary conditions are derived and then space–time spectral collocation method is applied to discretise spatial derivatives and time derivatives. This method solves partial differential equations numerically with errors bounded by an exponentially decaying function which is dependent on the number of modes of analytic solution. Spectral methods, which converge spectrally in both space and time, have gained a significant attention recently. The problem is then reduced to a system consisting of easily solvable algebraic equations. Numerical examples are presented to show that this formulation has exponential rates of convergence in both space and time.     

Legendre–Galerkin spectral approximation for a nonlocal elliptic Kirchhof-type problem

We propose a numerical scheme to obtain an approximate solution of a nonlocal elliptic Kirchhof-type problem. We first reduce the problem to a nonlinear finite dimensional system by a Legendre–Galerkin spectral method and then solve it by an iterative process. Convergence of the iterative process and an error estimation of the approximate solution is provided. Numerical experiments are conducted to illustrate the performance of the proposed method.     

Spatial–Temporal gated graph attention network for skeleton-based action recognition

Pattern Analysis and Applications - Human body skeleton, acting as a spatiotemporal graph, is the key inspiration for researchers to implement a GCN-based method for action recognition. Most...     

Fractional Jacobi Galerkin spectral schemes for multi-dimensional time fractional advection–diffusion–reaction equations

One of the ongoing issues with time fractional diffusion models is the design of efficient high-order numerical schemes for the solutions of limited regularity. We construct in this paper two efficient Galerkin spectral algorithms for solving multi-dimensional time fractional advection–diffusion–reaction equations with constant and variable coefficients. The model solution is discretized in time with a spectral expansion of fractional-order Jacobi orthogonal functions. For the space discretization, the proposed schemes accommodate high-order Jacobi Galerkin spectral discretization. The numerical schemes do not require imposition of artificial smoothness assumptions in time direction as is required for most methods based on polynomial interpolation. We illustrate the flexibility of the algorithms by comparing the standard Jacobi and the fractional Jacobi spectral methods for three numerical examples. The numerical results indicate that the global character of the fractional Jacobi functions makes them well-suited to time fractional diffusion equations because they naturally take the irregular behavior of the solution into account and thus preserve the singularity of the solution.

     

A spatial–spectral kernel-based approach for the classification of remote-sensing images

Classification of remotely sensed images with very high spatial resolution is investigated. The proposed method deals with the joint use of the spatial and the spectral information provided by the remote-sensing images. A definition of an adaptive neighborhood system is considered. Based on morphological area filtering, the spatial information associated with each pixel is modeled as the set of connected pixels with an identical gray value (flat zone) to which the pixel belongs: The pixel's neighborhood is characterized by the vector median value of the corresponding flat zone. The spectral information is the original pixel's value, be it a scalar or a vector value. Using kernel methods, the spatial and spectral information are jointly used for the classification through a support vector machine formulation. Experiments on hyperspectral and panchromatic images are presented and show a significant increase in classification accuracies for peri-urban area: For instance, with the first data set, the overall accuracy is increased from 80% with a conventional support vectors machines classifier to 86% with the proposed approach. Comparisons with other contextual methods show that the method is competitive.     

Brinkman equation for a corrugated pipe using a spectral–Galerkin method

This study numerically investigates the fully developed flow of a Newtonian fluid in a porous-saturated corrugated pipe, on the basis of a Brinkman model. The variable coefficient Helmholtz equation, which is obtained by means of an epitrochoid transformation, is solved using a spectral–Galerkin method. The effects of both the Darcy number and corrugation on the velocity field are discussed and presented graphically. The nature of these effects is documented for the first time.     

Legendre–Gauss-type spectral collocation algorithms for nonlinear ordinary/partial differential equations

We propose new Legendre–Gauss collocation algorithms for ordinary differential equations. We also design Legendre–Gauss-type collocation algorithms for time-dependent nonlinear partial differential equations. The suggested algorithms enjoy spectral accuracy in both time and space, and can be implemented in a fast and stable manner. Numerical results exhibit the effectiveness.     

Error estimates of the space–time spectral method for parabolic control problems

This work is devoted to investigate the spectral approximation of optimal control of parabolic problems. The space–time method is used to boost high-order accuracy by applying dual Petrov–Galerkin spectral scheme in time and spectral method in space. The optimality conditions are derived, and the a priori error estimates indicate the convergence of the proposed method. Numerical tests confirm the theoretical results, and show the efficiency of the method.     

High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction–diffusion equations

This paper introduces a high-order time stepping scheme, that is based on using Fourier spectral in space and a fourth-order diagonal Padé approximation to the matrix exponential function for solving multi-dimensional space-fractional reaction–diffusion equations. The resulting time stepping scheme is developed based on an exponential time differencing approach such that it alleviates solving a large non-linear system at each time step while maintaining the stability of the scheme. The non-locality of the fractional operator in some other numerical schemes for these equations leads to full and dense matrices. This scheme is able to overcome such computational inefficiency due to the full diagonal representation of the fractional operator. It also attains spectral convergence for multiple spatial dimensions. The stability of the scheme is discussed through the investigation of the amplification symbol and plotting its stability regions, which provides an indication of the stability of the method. The convergence analysis is performed empirically to show that the scheme is fourth-order accurate in time, as expected. Numerical experiments on reaction–diffusion systems with application to pattern formation are discussed to show the effect of the fractional order in space-fractional reaction–diffusion equations and to validate the effectiveness of the scheme.     

Galerkin–Legendre spectral method for Neumann boundary value problems in three dimensions

In this paper, we investigate the Legendre spectral methods for problems with the essential imposition of Neumann boundary condition in three dimensions. A double diagonalization process has been employed, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of Neumann boundary condition. For analysing numerical errors, some results on Legendre orthogonal approximation in Jacobi weighted Sobolev space are established. As examples of applications, the spectral schemes are provided for two model problems. The convergences of the proposed schemes are proved, too. Numerical results demonstrate the spectral accuracy in space, and which confirm theoretical analysis well.     

A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in $L^2$ norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.     

Fully Petrov–Galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation

Distributed fractional derivative operators can be used for modeling of complex multiscaling anomalous transport, where derivative orders are distributed over a range of values rather than being just a fixed integer number. In this paper, we consider the space-time Petrov–Galerkin spectral method for a two-dimensional distributed-order time-fractional fourth-order partial differential equation. By applying a proper Gauss-quadrature rule to discretize the distributed integral operator, the problem is converted to a multi-term time-fractional equation. Then, the proposed method for solving the obtained equation is based on using Jacobi polyfractonomial, which are eigenfunctions of the first kind fractional Sturm–Liouville problem (FSLP), as temporal basis and Legendre polynomials for the spatial discretization. The eigenfunctions of the second kind FSLP are used as temporal basis in test space. This approach leads to finding the numerical solution of the problem through solving a system of linear algebraic equations. Finally, we provide some examples with smooth solutions and finite regular solutions to numerically demonstrate the efficiency, accuracy, and exponential convergence of the proposed method.

     

Accurate prediction of bird species richness patterns in an urban environment using Landsat‐derived NDVI and spectral unmixing

Urban landscapes are expanding rapidly and are reshaping the distribution of many animal and plant species. With these changes, the need to understand and to include urban biodiversity patterns in research and management programmes is becoming vital. Recent studies have shown that remote sensing tools can be useful in studies examining biodiversity patterns in natural landscapes. The present study aimed to explore whether remote sensing tools can be applied in biodiversity research in an urban landscape. More specifically, the study examined whether the Landsat‐derived Normalized Difference Vegetation Index (NDVI) and linear spectral unmixing of urban land cover can predict bird richness in the city of Jerusalem. Bird richness was sampled in 40 1‐ha sites over a range of urban environments in 329 surveys. NDVI and the per cent cover of built‐up area were strongly and negatively correlated with each other, and were both very successful in explaining the number of bird species in the study sites. Mean NDVI in each site was positively correlated with the site bird species richness. A hump‐shaped relationship between NDVI and species richness was observed (when calculated over increasing spatial scales), with a maximum value (Pearson's R = 0.87, p<0.001, n = 40) at a scale of 15 ha. We suggest that remote sensing approaches may provide planners and conservation biologists with an efficient and cost‐effective method to study and estimate biodiversity across urban environments that range between densely built‐up areas, residential neighbourhoods, urban parks and the peri‐urban environment.     

Correction to: Long-Short Temporal–Spatial Clues Excited Network for Robust Person Re-identification

International Journal of Computer Vision -