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

Due to the limited spatial resolution of multispectral/hyperspectral data, mixed pixels widely exist and various spectral unmixing techniques have been developed for information extraction at the subpixel level in recent years One of the challenging problems in spectral mixture analysis is how to model the data of a primary class Given that the within-class spectral variability (WSV) is inevitable, it is more realistic to associate a group of representative spectra with a pure class The unmixing method using the extended support vector machines (eSVMs) has handled this problem effectively However, it has simplified WSV in the mixed cases In this paper, a further development of eSVMs is presented to address two problems in multiple-endmember spectral mixture analysis: 1) one mixed pixel may be unmixed into different fractions (model overlap); and 2) one fraction may correspond to a group of mixed pixels (fraction overlap) Then, spectral unmixing resolution (SUR) is introduced to characterize how finely the mixture in a mixed pixel can be quantified The quantitative relationship between SUR and WSV of endmembers is derived via a geometry analysis in support vector machine feature space Thus, the possible SUR can be estimated when multiple endmembers for each class are given Moreover, if the requirement of SUR is fixed, the acceptance level of WSV is then limited, which can be used as a guide to remove outliers and purify endmembers for each primary class Experiments are presented to illustrate model and fraction overlap problems and the application of SUR in uncertainty analysis of spectral unmixing

On Spectral Unmixing Resolution Using Extended Support Vector Machines

In this paper, we address a spectral unmixing problem for hyperspectral images by introducing multiple-kernel learning (MKL) coupled with support vector machines. To effectively solve issues of spectral unmixing, an MKL method is explored to build new boundaries and distances between classes in multiple-kernel Hilbert space (MKHS). Integrating reproducing kernel Hilbert spaces (RKHSs) spanned by a series of different basis kernels in MKHS is able to provide increased power in handling general nonlinear problems than traditional single-kernel learning in RKHS. The proposed method is developed to solve multiclass unmixing problems. To validate the proposed MKL-based algorithm, both synthetic data and real hyperspectral image data were used in our experiments. The experimental results demonstrate that the proposed algorithm has a strong ability to capture interclass spectral differences and improve unmixing accuracy, compared to the state-of-the-art algorithms tested.

Spectral Unmixing in Multiple-Kernel Hilbert Space for Hyperspectral Imagery

Many target detectors commonly utilize a single a priori target spectral signature as an input. However, the detection results are greatly affected by the quality of the a priori target spectral signature because the spectral variability phenomenon is universal and anisotropic in hyperspectral image data. This paper proposes a sparse representation-based method to generate an optimized target spectrum from limited target training samples, which is able to alleviate the impact of spectral variability on hyperspectral target detection. When lacking comprehensive knowledge about the target object of interest, an optimized representative target spectrum should be expected to be reconstructed by the hyperspectral data themselves in a sparse representation manner following the characteristics of the data structure and then be generated by a set of selected candidate pixels that contain the target signal with a varying status. With the optimized a priori target signature, the experimental results of the detection of different characteristics of objects with three different types of hyperspectral images confirm the effectiveness, robustness, and generality performance of the proposed method.

A Sparse Representation Method for a Priori Target Signature Optimization in Hyperspectral Target Detection

Stratified spectral mixture analysis of medium resolution imagery for impervious surface mapping

Images captured by digital cameras are vulnerable to quality degradations due to non-ideal illumination conditions such as dominated lighting source colors, where images so obtained may not faithfully reproduce the scene chromatics accurately. While it is a complicated process to control the scene illumination, color correction used as a post-processing procedure, is becoming an attractive solution. This research has developed an approach for color correction based on a modified implementation of the gray world assumption. The image color is adjusted by employing a gamma correction to satisfy the gray world assumption and avoid color saturation as encountered in the conventional approach. In order to further improve the image visual quality, an intensity preservation criterion is adopted as an additional means to produce the resultant image. With the normalization of intensity in accordance with the original image, an enhanced image both in color and intensity, is finally obtained. A collection of color images are used in an experiment to verify the proposed algorithm. Results have indicated that the proposed method is effective in producing enhanced images in the context of color enhancements.

Xiuping Jia

Papers

On Spectral Unmixing Resolution Using Extended Support Vector Machines

Spectral Unmixing in Multiple-Kernel Hilbert Space for Hyperspectral Imagery

A Sparse Representation Method for a Priori Target Signature Optimization in Hyperspectral Target Detection

Stratified spectral mixture analysis of medium resolution imagery for impervious surface mapping

Gray world based color correction and intensity preservation for image enhancement