James D. B. Nelson

Band Selection for Hyperspectral Image Classification Using Mutual Information

Spectral band selection is a fundamental problem in hyperspectral data processing. In this letter, a new band-selection method based on mutual information (MI) is proposed. MI measures the statistical dependence between two random variables and can therefore be used to evaluate the relative utility of each band to classification. A new strategy is described to estimate the MI using a priori knowledge of the scene, reducing reliance on a ground truth reference map, by retaining bands with high associated MI values (subject to the so-called complementary conditions). Simulations of classification performance on 16 classes of vegetation from the AVIRIS 92AV3C data set show the effectiveness of the method, which outperforms an MI-based method using the associated reference map, an entropy-based method, and a correlation-based method. It is also competitive with the steepest ascent algorithm at much lower computational cost

Customizing Kernel Functions for SVM-Based Hyperspectral Image Classification

Previous research applying kernel methods such as support vector machines (SVMs) to hyperspectral image classification has achieved performance competitive with the best available algorithms. However, few efforts have been made to extend SVMs to cover the specific requirements of hyperspectral image classification, for example, by building tailor-made kernels. Observation of real-life spectral imagery from the AVIRIS hyperspectral sensor shows that the useful information for classification is not equally distributed across bands, which provides potential to enhance the SVMs performance through exploring different kernel functions. Spectrally weighted kernels are, therefore, proposed, and a set of particular weights is chosen by either optimizing an estimate of generalization error or evaluating each bands utility level. To assess the effectiveness of the proposed method, experiments are carried out on the publicly available 92AV3C dataset collected from the 220-dimensional AVIRIS hyperspectral sensor. Results indicate that the method is generally effective in improving performance: spectral weighting based on learning weights by gradient descent is found to be slightly better than an alternative method based on estimating ;relevance; between band information and ground truth.

A fast separability-based feature-selection method for high-dimensional remotely sensed image classification

Because of the difficulty of obtaining an analytic expression for Bayes error, a wide variety of separability measures has been proposed for feature selection. In this paper, we show that there is a general framework based on the criterion of mutual information (MI) that can provide a realistic solution to the problem of feature selection for high-dimensional data. We give a theoretical argument showing that the MI of multi-dimensional data can be broken down into several one-dimensional components, which makes numerical evaluation much easier and more accurate. It also reveals that selection based on the simple criterion of only retaining features with high associated MI values may be problematic when the features are highly correlated. Although there is a direct way of selecting features by jointly maximising MI, this suffers from combinatorial explosion. Hence, we propose a fast feature-selection scheme based on a greedy optimisation strategy. To confirm the effectiveness of this scheme, simulations are carried out on 16 land-cover classes using the 92AV3C data set collected from the 220-dimensional AVIRIS hyperspectral sensor. We replicate our earlier positive results (which used an essentially heuristic method for MI-based band-selection) but with much reduced computational cost and a much sounder theoretical basis.

Dual-tree wavelets for estimation of locally varying and anisotropic fractal dimension

The dual-tree wavelet transform is here applied to the problem of fractal dimension estimation. The Hurst parameter of fractional Brownian surfaces is estimated using various wavelet bases. Results are given for global, local, anisotropic, and both local and anisotropic Hurst parameters. It is shown that the directional selectivity of the dual-tree wavelets can be exploited effectively to compute and distinguish Hurst parameters that vary non-trivially with direction and space.

Adaptive band selection for hyperspectral image fusion using mutual information

Hyperspectral imagery consists of hundreds of spectra or bands whose intensity is measured at various wavelength. Fusing the multiple spectral bands can provide more potential to differentiate between natural and man-made objects, and significantly improve the capability of target detection and classification. Spectral band or wavelength selection is one of the fundamental problems in hyperspectral data fusion. It is one instance of the classical optimal subset selection problem, which is known to be computationally hard. In this paper, we propose a new information-based band selection method for hyperspectral image fusion, which uses an adaptive measurement of mutual information (MI). As derived from the concept of entropy, MI measures the statistical dependence between two random variables and therefore can be used to evaluate the relative utility of each band to classification. Experiments on the AVIRIS dataset show that the method effectively identifies redundant spectral bands. Removing 15% of the total bands increases accuracy by 1.76% relative to performance on all bands, whereas removing 45% of the bands gives only 1.34% loss of accuracy.

Signal theory for SVM kernel design with applications to parameter estimation and sequence kernels

Fourier-based regularisation is considered for the support vector machine (SVM) classification problem over absolutely integrable loss functions. By considering the problem in a signal theory setting, we show that a principled and finite kernel hyperparameter search space can be discerned a priori by using the sinc kernel. The training and validation phase required to optimise the SVM can thus be limited to this hyperparameter search space. The method is adapted to a recently proposed max sequence kernel such that positive semi-definiteness, and so convergence, is guaranteed.

Enhanced Shift and Scale Tolerance for Rotation Invariant Polar Matching With Dual-Tree Wavelets

Polar matching is a recently developed shift and rotation invariant object detection method that is based upon dual-tree complex wavelet transforms or equivalent multiscale directional filterbanks. It can be used to facilitate both keypoint matching, neighborhood search detection, or detection and tracking with particle filters. The theory is extended here to incorporate an allowance for local spatial and dilation perturbations. With experiments, we demonstrate that the robustness of the polar matching method is strengthened at modest computational cost.

Applied Multi-Dimensional Fusion

The purpose of the Applied Multi-dimensional Fusion Project is to investigate the benefits that data fusion and related techniques may bring to future military Intelligence Surveillance Target Acquisition and Reconnaissance systems. In the course of this work, it is intended to show the practical application of some of the best multi-dimensional fusion research in the UK. This paper highlights the work done in the area of multi-spectral synthetic data generation, super-resolution, joint fusion and blind image restoration, multi-resolution target detection and identification and assessment measures for fusion. The paper also delves into the future aspirations of the work to look further at the use of hyper-spectral data and hyper-spectral fusion. The paper presents a wide work base in multi-dimensional fusion that is brought together through the use of common synthetic data, posing real-life problems faced in the theatre of war. Work done to date has produced practical pertinent research products with direct applicability to the problems posed.

Video Tracking Using Dual-Tree Wavelet Polar Matching and Rao-Blackwellised Particle Filter

We describe a video tracking application using the dual-tree Polar Matching Algorithm. We develop the dynamical and observation models in a probabilistic setting and study the empirical probability distribution of the Polar Matching output. We model the visible and occluded target statistics using Beta distributions. This is incorporated into a Track-Before-Detect (TBD) solution for the overall observation likelihood of each video frame and provides a principled derivation of the observation likelihood. Due to the nonlinear nature of the problem, we design a Rao-Blackwellised Particle Filter (RBPF) for the sequential inference. Computer simulations demonstrate the ability of the algorithm to track a simulated video moving target in an urban environment with complete and partial occlusions.

Signal Theory for SVM Kernel Parameter Estimation

Fourier-based regularisation is considered for the support vector machine classification problem over absolutely integrable loss functions. By invoking the modest assumption that the decision function belongs to a Paley-Wiener space, it is shown that the classification problem can be developed in the context of signal theory. Furthermore, by employing the Paley-Wiener reproducing kernel, namely the sine function, it is shown that a principled and finite kernel hyper-parameter search space can be discerned, a priori. Subsequent experiments, performed on a commonly available hyper-spectral image data set, reveal that the approach yields results that surpass state-of-the-art benchmarks.