IMAGE ANALYSIS, CLASSIFICATION, and CHANGE DETECTION in REMOTE SENSING

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1 SECOND EDITION IMAGE ANALYSIS, CLASSIFICATION, and CHANGE DETECTION in REMOTE SENSING ith Algorithms for ENVI/IDL Morton J. Canty с*' Q\ CRC Press Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

2 Contents Preface to the Second Edition Preface to the First Edition xi xiii 1. Images, Arrays, and Matrices Multispectral Satellite Images Algebra of Vectors and Matrices Elementary Properties Square Matrices Singular Matrices Symmetric, Positive Definite Matrices Linear Dependence and Vector Spaces Eigenvalues and Eigenvectors Singular Value Decomposition Vector Derivatives Finding Minima and Maxima Exercises Image Statistics Random Variables Discrete Random Variables Continuous Random Variables Normal Distribution Random Vectors Parameter Estimation Sampling a Distribution Interval Estimation Provisional Means Hypothesis Testing and Sample Distribution Functions Chi-Square Distribution Student-t Distribution F-Distribution Conditional Probabilities, Bayes' Theorem, and Classification Ordinary Linear Regression One Independent Variable More Than One Independent Variable Regularization, Duality, and the Gram Matrix Entropy and Information Kullback-Leibler Divergence Mutual Information Exercises 65

3 vi Contents 3. Transformations Discrete Fourier Transform Discrete Wavelet Transform Haar Wavelets Image Compression Multiresolution Analysis Dilation Equation and Refinement Coefficients Cascade Algorithm Mother Wavelet Daubechies D4 Scaling Function Principal Components Primal Solution Dual Solution Minimum Noise Fraction Additive Noise Minimum Noise Fraction Transformation in ENVI Spatial Correlation Maximum Autocorrelation Factor Noise Estimation Exercises Filters, Kernels, and Fields Convolution Theorem Linear Filters Ill 4.3 Wavelets and Filter Banks One-Dimensional Arrays Two-Dimensional Arrays Kernel Methods Valid Kernels Kernel PCA Gibbs-Markov Random Fields Exercises Image Enhancement and Correction Lookup Tables and Histogram Functions Filtering and Feature Extraction Edge Detection Invariant Moments Panchromatic Sharpening HSV Fusion Brovey Fusion PCA Fusion DWT Fusion A Trous Fusion 155

4 Contents vii Quality Index Topographie Correction Rotation, Scaling, and Translation Imaging Transformations Camera Models and RFM Approximations Stereo Imaging and Digital Elevation Models Slope and Aspect Illumination Correction Image-Image Registration Frequency-Domain Registration Feature Matching High-Pass Filtering Closed Contours Chain Codes and Moments Contour Matching Consistency Check Implementation in IDL Resampling and Warping Exercises Supervised Classification: Part Maximum a Posteriori Probability Training Data and Separability Maximum Likelihood Classification ENVI's Maximum Likelihood Classifier Modified Maximum Likelihood Classifier Gaussian Kernel Classification Neural Networks Neural Network Classifier Cost Functions Backpropagation Overfitting and Generalization Support Vector Machines Linearly Separable Classes Primal Formulation Dual Formulation Quadratic Programming and Support Vectors Overlapping Classes Solution with Sequential Minimal Optimization Multiclass SVMs Kernel Substitution Modified SVM Classifier Exercises 232

5 viii Contents 7. Supervised Classification: Part Postprocessing Majority Filtering Probabilistic Label Relaxation Evaluation and Comparison of Classification Accuracy Accuracy Assessment Model Comparison Adaptive Boosting Hyperspectral Analysis Spectral Mixture Modeling Unconstrained Linear Unmixing Intrinsic End-Members and Pixel Purity Exercises Unsupervised Classification Simple Cost Functions Algorithms That Minimize the Simple Cost Functions K-Means Clustering Kernel K-Means Clustering Extended K-Means Clustering Agglomerative Hierarchical Clustering Fuzzy K-Means Clustering Gaussian Mixture Clustering Expectation Maximization Simulated Annealing Partition Density Implementation Notes Including Spatial Information Multiresolution Clustering Spatial Clustering Benchmark Kohonen Self-Organizing Map Image Segmentation Segmenting a Classified Image Object-Based Classification Mean Shift Exercises Change Detection Algebraic Methods PostClassification Comparison Principal Components Analysis Iterated PCA Kernel PCA Multivariate Alteration Detection 319

6 Contents ix Canonical Correlation Analysis Orthogonality Properties Scale Invariance Iteratively Reweighted MAD Correlation with the Original Observations Regularization Postprocessing Decision Thresholds and Unsupervised Classification of Changes Radiometric Normalization Exercises 338 Appendix A: Mathematical Tools 343 A.l Cholesky Decomposition 343 A.2 Vector and Inner Product Spaces 345 A.3 Least Squares Procedures 347 A.3.1 Recursive Linear Regression 347 A.3.2 Orthogonal Linear Regression 350 Appendix B: Efficient Neural Network Training Algorithms 355 B.l Hessian Matrix 355 B.l.l R-Operator 356 B.l.1.1 Determination of R v {и} 358 B.l.1.2 Determination of R v {8 0 } 359 B.l.1.3 Determination of R v {8 h } 359 B.1.2 Calculating the Hessian 360 B.2 Scaled Conjugate Gradient Training 360 B.2.1 Conjugate Directions 362 B.2.2 Minimizing a Quadratic Function 363 B.2.3 Algorithm 366 B.3 Kaiman Filter Training 368 B.3.1 Linearization 371 B.3.2 Algorithm 372 B.4 A Neural Network Classifier with Hybrid Training 379 Appendix C: ENVI Extensions in IDL 381 C.l Installation 381 C.2 Extensions 382 C.2.1 Kernel Principal Components Analysis 384 C.2.2 Discrete Wavelet Transform Fusion 386 C.2.3 Ä Trous Wavelet Transform Fusion 388 C.2.4 Quality Index 389 C.2.5 Calculating Heights of Man-Made Structures in High-Resolution Imagery 390 C.2.6 Illumination Correction 392

7 x Contents C.2.7 Image Registration 393 C.2.8 Maximum Likelihood Classification 394 C.2.9 Gaussian Kernel Classification 396 C.2.10 Neural Network Classification 397 C.2.11 Support Vector Machine Classification 399 C.2.12 Probabilistic Label Relaxation 399 C.2.13 Classifier Evaluation and Comparison 401 C.2.14 Adaptive Boosting a Neural Network Classifier 402 C.2.15 Kernel K-Means Clustering 404 C.2.16 Agglomerative Hierarchical Clustering 405 C.2.17 Fuzzy K-Means Clustering 406 C.2.18 Gaussian Mixture Clustering 407 C.2.19 Kohonen Self-Organizing Map 409 C.2.20 Classified Image Segmentation 410 C.2.21 Mean Shift Segmentation 411 C.2.22 Multivariate Alteration Detection 412 C.2.23 Viewing Changes 415 C.2.24 Radiometric Normalization 416 Appendix D: Mathematical Notation 419 References 421 Index 429

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