Image Analysis, Classification and Change Detection in Remote Sensing

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1 Image Analysis, Classification and Change Detection in Remote Sensing WITH ALGORITHMS FOR ENVI/IDL Morton J. Canty Taylor &. Francis Taylor & Francis Group Boca Raton London New York CRC is an imprint of the Taylor & Francis Group, an informa business

2 Contents List of Figures Program Listings xiii xvii 1 Images, Arrays, and Matrices Multispectral satellite images Algebra of vectors and matrices Elementary properties Square matrices Singular matrices Symmetric, positive definite matrices Eigenvalues and eigenvectors Vector derivatives Finding minima and maxima Exercises 19 2 Image Statistics Random variables Discrete random variables Continuous random variables The normal distribution Random vectors Parameter estimation Sampling a distribution Interval estimation Provisional means Hypothesis testing and sample distribution functions The chi-square distribution The Student-t distribution The F-distribution Bayes' Theorem and classification Ordinary linear regression Exercises 47 vn

3 viii Image Analysis, Classification, and Change Detection in Remote Sensing 3 Transformations The discrete Fourier transform The discrete wavelet transform Haar wavelets Image compression Multiresolution analysis Principal components Maximum noise fraction Additive noise The maximum noise fraction transformation in ENVI Spatial correlation Maximum autocorrelation factor Noise estimation Exercises 79 4 Convolutions, Filters, and Fields The Convolution Theorem Linear filters Wavelets and filter banks One dimensional arrays Two-dimensional arrays Gibbs-Markov random fields Exercises Image Enhancement and Correction Lookup tables and histogram functions High-pass spatial filtering Panchromatic sharpening HSV fusion Brovey fusion PCA fusion DWT fusion A trous fusion A quality index Topographic correction Rotation, scaling, translation transformations 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 Resampling and warping 147

4 Contents ix 5.6 Exercises Supervised Classification Maximum a posteriori probability Training data and separability Maximum likelihood classification ENVI's maximum likelihood classifier A modified maximum likelihood classifier Gaussian kernel classification Neural networks The neural network classifier Cost functions Backpropagation Overfitting and generalization Postprocessing Majority filtering Probabilistic label relaxation Evaluation and comparison of classification accuracy Accuracy assessment Model comparison Hyperspectral analysis Spectral mixture modeling Unconstrained linear unmixing Intrinsic end-members and pixel purity Orthogonal subspace projection Exercises Unsupervised Classification Simple cost functions Algorithms that minimize the simple cost functions.- v K-means clustering Extended K-means clustering Agglomerative hierarchical clustering Fuzzy K-means clustering Fuzzy maximum likelihood estimation clustering Relation to the expectation maximization algorithm Simulated annealing Partition density Implementation notes Including spatial information Multiresolution clustering Spatial clustering A benchmark The Kohonen self-organizing map Exercises 230

5 x Image Analysis, Classification, and Change Detection in Remote Sensing 8 Change Detection Algebraic methods Principal components Postclassification comparison... : Multivariate alteration detection Canonical correlation analysis Orthogonality properties Scale invariance Iteratively reweighted MAD Correlation with the original observations Postprocessing Decision thresholds and unsupervised classification of changes Radiometric normalization Exercises 257 A Mathematical Tools 261 A.I Cholesky decomposition 261 A.2 Least squares procedures 263 A.2.1 Linear regression on more than one variable 263 A.2.2 Recursive linear regression 265 A.2.3 Orthogonal linear regression 267 B Efficient Neural Network Training Algorithms 271 B.I The Hessian matrix 271 ' B.I.I The ^-operator 272 B.1.2 Calculating the Hessian 276 B.2 Scaled conjugate gradient training 276 B.2.1 Conjugate directions 276 B.2.2 Minimizing a quadratic function 279 B.2.3 The algorithm 282 B.3 Kalman filter training 286 B.3.1 Linearization 287 B.3.2 The algorithm 288 B.4 A neural network classifier with hybrid training 295 C ENVI Extensions in IDL 297 C.I Installation 297 C.2 Panchromatic sharpening 298 C.2.1 Discrete wavelet transform fusion 298 C.2.2 A trous wavelet transform fusion 300 C.2.3 Quality index 302 C.3 Topographic modeling and registration 305 C.3.1 Calculating heights of man-made structures in high resolution imagery 305 C.3.2 Illumination correction 307

6 Contents xi C.3.3 Image registration 308 C.4 Supervised classification 310 C.4.1 Maximum likelihood classifier 310 C.4.2 Gaussian Kernel classifier 310 C.4.3 Neural network classifier 311 C.4.4 Probabilistic label relaxation 316 C.4.5 Classifier evaluation and comparison 318 C.5 Unsupervised classification 319 C.5.1 Agglomerative hierarchical clustering 319 C.5.2 Fuzzy K-means clustering 321 C.5.3 Fuzzy maximum likelihood estimation clustering C.5.4 Kohonen self-organizing map 325 C.6 Change detection 326 C.6.1 Multivariate alteration detection 326 C.6.2 Viewing changes 329 C.6.3 Radiometric normalization 330 Mathematical Notation 333 References 335 Index 343

IMAGE ANALYSIS, CLASSIFICATION, and CHANGE DETECTION in REMOTE SENSING

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