Image analysis, classification and change detection in remote sensing : with algorithms for Python

532 Pages·2019·33.806 MB·English

by  Canty, Morton John

Image Analysis,
Classification, and Change
Detection in Remote
Sensing
With Algorithms for Python
Fourth edition

Image Analysis,
Classification, and Change
Detection in Remote
Sensing
With Algorithms for Python
Fourth edition
Morton John Canty
CRC Press
Taylor & Francis Group
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Library of Congress Cataloging-in-Publication Data
Names: Canty, Morton John, author.
Title: Image analysis, classification and change detection in remote sensing
: with algorithms for Python / by Morton J. Canty.
Description: Fourth edition. | Boca Raton, FL : CRC Press/Taylor & Francis
Group, 2019. | Includes bibliographical references and index.
Identifiers: LCCN 2018051975| ISBN 9781138613225 (hardback : acid-free paper)
| ISBN 9780429464348 (ebook)
Subjects: LCSH: Remote sensing--Mathematics. | Image analysis--Mathematics. |
Image analysis--Data processing. | Python (Computer program language)
Classification: LCC G70.4 .C36 2019 | DDC 621.36/70285--dc23
LC record available at https://lccn.loc.gov/2018051975
Visit the Taylor & Francis Web site at
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Contents
Preface to the First Edition xiii
Preface to the Second Edition xv
Preface to the Third Edition xvii
Preface to the Fourth Edition xx
Author Biography xxi
1 Images, Arrays, and Matrices 1
1.1 Multispectral satellite images . . . . . . . . . . . . . . . . . . 4
1.2 Synthetic aperture radar images . . . . . . . . . . . . . . . . . 7
1.3 Algebra of vectors and matrices . . . . . . . . . . . . . . . . . 10
1.3.1 Elementary properties . . . . . . . . . . . . . . . . . . 11
1.3.2 Square matrices . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Singular matrices . . . . . . . . . . . . . . . . . . . . . 15
1.3.4 Symmetric, positive definite matrices . . . . . . . . . . 15
1.3.5 Linear dependence and vector spaces . . . . . . . . . . 16
1.4 Eigenvalues and eigenvectors . . . . . . . . . . . . . . . . . . 17
1.5 Singular value decomposition . . . . . . . . . . . . . . . . . . 19
1.6 Finding minima and maxima . . . . . . . . . . . . . . . . . . 21
1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Image Statistics 31
2.1 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.1 Discrete random variables . . . . . . . . . . . . . . . . 32
2.1.2 Continuous random variables . . . . . . . . . . . . . . 33
2.1.3 Random vectors . . . . . . . . . . . . . . . . . . . . . 36
2.1.4 The normal distribution . . . . . . . . . . . . . . . . . 39
2.1.5 The gamma distribution and its derivatives . . . . . . 41
2.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . 44
2.2.1 Random samples . . . . . . . . . . . . . . . . . . . . . 44
2.2.2 Sample distributions and interval estimators . . . . . . 47
2.3 Multivariate distributions . . . . . . . . . . . . . . . . . . . . 50
2.3.1 Vector sample functions and the data matrix . . . . . 51
2.3.2 Provisionalmeans . . . . . . . . . . . . . . . . . . . . 53
v
vi Image Analysis, Classification, and Change Detection in Remote Sensing
2.3.3 Real and complex multivariate sample distributions. . 55
2.4 Bayes’ Theorem, likelihood and classification . . . . . . . . . 57
2.5 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Ordinary linear regression . . . . . . . . . . . . . . . . . . . . 65
2.6.1 One independent variable . . . . . . . . . . . . . . . . 65
2.6.2 Coefficient of determination (R2) . . . . . . . . . . . . 67
2.6.3 More than one independent variable . . . . . . . . . . 68
2.6.4 Regularization,duality and the Gram matrix . . . . . 72
2.7 Entropy and information . . . . . . . . . . . . . . . . . . . . . 73
2.7.1 Kullback–Leibler divergence . . . . . . . . . . . . . . . 75
2.7.2 Mutual information. . . . . . . . . . . . . . . . . . . . 76
2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3 Transformations 83
3.1 The discrete Fourier transform . . . . . . . . . . . . . . . . . 83
3.2 The discrete wavelet transform . . . . . . . . . . . . . . . . . 88
3.2.1 Haar wavelets . . . . . . . . . . . . . . . . . . . . . . . 89
3.2.2 Image compression . . . . . . . . . . . . . . . . . . . . 93
3.2.3 Multiresolution analysis . . . . . . . . . . . . . . . . . 96
3.3 Principal components . . . . . . . . . . . . . . . . . . . . . . 103
3.3.1 Principal components on the GEE . . . . . . . . . . . 105
3.3.2 Image compression and reconstruction . . . . . . . . . 107
3.3.3 Primal solution . . . . . . . . . . . . . . . . . . . . . . 111
3.3.4 Dual solution . . . . . . . . . . . . . . . . . . . . . . . 111
3.4 Minimum noise fraction . . . . . . . . . . . . . . . . . . . . . 112
3.4.1 Additive noise. . . . . . . . . . . . . . . . . . . . . . . 113
3.4.2 Minimum noise fraction via PCA . . . . . . . . . . . . 116
3.5 Spatial correlation . . . . . . . . . . . . . . . . . . . . . . . . 117
3.5.1 Maximum autocorrelationfactor . . . . . . . . . . . . 117
3.5.2 Noise estimation . . . . . . . . . . . . . . . . . . . . . 119
3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4 Filters, Kernels, and Fields 127
4.1 The Convolution Theorem . . . . . . . . . . . . . . . . . . . . 127
4.2 Linear filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.3 Wavelets and filter banks . . . . . . . . . . . . . . . . . . . . 135
4.3.1 One-dimensional arrays . . . . . . . . . . . . . . . . . 136
4.3.2 Two-dimensionalarrays . . . . . . . . . . . . . . . . . 141
4.4 Kernel methods . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.4.1 Valid kernels . . . . . . . . . . . . . . . . . . . . . . . 144
4.4.2 Kernel PCA . . . . . . . . . . . . . . . . . . . . . . . . 149
4.5 Gibbs–Markov random fields . . . . . . . . . . . . . . . . . . 152
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Contents vii
5 Image Enhancement and Correction 159
5.1 Lookup tables and histogram functions . . . . . . . . . . . . . 159
5.2 High-pass spatial filtering and feature extraction . . . . . . . 161
5.2.1 Sobel filter . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2.2 Laplacian-of-Gaussianfilter . . . . . . . . . . . . . . . 164
5.2.3 OpenCV and GEE algorithms . . . . . . . . . . . . . . 166
5.2.4 Invariant moments . . . . . . . . . . . . . . . . . . . . 171
5.3 Panchromatic sharpening . . . . . . . . . . . . . . . . . . . . 177
5.3.1 HSV fusion . . . . . . . . . . . . . . . . . . . . . . . . 178
5.3.2 Brovey fusion . . . . . . . . . . . . . . . . . . . . . . . 179
5.3.3 PCA fusion . . . . . . . . . . . . . . . . . . . . . . . . 179
5.3.4 DWT fusion . . . . . . . . . . . . . . . . . . . . . . . . 180
5.3.5 A` trous fusion . . . . . . . . . . . . . . . . . . . . . . . 181
5.3.6 A quality index . . . . . . . . . . . . . . . . . . . . . . 184
5.4 Radiometric correction of polarimetric SAR imagery . . . . . 185
5.4.1 Speckle statistics . . . . . . . . . . . . . . . . . . . . . 185
5.4.2 Multi-look data . . . . . . . . . . . . . . . . . . . . . . 188
5.4.3 Speckle filtering . . . . . . . . . . . . . . . . . . . . . . 193
5.5 Topographic correction . . . . . . . . . . . . . . . . . . . . . . 200
5.5.1 Rotation, scaling and translation . . . . . . . . . . . . 201
5.5.2 Imaging transformations . . . . . . . . . . . . . . . . . 202
5.5.3 Camera models and RFM approximations . . . . . . . 203
5.5.4 Stereo imaging and digital elevation models . . . . . . 205
5.5.5 Slope and aspect . . . . . . . . . . . . . . . . . . . . . 210
5.5.6 Illumination correction . . . . . . . . . . . . . . . . . . 211
5.6 Image–image registration . . . . . . . . . . . . . . . . . . . . 216
5.6.1 Frequency domain registration . . . . . . . . . . . . . 217
5.6.2 Feature matching . . . . . . . . . . . . . . . . . . . . . 219
5.6.3 Re-sampling with ground control points . . . . . . . . 223
5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6 Supervised Classification Part 1 231
6.1 Maximizing the a posteriori probability . . . . . . . . . . . . 233
6.2 Training data and separability . . . . . . . . . . . . . . . . . . 234
6.3 Maximum likelihood classification . . . . . . . . . . . . . . . . 239
6.3.1 Naive Bayes on the GEE. . . . . . . . . . . . . . . . . 240
6.3.2 Python scripts for supervised classification. . . . . . . 241
6.4 Gaussian kernel classification . . . . . . . . . . . . . . . . . . 245
6.5 Neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . 248
6.5.1 The neural network classifier . . . . . . . . . . . . . . 253
6.5.2 Cost functions . . . . . . . . . . . . . . . . . . . . . . 256
6.5.3 Backpropagation . . . . . . . . . . . . . . . . . . . . . 258
6.5.4 A deep learning network . . . . . . . . . . . . . . . . . 264
6.5.5 Overfitting and generalization . . . . . . . . . . . . . . 268
6.6 Support vector machines . . . . . . . . . . . . . . . . . . . . . 270
viii Image Analysis, Classification, and Change Detection in Remote Sensing
6.6.1 Linearly separable classes . . . . . . . . . . . . . . . . 270
6.6.2 Overlapping classes . . . . . . . . . . . . . . . . . . . . 276
6.6.3 Solution with sequential minimal optimization. . . . . 278
6.6.4 Multiclass SVMs . . . . . . . . . . . . . . . . . . . . . 279
6.6.5 Kernel substitution . . . . . . . . . . . . . . . . . . . . 280
6.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
7 Supervised Classification Part 2 289
7.1 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 289
7.1.1 Majority filtering . . . . . . . . . . . . . . . . . . . . . 290
7.1.2 Probabilistic label relaxation . . . . . . . . . . . . . . 290
7.2 Evaluation and comparison of classification accuracy . . . . . 293
7.2.1 Accuracy assessment . . . . . . . . . . . . . . . . . . . 293
7.2.2 Accuracy assessment on the GEE . . . . . . . . . . . . 298
7.2.3 Cross-validationon parallel architectures. . . . . . . . 299
7.2.4 Model comparison . . . . . . . . . . . . . . . . . . . . 302
7.3 Adaptive boosting . . . . . . . . . . . . . . . . . . . . . . . . 306
7.4 Classification of polarimetric SAR imagery . . . . . . . . . . . 312
7.5 Hyperspectral image analysis . . . . . . . . . . . . . . . . . . 314
7.5.1 Spectral mixture modeling . . . . . . . . . . . . . . . . 314
7.5.2 Unconstrained linear unmixing . . . . . . . . . . . . . 317
7.5.3 Intrinsic end-members and pixel purity . . . . . . . . . 318
7.5.4 Anomaly detection: The RX algorithm . . . . . . . . . 319
7.5.5 Anomaly detection: The kernel RX algorithm . . . . . 322
7.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
8 Unsupervised Classification 329
8.1 Simple cost functions . . . . . . . . . . . . . . . . . . . . . . . 330
8.2 Algorithms that minimize the simple cost functions . . . . . . 332
8.2.1 K-means clustering . . . . . . . . . . . . . . . . . . . . 333
8.2.2 Kernel K-means clustering . . . . . . . . . . . . . . . . 338
8.2.3 Extended K-means clustering . . . . . . . . . . . . . . 341
8.2.4 Agglomerative hierarchicalclustering . . . . . . . . . . 344
8.2.5 Fuzzy K-means clustering . . . . . . . . . . . . . . . . 347
8.3 Gaussian mixture clustering . . . . . . . . . . . . . . . . . . . 349
8.3.1 Expectation maximization . . . . . . . . . . . . . . . . 350
8.3.2 Simulated annealing . . . . . . . . . . . . . . . . . . . 353
8.3.3 Partition density . . . . . . . . . . . . . . . . . . . . . 353
8.3.4 Implementation notes . . . . . . . . . . . . . . . . . . 354
8.4 Including spatial information . . . . . . . . . . . . . . . . . . 354
8.4.1 Multiresolution clustering . . . . . . . . . . . . . . . . 354
8.4.2 Spatial clustering . . . . . . . . . . . . . . . . . . . . . 357
8.5 A benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
8.6 The Kohonen self-organizing map . . . . . . . . . . . . . . . . 362
8.7 Image segmentation and the mean shift . . . . . . . . . . . . 366
Contents ix
8.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
9 Change Detection 375
9.1 Naive methods . . . . . . . . . . . . . . . . . . . . . . . . . . 376
9.2 Principal components analysis (PCA) . . . . . . . . . . . . . 378
9.2.1 Iterated PCA . . . . . . . . . . . . . . . . . . . . . . . 380
9.2.2 Kernel PCA . . . . . . . . . . . . . . . . . . . . . . . . 382
9.3 Multivariate alteration detection (MAD) . . . . . . . . . . . . 384
9.3.1 Canonical correlation analysis (CCA). . . . . . . . . . 385
9.3.2 Orthogonality properties . . . . . . . . . . . . . . . . . 388
9.3.3 Iteratively re-weighted MAD . . . . . . . . . . . . . . 389
9.3.4 Scale invariance . . . . . . . . . . . . . . . . . . . . . . 391
9.3.5 Correlationwith the original observations . . . . . . . 392
9.3.6 Regularization . . . . . . . . . . . . . . . . . . . . . . 394
9.3.7 Postprocessing . . . . . . . . . . . . . . . . . . . . . . 396
9.4 Unsupervised change classification . . . . . . . . . . . . . . . 397
9.5 iMAD on the Google Earth Engine . . . . . . . . . . . . . . . 399
9.6 Change detection with polarimetric SAR imagery . . . . . . . 401
9.6.1 Scalar imagery: the gamma distribution . . . . . . . . 402
9.6.2 Polarimetric imagery: the complex Wishart distribu-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
9.6.3 Python software . . . . . . . . . . . . . . . . . . . . . 409
9.6.4 SAR change detection on the Google Earth Engine . . 413
9.7 Radiometric normalization of visual/infrared images . . . . . 415
9.7.1 Scatterplot matching . . . . . . . . . . . . . . . . . . . 416
9.7.2 Automatic radiometric normalization . . . . . . . . . . 419
9.8 RESTful change detection on the GEE . . . . . . . . . . . . . 422
9.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
A Mathematical Tools 427
A.1 Cholesky decomposition . . . . . . . . . . . . . . . . . . . . . 427
A.2 Vector and inner product spaces . . . . . . . . . . . . . . . . 429
A.3 Complex numbers, vectors and matrices . . . . . . . . . . . . 430
A.4 Least squares procedures . . . . . . . . . . . . . . . . . . . . . 432
A.4.1 Recursive linear regression . . . . . . . . . . . . . . . . 432
A.4.2 Orthogonallinear regression . . . . . . . . . . . . . . . 434
A.5 Proof of Theorem 7.1 . . . . . . . . . . . . . . . . . . . . . . . 437
B Efficient Neural Network Training Algorithms 441
B.1 The Hessian matrix . . . . . . . . . . . . . . . . . . . . . . . . 441
B.1.1 The R-operator . . . . . . . . . . . . . . . . . . . . . . 442
B.1.2 Calculating the Hessian . . . . . . . . . . . . . . . . . 445
B.2 Scaled conjugate gradient training . . . . . . . . . . . . . . . 447
B.2.1 Conjugate directions . . . . . . . . . . . . . . . . . . . 447
B.2.2 Minimizing a quadratic function . . . . . . . . . . . . 449