There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper addresses the problem of the classification of hyperspectral remote sensing images by support vector machines (SVMs) First, we propose a theoretical discussion and experimental analysis aimed at understanding and assessing the potentialities of SVM classifiers in hyperdimensional feature spaces Then, we assess the effectiveness of SVMs with respect to conventional feature-reduction-based approaches and their performances in hypersubspaces of various dimensionalities To sustain such an analysis, the performances of SVMs are compared with those of two other nonparametric classifiers (ie, radial basis function neural networks and the K-nearest neighbor classifier) Finally, we study the potentially critical issue of applying binary SVMs to multiclass problems in hyperspectral data In particular, four different multiclass strategies are analyzed and compared: the one-against-all, the one-against-one, and two hierarchical tree-based strategies Different performance indicators have been used to support our experimental studies in a detailed and accurate way, ie, the classification accuracy, the computational time, the stability to parameter setting, and the complexity of the multiclass architecture The results obtained on a real Airborne Visible/Infrared Imaging Spectroradiometer hyperspectral dataset allow to conclude that, whatever the multiclass strategy adopted, SVMs are a valid and effective alternative to conventional pattern recognition approaches (feature-reduction procedures combined with a classification method) for the classification of hyperspectral remote sensing data

/pdf/classification-of-hyperspectral-remote-sensing-images-with-51xjutm0y6.pdf

Classification of hyperspectral remote sensing images with support vector machines

A wide range of methods for analysis of airborne- and satellite-derived imagery continues to be proposed and assessed. In this paper, we review remote sensing implementations of support vector machines (SVMs), a promising machine learning methodology. This review is timely due to the exponentially increasing number of works published in recent years. SVMs are particularly appealing in the remote sensing field due to their ability to generalize well even with limited training samples, a common limitation for remote sensing applications. However, they also suffer from parameter assignment issues that can significantly affect obtained results. A summary of empirical results is provided for various applications of over one hundred published works (as of April, 2010). It is our hope that this survey will provide guidelines for future applications of SVMs and possible areas of algorithm enhancement.

https://www.aboutgis.com/Publications/Mountrakis_SVM_review_in_remote_sensing_ISPRS2010.pdf

Support vector machines in remote sensing: A review

The Nature of Remote Sensing: Introduction. Remote Sensing. Information Extraction from Remote-Sensing Images. Spectral Factors in Remote Sensing. Spectral Signatures. Remote-Sensing Systems. Optical Sensors. Temporal Characteristics. Image Display Systems. Data Systems. Summary. Exercises. References. Optical Radiation Models: Introduction. Visible to Short Wave Infrared Region. Solar Radiation. Radiation Components. Surface-Reflected. Unscattered Component. Surface-Reflected. Atmosphere-Scattered Component. Path-Scattered Component. Total At-Sensor. Solar Radiance. Image Examples in the Solar Region. Terrain Shading. Shadowing. Atmospheric Correction. Midwave to Thermal Infrared Region. Thermal Radiation. Radiation Components. Surface-Emitted Component. Surface-Reflected. Atmosphere-Emitted Component. Path-Emitted Component. Total At-Sensor. Emitted Radiance. Total Solar and Thermal Upwelling Radiance. Image Examples in the Thermal Region. Summary. Exercises. References. Sensor Models: Introduction. Overall Sensor Model. Resolution. The Instrument Response. Spatial Resolution. Spectral Resolution. Spectral Response. Spatial Response. Optical PSFopt. Image Motion PSFIM. Detector PSFdet. Electronics PSFel. Net PSFnet. Comparison of Sensor PSFs. PSF Summary for TM. Imaging System Simulation. Amplification. Sampling and Quantization. Simplified Sensor Model. Geometric Distortion. Orbit Models. Platform Attitude Models. Scanner Models. Earth Model. Line and Whiskbroom ScanGeometry. Pushbroom Scan Geometry. Topographic Distortion. Summary. Exercises. References. Data Models: Introduction. A Word on Notation. Univariate Image Statistics. Histogram. Normal Distribution. Cumulative Histogram. Statistical Parameters. Multivariate Image Statistics. Reduction to Univariate Statistics. Noise Models. Statistical Measures of Image Quality. Contrast. Modulation. Signal-to-Noise Ratio (SNR). Noise Equivalent Signal. Spatial Statistics. Visualization of Spatial Covariance. Covariance with Semivariogram. Separability and Anisotropy. Power Spectral Density. Co-occurrence Matrix. Fractal Geometry. Topographic and Sensor Effects. Topography and Spectral Statistics. Sensor Characteristics and Spectral Stastistics. Sensor Characteristics and Spectral Scattergrams. Summary. Exercises. References. Spectral Transforms: Introduction. Feature Space. Multispectral Ratios. Vegetation Indexes. Image Examples. Principal Components. Standardized Principal Components (SPC) Transform. Maximum Noise Fraction (MNF) Transform. Tasseled Cap Tranformation. Contrast Enhancement. Transformations Based on Global Statistics. Linear Transformations. Nonlinear Transformations. Normalization Stretch. Reference Stretch. Thresholding. Adaptive Transformation. Color Image Contrast Enhancement. Min-max Stretch. Normalization Stretch. Decorrelation Stretch. Color Spacer Transformations. Summary. Exercises. References. Spatial Transforms: Introduction. An Image Model for Spatial Filtering. Convolution Filters. Low Pass and High Pass Filters. High Boost Filters. Directional Filters. The Border Region. Characterization of Filtered Images. The Box Filter Algorithm. Cascaded Linear Filters. Statistical Filters. Gradient Filters. Fourier Synthesis. Discrete Fourier Transforms in 2-D. The Fourier Components. Filtering with the Fourier Transform. Transfer Functions. The Power Spectrum. Scale Space Transforms. Image Resolution Pyramids. Zero-Crossing Filters. Laplacian-of-Gaussian (LoG) Filters. Difference-of-Gaussians (DoG) Filters.Wavelet Transforms. Summary. Exercises. References. Correction and Calibration: Introduction. Noise Correction. Global Noise. Sigma Filter. Nagao-Matsuyama Filter. Local Noise. Periodic Noise. Distriping 359. Global,Linear Detector Matching. Nonlinear Detector Matching. Statistical Modification to Linear and Nonlinear Detector. Matching. Spatial Filtering Approaches. Radiometric Calibration. Sensor Calibration. Atmospheric Correction. Solar and Topographic Correction. Image Examples. Calibration and Normalization of Hyperspectral Imagery. AVIRIS Examples. Distortion Correction. Polynomial Distortion Models. Ground Control Points (GCPs). Coordinate Transformation. Map Projections. Resampling. Summary. Exercises References. Registration and Image Fusion: Introduction. What is Registration? Automated GCP Location. Area Correlation. Other Spatial Features. Orthrectification. Low-Resolution DEM. High-Resolution DEM. Hierarchical Warp Stereo. Multi-Image Fusion. Spatial Domain Fusion. High Frequency Modulation. Spectral Domain Fusion. Fusion Image Examples. Summary. Exercises. References. Thematic Classification: Introduction. The Importance of Image Scale. The Notion of Similarity. Hard Versus Soft Classification. Training the Classifier. Supervised Training. Unsupervised Training. K-Means Clustering Algorithm. Clustering Examples. Hybrid Supervised/Unsupervised Training. Non-Parametric Classification Algorithms. Level-Slice. Nearest-Mean. Artificial Neural Networks (ANNs). Back-Propagation Algorithm. Nonparametric Classification Examples. Parametric Classification Algorithms. Estimation of Model-Parameters. Discriminant Functions. The Normal Distribution Model. Relation to the Nearest-Mean Classifier. Supervised Classification Examples and Comparison to Nonparametric Classifiers. Segmentation. Region Growing. Region Labeling. Sub-Pixel Classification. The Linear Mixing Model. Unmixing Model. Hyperspectral Image Analysis. Visualization of the Image Cube. Feature Extraction. Image Residuals. Pre-Classification Processing and Feature Extraction. Classification Algorithms. Exercises. Error Analysis. Multitemporal Images. Summary. References. Index.

Remote sensing, models, and methods for image processing

Theory of fuzzy integrals and its applications

In this study, a subspace detection technique is developed using a hybrid approach which combines both feature extraction and feature selection for the task of hyperspectral image classification. The proposed approach applies Kernel Principal Component Analysis (KPCA) at the first step, then feature selection from the KPCA images is accomplished by combining the KPCA score with a Jeffries-Matusita (JM) distance based ranking score. Experimental analysis is carried out on a hyperspectral image acquired by the AVIRIS sensor and the results show the advantage of the proposed approach in terms of classification accuracy in the tested cases.

Subspace detection based on the combination of nonlinear feature extraction and feature selection

Reducing the dimensionality of high dimensional data without losing its essential information is an important task in information processing. For hyperspectral data, Principal Component Analysis (PCA) is a common dimensionality reduction method which removes the correlation between bands by finding the lower dimensional projections of the original data which have maximum variance. However, since PCA does not take class label information into account, it does not always provide the best set of reduced features for class discrimination. Our proposed approach for dimensionality reduction is based on a measure of Mutual Information (MI). Our new algorithm, called MI-PCA, uses a mutual information measure to find those principal components which are spatially most similar to all the target classes. Our MI-PCA approach selects features which contain the most information about the output class structures and are also uncorrelated. We provide both theoretical and experimental analysis of this method in the paper. Experiments were conducted using hyperspectral data with 191 bands, covering the Washington DC area. The results show that 2 features selected out of 191 using MI-PCA provides 98% and 93% classification accuracy for training and test data respectively, with a Support Vector Machines (SVM) classifier. Whereas, to obtain a similar accuracy, the first 5 principle components are needed for a PCA-only approach. We also compared our approach with measuring the mutual information between the original bands and the class labels. However this approach performed poorly compared to our algorithm as the best features selected were all highly correlated with each other and could only provide discrimination between a small subset of the classes.

Supervised Feature Reduction Based on a Mutual Information Measure for Hyperspectral Image Classification

Hyperspectral imagery (HSI) contains hundreds of bands, which provides a wealth of spectral information and enables better characterization of features. However, the excessive dimensionality also poses a dimensional disaster for subsequent processing. Fortunately, band selection gives a straightforward and effective way to pick out a subset of bands with rich information and low correlation. Although many hyperspectral band selection methods, especially clustering-based ones, have been proposed by researchers in recent years, the contextual information of adjacent bands and the spatial structural information of materials are not well investigated. Therefore, in this paper, a multiscale superpixel-level group clustering framework (MSGCF) is proposed for hyperspectral band selection. Different from previous, a new superpixel-level distance measure is elaborately utilized to group and cluster the spectral bands, which jointly considers the spectral context and spatial structure information. Concretely, to preserve the spatial structural information of HSI, multiple superpixel segmentation is firstly performed to generate superpixel maps in multi-scales, which enables complementarity of multiple superpixel segmentation algorithms and adaptation to diverse scales of land cover types. Secondly, the grouping and clustering paradigm is introduced to conduct the contextual information among bands. Here the maximum points of superpixel-level KL-ℓ1 distance of adjacent bands are adopted as partition points to separate bands into groups, which encourages adjacent bands with strong correlation to be divided into the same group. Thirdly, a superpixel-level fast density-based clustering method (SuFDPC) with superpixel-level ℓ2,1 distance is developed to select representative bands in every group. Finally, band selection results are achieved with a ranking-based voting strategy by concerning information entropy and frequency of occurrence in a unified scheme. A series of ablation analyses and experimental comparisons on four real HSI datasets have been conducted, as well as similarity comparisons for the selected bands. The experimental results consistently demonstrated the effectiveness of our MSGCF approach. The codes of this work will be available at http://jiasen.tech/papers/ for the sake of reproducibility.

A Multiscale Superpixel-level Group Clustering Framework for Hyperspectral Band Selection

The probabilistic mixture model for sub-pixel analysis is investigated and further developed. The probability distribution for each endmember is estimated by using a cluster-space data representation which is adaptable to individual class data distribution shapes. The proposed method is easy to implement and suitable for hyperspectral image data processing. Experiments using HyMap data are presented, showing the detailed sub-pixel estimation.

Cluster-space hyperspectral data representation for mixed pixel analysis

Spatial resolution is one of the central issues in land cover mapping from remote sensing imagery, and sub-pixel land cover mapping is difficult and challenging in this domain. Soft classification can provide more information than hard classification. However, the spatial location of land cover compositions within each pixel is unknown. To solve this problem, super-resolution mapping methods have been developed in recent years. In this paper, a landscape structure based approach for super-resolution land cover mapping is introduced to generate super-resolution land cover maps from remote sensing data. The method was used to map simulated target images and a real landscape and the results indicate that this approach has the ability to reconstruct complicated landscape with linear features, and large or small patches relative to the pixel size.

Xiuping Jia

Papers

Subspace detection based on the combination of nonlinear feature extraction and feature selection

Supervised Feature Reduction Based on a Mutual Information Measure for Hyperspectral Image Classification

A Multiscale Superpixel-level Group Clustering Framework for Hyperspectral Band Selection

Cluster-space hyperspectral data representation for mixed pixel analysis

Landscape structure based super-resolution mapping from remotely sensed imagery