Multiscale stochastic hierarchical image segmentation by spectral clustering

This paper proposes a sampling based hierarchical approach for solving the computational demands of the spectral clustering methods when applied to the problem of image segmentation. The authors first define the distance between a pixel and a cluster, and then derive a new theorem to estimate the number of samples needed for clustering. Finally, by introducing a scale parameter into the simi- larity function, a novel spectral clustering based image segmentation method has been developed. An important characteristic of the approach is that in the course of image segmentation one needs not only to tune the scale parameter to merge the small size clusters or split the large size clusters but also take samples from the data set at the different scales. The multiscale and stochastic nature makes it feasible to apply the method to very large grouping problem. In addition, it also makes the segmentation compute in time that is linear in the size of the image. The experimental results on various synthetic and real world images show the effective- ness of the approach.     

Hyperspectral image super-resolution with spectral–spatial network

ABSTRACT

The super-resolution problem for hyperspectral images is currently one of the most challenging topics in remote sensing. Increasingly effective methods have been presented to solve this ill-posed problem under certain circumstances. In this article, we propose a new approach named the spectral–spatial network (SSN), which can effectively increase spatial resolution while keeping spectral information. The SSN consists of two sections: a spatial section and a spectral section that contribute to enhancing spatial resolution and preserving spectral information, respectively. The spatial section is proposed to learn end-to-end mapping between single-band images, from low-resolution and high-resolution hyperspectral images. In this section, we enhance the traditional sub-pixel convolutional layer by adding a maximum variance principle that can realize nonlinear fitting through piecewise linearization. The spectral section aims to fine-tune spectral caves to keep the spectral signature with a spectral angle error loss function. In order to make the SSN converge quickly, we also develop a corresponding three-step training method. The experimental results on two databases, with both indoor and outdoor scenes, show that our proposed method performs better than the existing state-of-the-art methods.     

Land‐cover mixing and spectral vegetation indices

Vegetation indices have been widely used as indicators of seasonal and inter‐annual variations in vegetation caused by either human activities or climate, with the overall goal of observing and documenting changes in the Earth system. While existing satellite remote sensing systems, such as NASA's Multi‐angle Imaging SpectroRadiometer (MISR) and Moderate Resolution Imaging Spectroradiometer (MODIS), are providing improved vegetation index data products through correcting for the distortions in surface reflectance caused by atmospheric particles as well as ground covers below vegetation canopy, the impact of land‐cover mixing on vegetation indices has not been fully addressed. In this study, based on real image spectral samples for two‐component mixtures of forest and common nonforest land‐cover types directly extracted from a 1.1?km MISR image by referencing a 30?m land‐cover classification, the effect of land‐cover mixing on the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI) has been quantitatively evaluated. When the areal fraction of forest was lower than 80%, both NDVI and EVI varied greatly with mixed land‐cover types, although EVI varied less than NDVI. Such a phenomenon can cause errors in applications based on use of these vegetation indices. This study suggests that methods that reduce land‐cover mixing effects should be introduced when developing new spectral vegetation indices.     

Solving the Grad–Shafranov equation with spectral elements

The development of a generalized two dimensional MHD equilibrium solver within the nimrod framework [Sovinec, et al., J. Comput. Phys. 195 (2004) 355] is discussed. Spectral elements are used to represent the poloidal plane. To permit the generation of spheromak and other compact equilibria, special consideration is given to ensure regularity at the geometric axis (R=0)$(R=0)$. The scalar field Λ=ψ/R²$\Lambda =\psi /R^2$ is used as the dependent variable to express the Grad–Shafranov operator as a total divergence. With the correct gauge, regularity along the geometric axis is satisfied. The convergence properties of the spectral elements are investigated by comparing numerically generated equilibria against known analytic solutions. Equilibria accurate to double precision error are generated with sufficient resolution. Depending on the equilibrium, either geometric or algebraic convergence is observed as the polynomial degree of the spectral-element basis is increased.     

A multiresolution spectral angle‐based hyperspectral classification method

Due to the lack of training samples, hyperspectral classification often adopts the minimum distance classification method based on spectral metrics. This paper proposes a novel multiresolution spectral‐angle‐based hyperspectral classification method, where band subsets will be selected to simultaneously minimize the average within‐class spectral angle and maximize the average between‐class spectral angle. The method adopts a pairwise classification framework (PCF), which decomposes the multiclass problem into two‐class problems. Based on class separability criteria, the original set of bands is recursively decomposed into band subsets for each two‐class problem. Each subset is composed of adjacent bands. Then, the subsets with high separability are selected to generate subangles, which will be combined to measure the similarity. Following the PCF, the outputs of all the two‐class classifiers are combined to obtain the final output. Tested with an Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data set for a six‐class problem, the results demonstrate that our method outperforms the previous spectral metric‐based classification methods.     

Multi-scale superpixel spectral–spatial classification of hyperspectral images

A novel multi-scale superpixel-based spectral–spatial classification (MS-SSC) approach is proposed for hyperspectral images in this study. Superpixels are considered as the basic processing units for spectral–spatial-based classification. The use of multiple scales allows the capturing of local spatial structures of various sizes. The proposed technique consists of three steps. In the first step, hierarchical superpixel segmentations are performed from fine to coarse scales for the original hyperspectral image and the spectral information of each superpixel is used for classification at each scale. In the second step, each single scale superpixel-based classification is improved by combining with the segmentations at a higher level. Finally, the multi-scale classification is achieved via decision fusion. Experimental results are presented for two hyperspectral images and compared with recently advanced pixel-wise and pixel-based spectral–spatial classification approaches. The experiments demonstrate that the proposed method works effectively on the homogeneous regions and is also able to preserve the small local spatial structures in the image.     

Arabic writer identification based on hybrid spectral–statistical measures

Many techniques have been reported for handwriting-based writer identification. None of these techniques assume that the written text is in Arabic. In this paper we present a new technique for feature extraction based on hybrid spectral–statistical measures (SSMs) of texture. We show its effectiveness compared with multiple-channel (Gabor) filters and the grey-level co-occurrence matrix (GLCM), which are well-known techniques yielding a high performance in writer identification in Roman handwriting. Texture features were extracted for wide range of frequency and orientation because of the nature of the spread of Arabic handwriting compared with Roman handwriting, and the most discriminant features were selected with a model for feature selection using hybrid support vector machine–genetic algorithm techniques. Four classification techniques were used: linear discriminant classifier (LDC), support vector machine (SVM), weighted Euclidean distance (WED), and the K nearest neighbours (K_NN) classifier. Experiments were performed using Arabic handwriting samples from 20 different people and very promising results of 90.0% correct identification were achieved.     

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.     

Quantifying high‐resolution impervious surfaces using spectral mixture analysis

Impervious surface distribution and its temporal changes are considered key urbanization indicators and are utilized for analysing urban growth and influences of urbanization on natural environments. Recently, urban impervious surface information was extracted from medium/coarse resolution remote sensing imagery (e.g. Landsat ETM+ and AVHRR) through spectral analytical methods (e.g. spectral mixture analysis (SMA), regression tree, etc.). Few studies, however, have attempted to generate impervious surface information from high resolution remotely sensed imagery (e.g. IKONOS and Quickbird). High resolution images provide detailed information about urban features and are, therefore, more valuable for urban analysis. The improved spatial resolution, however, also brings new challenges when existing spectral analytical methods are applied. In particular, a higher spatial resolution leads to reduced boundary effects and increased within‐class variability. Taking Grafton, Wisconsin, USA as a study site, this paper analyses the spectral characteristics of IKONOS imagery and explores the applicability of SMA for impervious surface estimation. Results suggest that with improved spatial resolution, IKONOS imagery contains 40–50% of mixed urban pixels for the study area, and the within‐class variability is a severe problem for spectral analysis. To address this problem, this paper proposes two approaches, interior end‐member set selection and spectral normalization, for SMA. Analysis of results indicates that these approaches can reasonably reduce the problems associated with boundary effects and within‐class variability, therefore generating better impervious surface estimates.     

Similarity measures for spectral discrimination of salt‐affected soils

This paper illustrates a pilot study designed to examine the spectral response of soils due to salt variations. The aim of the study includes determining whether salt‐affected soils can be discriminated based on their spectral characteristics, by establishing a relationship between soil properties and soil spectra and by testing if variations in the spectra of salt‐affected soil samples are statistically significant. To answer the research questions, a laboratory experiment was designed to simulate salt transport to a column of soil in order to provide direct measurements of soil spectra and soil properties when salt concentration in a soil sample changes. The measured spectra were examined by the application of spectral matching techniques to quantify the variations and ascertain a relationship that supports the spectral identification of saline soils. The Ward's grouping method was conducted as an exploratory tool to statistically create homogeneous classes among data, which were obtained from the application of the spectral matching techniques to salt affected soil spectra. A nonparametric statistical test (Mann–Whitney U‐test) was used to determine whether the differences between the classes are statistically significant. The results of spectral matching techniques showed differences in absorption strength, absolute reflectance and spectral angle in the near and shortwave infrared regions. The results also showed significant correlations between soil electrical conductivity (EC) and spectral similarity measures, indicating that similarity between the samples' spectra decreases as the salt concentration in the soil increases. The generated clusters indicate two classes at the highest level, which were subdivided at the next level and further subdivided into multiple subclasses as the dissimilarity decreased. The spectral data were grouped into classes and were used to test the null hypothesis by applying the Mann–Whitney U‐test. The results indicate a significance level of α<0.02 between salinity classes and α<0.05 per waveband, meaning variations between the classes are higher than within each class.     

Distance decay in spectral space in analysing ecosystem β‐diversity

The use of spectral distance for explaining the phenomenon of distance decay in species similarity between two sites (based on the niche difference model) is presented here. Distance decay is based on the first law of geography: ‘the similarity between two sites decays with increasing the distance between them’. From an ecological point of view, this could be expressed as: ‘the β‐diversity between two sites should increase with an increase in spatial distance’. Beta‐diversity is defined as the amount of turnover in species composition from one site to another; and it plays a key role in biodiversity management and conservation, as it allows the detection of spatial gradients that act functionally in determining the spatial variation in species composition. This work demonstrates how the celebrated distance decay pattern achieved by means of spatial distance can be attained even with spectral distance, measured on Landsat near‐infrared images. It is argued that spectral heterogeneity represents a good proxy of β‐diversity of an area, becoming a valuable tool in biodiversity characterization at regional and global scales.     

On the analogue methods for power spectral density estimation†

This paper examines an analogue method for power spectral density estimation which employs an asymmetrical modulation. The approximate expressions for the expected value and for the dispersion of the estimate thus obtained are worked out by means of simplifying hypotheses.

Then a comparison is drawn between the method under examination and another one with symmetrical modulation; it is shown that in some cases the former has advantageous results in that at a parity of estimate dispersion it demands a smaller number of components.     

Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems

This paper presents a method for designing inputs to identify linear continuous-time multiple-input multiple-output (MIMO) systems. The goal here is to design a T-optimal band-limited spectrum satisfying certain input/output power constraints. The input power spectral density matrix is parametrized as the product φu(jω) =1/2H(jω){H^H}(jω), where H(jω) is a matrix polynomial. This parametrization transforms the T-optimal cost function and the constraints into a quadratically constrained quadratic program (QCQP). The QCQP turns out to be a non-convex semidefinite program with a rank one constraint. A convex relaxation of the problem is first solved. A rank one solution is constructed from the solution to the relaxed problem. This relaxation admits no gap between its solution and the original non-convex QCQP problem. The constructed rank one solution leads to a spectrum that is optimal. The proposed input design methodology is experimentally validated on a cantilever beam bonded with piezoelectric plates for sensing and actuation. Subspace identification algorithm is used to estimate the system from the input-output data.     

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.     

A spectral–textural kernel-based classification method of remotely sensed images

Most studies have been based on the original computation mode of semivariogram and discrete semivariance values. In this paper, a set of texture features are described to improve the accuracy of object-oriented classification in remotely sensed images. So, we proposed a classification method support vector machine (SVM) with spectral information and texture features (ST-SVM), which incorporates texture features in remotely sensed images into SVM. Using kernel methods, the spectral information and texture features are jointly used for the classification by a SVM formulation. Then, the texture features were calculated based on segmented block matrix image objects using the panchromatic band. A comparison of classification results on real-world data sets demonstrates that the texture features in this paper are useful supplement information for the spectral object-oriented classification, and proposed ST-SVM classification accuracy than the traditional SVM method with only spectral information.     

Hyperspectral image classification using a spectral–spatial random walker method

This article proposes a spectral–spatial method for classification of hyperspectral images (HSIs) by modifying traditional random walker (RW). The proposed method consists of suggesting two main modifications. First, to construct a spatial edge weighting function, low-frequency edge weighting function is proposed. In this function, the detail weights are removed. Second, to enhance the classification accuracy, a fusion of spectral and spatial Laplacian matrix in RW is suggested. This fusion can improve the classification performances compared to traditional RW using only spatial Laplacian matrix. In comparison with some of the state-of-the-art RW and spectral–spatial classifier methods, the experimental results of the proposed method (spectral–spatial RW) show that the proposed method significantly increases the classification accuracy of HSI.     

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.     

Land cover change detection with a cross‐correlogram spectral matching algorithm

Timely extraction of reliable land cover change information is increasingly needed at a wide continuum of scales. Few methods developed from previous studies have proved to be robust when noise, changes in atmospheric and illumination conditions, and other scene‐ and sensor‐dependent variables are present in the multitemporal images. In this study, we developed a new method based on cross‐correlogram spectral matching (CCSM) with the aim of identifying interannual land cover changes from time‐series Normalized Difference Vegetation Index (NDVI) data. In addition, a new change index is proposed with integration of two parameters that are measured from the cross‐correlogram: the root mean square (RMS) and (1?R _max), where R _max is the maximum correlation coefficient in a correlogram. Subsequently, a method was proposed to derive the optimal threshold for judging ‘change’ or ‘non‐change’ with the acquired change index. A pilot study was carried out using SPOT VGT‐S images acquired in 1998 and 2000 at Xianghai Park in Jilin Province. The results indicate that CCSM is superior to a traditional Change Vector Analysis (CVA) when noise is present with the data. Because of an error associated with the ground truthing data, a more comprehensive assessment of the developed method is still in process using better ground truthing data and images at a larger time interval. It is worth noting that this method can be applied not only to NDVI datasets but also to other index datasets reflecting surface conditions sampled at different time intervals. In addition, it can be applied to datasets from different satellites without the need to normalize sensor differences.