Richards J.A., Jia X. Remote Sensing Digital Image Analysis: An Introduction
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Preface to the First Edition XIII
adopted and is clear from the context of that discussion. In other cases the convention
for Landsat 4 has been used as much as possible.
Finally, it is a pleasure to acknowledge the contributions made by others to the
production of this book. The manuscript was typed by Mrs Moo Song and Mrs
Alisa Moen, both of whom undertook the task tirelessly and with great patience
and forbearance. Assistance with computing was given by Leanne Bischof, at all
times cheerfully and accurately. The author’s colleagues and students also played
their part, both through direct discussion and by that process of gradual learning that
occurs over many years of association. Particular thanks are expressed to two people.
The author counts himself fortunate to be a friend and colleague of Professor Philip
Swain of Purdue University, who in his own way, has had quite an impact on the
author’s thinking about digital data analysis, particularly in remote sensing. Also,
the author has had the good fortune to work with Tong Lee, a graduate student with
extraordinary insight and ability, who also has contributed to the material through
his many discussions with the author on the theoretical foundations of digital image
processing.
The support and encouragement the author has received from his family during
the preparation of this work has been immeasurable. It is fitting therefore to conclude
in gratitude to Glenda, Matthew and Jennifer, for their understanding and enthusiasm.
Kensington, Australia, May 1986 John A. Richards
Contents
1 Sources and Characteristics of Remote Sensing Image Data ........ 1
1.1 Introduction to Data Sources ................................. 1
1.1.1 Characteristics of Digital Image Data .................. 1
1.1.2 Spectral Ranges Commonly Used in Remote Sensing .... 4
1.1.3 Concluding Remarks ................................ 8
1.2 Remote Sensing Platforms .................................. 9
1.3 Image Data Sources in the Microwave Region .................. 12
1.3.1 Side Looking Airborne Radar
and Synthetic Aperture Radar ........................ 12
1.4 Spatial Data Sources in General .............................. 15
1.4.1 Types of Spatial Data ............................... 15
1.4.2 Data Formats ...................................... 17
1.4.3 Geographic Information Systems (GIS) ................ 18
1.4.4 The Challenge to Image Processing and Analysis ........ 20
1.5 A Comparison of Scales in Digital Image Data .................. 21
2 Error Correction and Registration of Image Data ................ 27
2.1 Sources of Radiometric Distortion ............................ 27
2.1.1 The Effect of the Atmosphere on Radiation ............. 28
2.1.2 Atmospheric Effects on Remote Sensing Imagery ........ 31
2.1.3 Instrumentation Errors .............................. 31
2.2 Correction of Radiometric Distortion .......................... 32
2.2.1 Detailed Correction of Atmospheric Effects ............. 33
2.2.2 Bulk Correction of Atmospheric Effects ................ 34
2.2.3 Correction of Instrumentation Errors .................. 36
2.3 Sources of Geometric Distortion ............................. 37
2.3.1 Earth Rotation Effects ............................... 38
2.3.2 Panoramic Distortion ............................... 39
2.3.3 Earth Curvature .................................... 42
2.3.4 Scan Time Skew ................................... 43
XVI Contents
2.3.5 Variations in Platform Altitude, Velocity and Attitude ..... 43
2.3.6 Aspect Ratio Distortion .............................. 44
2.3.7 Sensor Scan Nonlinearities ........................... 45
2.4 Correction of Geometric Distortion ........................... 46
2.4.1 Use of Mapping Polynomials for Image Correction ...... 46
2.4.1.1 Mapping Polynomials
and Ground Control Points ................... 47
2.4.1.2 Resampling ............................... 48
2.4.1.3 Interpolation ............................... 48
2.4.1.4 Choice of Control Points .................... 51
2.4.1.5 Example of Registration to a Map Grid ........ 51
2.4.2 Mathematical Modelling ............................. 54
2.4.2.1 Aspect Ratio Correction ..................... 54
2.4.2.2 Earth Rotation Skew Correction .............. 55
2.4.2.3 Image Orientation to North-South ............. 55
2.4.2.4 Correction of Panoramic Effects .............. 55
2.4.2.5 Combining the Corrections .................. 56
2.5 Image Registration ......................................... 56
2.5.1 Georeferencing and Geocoding ....................... 56
2.5.2 Image to Image Registration ......................... 57
2.5.3 Control Point Localisation by Correlation .............. 57
2.5.4 Example of Image to Image Registration ............... 58
2.6 Miscellaneous Image Geometry Operations .................... 59
2.6.1 Image Rotation .................................... 61
2.6.2 Scale Changing and Zooming ........................ 61
3 The Interpretation of Digital Image Data ....................... 67
3.1 Approaches to Interpretation ................................. 67
3.2 Forms of Imagery for Photointerpretation ...................... 69
3.3 Computer Processing for Photointerpretation ................... 72
3.4 An lntroduction to Quantitative Analysis – Classification ......... 72
3.5 Multispectral Space and Spectral Classes ...................... 75
3.6 Quantitative Analysis by Pattern Recognition ................... 77
3.6.1 Pixel Vectors and Labelling .......................... 77
3.6.2 Unsupervised Classification .......................... 78
3.6.3 Supervised Classification ............................ 78
4 Radiometric Enhancement Techniques ......................... 83
4.1 Introduction ............................................... 83
4.1.1 Point Operations and Look Up Tables .................. 83
4.1.2 Scalar and Vector Images ............................. 83
4.2 The Image Histogram ....................................... 84
4.3 Contrast Modification in Image Data .......................... 84
4.3.1 Histogram Modification Rule ......................... 84
4.3.2 Linear Contrast Modification ......................... 86
Contents XVII
4.3.3 Saturating Linear Contrast Enhancement ................ 88
4.3.4 Automatic Contrast Enhancement...................... 88
4.3.5 Logarithmic and Exponential Contrast Enhancement ...... 89
4.3.6 Piecewise Linear Contrast Modification ................ 89
4.4 Histogram Equalization ..................................... 90
4.4.1 Use of the Cumulative Histogram ...................... 90
4.4.2 Anomalies in Histogram Equalization .................. 95
4.5 Histogram Matching ........................................ 97
4.5.1 Principle of Histogram Matching ...................... 97
4.5.2 Image to Image Contrast Matching .................... 98
4.5.3 Matching to a Mathematical Reference ................. 99
4.6 Density Slicing ............................................101
4.6.1 Black and White Density Slicing ......................101
4.6.2 Colour Density Slicing and Pseudocolouring ............104
5 Geometric Enhancement Using Image Domain Techniques ........ 109
5.1 Neighbourhood Operations ..................................109
5.2 Template Operators .........................................109
5.3 Geometric Enhancement as a Convolution Operation .............110
5.4 Image Domain Versus Fourier Transformation Approaches ........113
5.5 Image Smoothing (Low Pass Filtering) .........................115
5.5.1 Mean Value Smoothing ..............................115
5.5.2 Median Filtering ....................................116
5.6 Edge Detection and Enhancement .............................118
5.6.1 Linear Edge Detecting Templates ......................120
5.6.2 Spatial Derivative Techniques .........................121
5.6.2.1 The Roberts Operator ........................121
5.6.2.2 The Sobel Operator .........................122
5.6.2.3 The Prewitt Operator ........................122
5.6.3 Thinning, Linking and Border Responses ...............123
5.6.4 Edge Enhancement by Subtractive Smoothing
(Sharpening) .......................................123
5.7 Line Detection .............................................125
5.7.1 Linear Line Detecting Templates ......................125
5.7.2 Non-linear and Semi-linear Line Detecting Templates .....125
5.8 General Convolution Filtering ................................127
5.9 Detecting Geometric Properties ..............................128
5.9.1 Texture ...........................................128
5.9.2 Spatial Correlation – The Semivariogram ...............131
5.9.3 Shape Detection ....................................132
6 Multispectral Transformations of Image Data ................... 137
6.1 The Principal Components Transformation .....................137
6.1.1 The Mean Vector and Covariance Matrix ................138
6.1.2 A Zero Correlation, Rotational Transform ...............141
XVIII Contents
6.1.3 Examples – Some Practical Considerations ..............145
6.1.4 The Effect of an Origin Shift ..........................150
6.1.5 Application of Principal Components
in Image Enhancement and Display ....................150
6.1.6 The Taylor Method of Contrast Enhancement ............151
6.1.7 Other Applications of Principal Components Analysis ....154
6.2 Noise Adjusted Principal Components Transformation ...........154
6.3 The Kauth-Thomas Tasseled Cap Transformation ................156
6.4 Image Arithmetic, Band Ratios and Vegetation Indices ...........160
7 Fourier Transformation of Image Data ......................... 165
7.1 Introduction ...............................................165
7.2 Special Functions ..........................................165
7.2.1 The Complex Exponential Function ....................166
7.2.2 The Dirac Delta Function ............................166
7.2.2.1 Properties of the Delta Function ...............167
7.2.3 The Heaviside Step Function ..........................168
7.3 Fourier Series ..............................................168
7.4 The Fourier Transform ......................................169
7.5 Convolution ...............................................171
7.5.1 The Convolution Integral .............................171
7.5.2 Convolution with an Impulse .........................171
7.5.3 The Convolution Theorem ............................173
7.6 Sampling Theory ...........................................173
7.7 The Discrete Fourier Transform ...............................176
7.7.1 The Discrete Spectrum ...............................176
7.7.2 Discrete Fourier Transform Formulae ..................177
7.7.3 Properties of the Discrete Fourier Transform ............178
7.7.4 Computation of the Discrete Fourier Transform ..........179
7.7.5 Development of the Fast Fourier Transform Algorithm ....179
7.7.6 Computational Cost of the Fast Fourier Transform ........183
7.7.7 Bit Shuffling and Storage Considerations ...............184
7.8 The Discrete Fourier Transform of an Image ....................184
7.8.1 Definition .........................................184
7.8.2 Evaluation of the Two Dimensional, Discrete Fourier
Transform .........................................185
7.8.3 The Concept of Spatial Frequency .....................185
7.8.4 Image Filtering for Geometric Enhancement ............187
7.8.5 Convolution in Two Dimensions .......................188
7.9 Concluding Remarks ........................................189
8 Supervised Classification Techniques .......................... 193
8.1 Steps in Supervised Classification ............................193
8.2 Maximum Likelihood Classification ..........................194
8.2.1 Bayes’ Classification ................................194
Contents XIX
8.2.2 The Maximum Likelihood Decision Rule ...............195
8.2.3 Multivariate Normal Class Models ....................196
8.2.4 Decision Surfaces ..................................196
8.2.5 Thresholds ........................................197
8.2.6 Number of Training Pixels Required for Each Class ......199
8.2.7 A Simple Illustration ................................199
8.3 Minimum Distance Classification ............................201
8.3.1 The Case of Limited Training Data ....................201
8.3.2 The Discriminant Function ...........................202
8.3.3 Degeneration of Maximum Likelihood
to Minimum Distance Classification ...................203
8.3.4 Decision Surfaces ..................................204
8.3.5 Thresholds ........................................204
8.4 Parallelepiped Classification .................................204
8.5 Classification Time Comparison of the Classifiers ...............206
8.6 Other Supervised Approaches ................................206
8.6.1 The Mahalanobis Classifier ..........................206
8.6.2 Table Look Up Classification .........................207
8.6.3 The kNN (Nearest Neighbour) Classifier ...............207
8.7 Gaussian Mixture Models ...................................208
8.8 Context Classification ......................................209
8.8.1 The Concept of Spatial Context .......................209
8.8.2 Context Classification by Image Pre-processing .........210
8.8.3 Post Classification Filtering ..........................211
8.8.4 Probabilistic Label Relaxation ........................211
8.8.4.1 The Basic Algorithm ........................211
8.8.4.2 The Neighbourhood Function ................212
8.8.4.3 Determining the Compatibility Coefficients .....213
8.8.4.4 The Final Step – Stopping the Process .........214
8.8.4.5 Examples .................................215
8.8.5 Handling Spatial Context by Markov Random Fields .....216
8.9 Non-parametric Classification: Geometric Approaches ...........219
8.9.1 Linear Discrimination ...............................220
8.9.1.1 Concept of a Weight Vector ..................220
8.9.1.2 Testing Class Membership ...................221
8.9.1.3 Training ..................................221
8.9.1.4 Setting the Correction Increment ..............223
8.9.1.5 Classification – The Threshold Logic Unit ......224
8.9.1.6 Multicategory Classification .................225
8.9.2 Support Vector Classifiers ............................226
8.9.2.1 Linearly Separable Data .....................226
8.9.2.2 Linear Inseparability –
The Use of Kernel Functions .................230
8.9.2.3 Multicategory Classification .................231
XX Contents
8.9.3 Networks of Classifiers – Solutions of Nonlinear Problems 231
8.9.4 The Neural Network Approach .......................232
8.9.4.1 The Processing Element .....................232
8.9.4.2 Training the Neural Network –
Backpropagation ...........................234
8.9.4.3 Choosing the Network Parameters ............238
8.9.4.4 Examples .................................238
9 Clustering and Unsupervised Classification ..................... 249
9.1 Delineation of Spectral Classes ..............................249
9.2 Similarity Metrics and Clustering Criteria ......................249
9.3 The Iterative Optimization (Migrating Means)
Clustering Algorithm .......................................251
9.3.1 The Basic Algorithm ................................252
9.3.2 Mergings and Deletions .............................252
9.3.3 Splitting Elongated Clusters ..........................254
9.3.4 Choice of Initial Cluster Centres ......................254
9.3.5 Clustering Cost ....................................254
9.4 Unsupervised Classification and Cluster Maps ..................255
9.5 A Clustering Example ......................................255
9.6 A Single Pass Clustering Technique ...........................257
9.6.1 Single Pass Algorithm ...............................257
9.6.2 Advantages and Limitations ..........................259
9.6.3 Strip Generation Parameter ..........................259
9.6.4 Variations on the Single Pass Algorithm ................259
9.6.5 An Example .......................................260
9.7 Agglomerative Hierarchical Clustering ........................260
9.8 Clustering by Histogram Peak Selection .......................263
10 Feature Reduction ........................................... 267
10.1 Feature Reduction and Separability ...........................267
10.2 Separability Measures
for Multivariate Normal Spectral Class Models .................268
10.2.1 Distribution Overlaps ...............................268
10.2.2 Divergence ........................................269
10.2.2.1 A General Expression .......................269
10.2.2.2 Divergence of a Pair of Normal Distributions . . . 270
10.2.2.3 Use of Divergence for Feature Selection .......271
10.2.2.4 A Problem with Divergence ..................272
10.2.3 The Jeffries-Matusita (JM) Distance ...................273
10.2.3.1 Definition .................................273
10.2.3.2 Comparison of Divergence and JM Distance ....274
10.2.4 Transformed Divergence .............................274
10.2.4.1 Definition .................................274
Contents XXI
10.2.4.2 Relation Between Transformed Divergence
and Probability of Correct Classification .......275
10.2.4.3 Use of Transformed Divergence in Clustering . . . 276
10.3 Separability Measures for Minimum Distance Classification ......276
10.4 Feature Reduction by Data Transformation .....................276
10.4.1 Feature Reduction
Using the Principal Components Transformation ........277
10.4.2 Canonical Analysis as a Feature Selection Procedure .....279
10.4.2.1 Within Class
and Among Class Covariance Matrices .........280
10.4.2.2 A Separability Measure ......................281
10.4.2.3 The Generalised Eigenvalue Equation ..........281
10.4.2.4 An Example ...............................283
10.4.3 Discriminant Analysis Feature Extraction (DAFE) .......285
10.4.4 Non-parametric Discriminant Analysis
and Decision Boundary Feature Extraction (DBFE) ......286
10.4.5 Non-parametric Weighted Feature Extraction (NWFE) . . . 290
10.4.6 Arithmetic Transformations ..........................292
11 Image Classification Methodologies ............................ 295
11.1 Introduction ...............................................295
11.2 Supervised Classification ...................................295
11.2.1 Outline ...........................................295
11.2.2 Determination of Training Data .......................296
11.2.3 Feature Selection ...................................297
11.2.4 Detecting Multimodal Distributions ...................297
11.2.5 Presentation of Results ..............................298
11.2.6 Effect of Resampling on Classification .................298
11.3 Unsupervised Classification .................................299
11.3.1 Outline, and Comparison with Supervised Methods ......299
11.3.2 Feature Selection ...................................301
11.4 A Hybrid Supervised/Unsupervised Methodology ...............301
11.4.1 The Essential Steps .................................301
11.4.2 Choice of the Clustering Regions .....................302
11.4.3 Rationalisation of the Number of Spectral Classes .......302
11.5 Assessment of Classification Accuracy ........................303
11.5.1 Using a Testing Set of Pixels .........................303
11.5.2 The Leave One Out Method of Accuracy Assessment –
Cross Validation ....................................307
11.6 Case Study 1: Irrigated Area Determination ....................307
11.6.1 Background .......................................308
11.6.2 The Study Region ..................................308
11.6.3 Clustering .........................................309
11.6.4 Signature Generation ................................312
11.6.5 Classification and Results ............................312
XXII Contents
11.6.6 Concluding Remarks ................................312
11.7 Case Study 2: Multitemporal Monitoring of Bush Fires ..........314
11.7.1 Background .......................................314
11.7.2 Simple Illustration of the Technique ...................314
11.7.3 The Study Area ....................................316
11.7.4 Registration .......................................316
11.7.5 Principal Components Transformation .................317
11.7.6 Classification of Principal Components Imagery .........319
11.8 Hierarchical Classification ..................................321
11.8.1 The Decision Tree Classifier .........................321
11.8.2 Decision Tree Design ...............................323
11.8.3 Progressive Two-Class Decision Classifier ..............324
11.8.4 Error Accumulation in a Decision Tree .................327
11.9 A Note on Hyperspectral Data Classification ...................328
12 Multisource, Multisensor Methods ............................. 333
12.1 The Stacked Vector Approach ................................334
12.2 Statistical Multisource Methods ..............................334
12.2.1 Joint Statistical Decision Rules .......................334
12.2.2 Committee Classifiers ...............................335
12.2.3 Opinion Pools and Consensus Theoretic Methods ........336
12.2.4 Use of Prior Probability .............................337
12.2.5 Supervised Label Relaxation .........................337
12.3 The Theory of Evidence ....................................338
12.3.1 The Concept of Evidential Mass ......................338
12.3.2 Combining Evidence – the Orthogonal Sum ............340
12.3.3 Decision Rule ......................................341
12.4 Knowledge-Based Image Analysis ............................342
12.4.1 Knowledge Processing: Emulating Photointerpretation . . . 342
12.4.2 Fundamentals of a Knowledge-Based
Image Analysis System ..............................344
12.4.2.1 Structure ..................................344
12.4.2.2 Representation of Knowledge: Rules ..........345
12.4.2.3 The Inference Mechanism ...................346
12.4.3 Handling Multisource and Multisensor Data ............347
12.4.4 An Example .......................................349
12.4.4.1 Rules as Justifiers for a Labelling Proposition . . . 350
12.4.4.2 Endorsement of a Labelling Proposition ........351
12.4.4.3 Knowledge Base and Results .................352
13 Interpretation of Hyperspectral Image Data ..................... 359
13.1 Data Characteristics ........................................359
13.2 The Challenge to Interpretation ..............................361
13.2.1 Data Volume .......................................362
13.2.2 Redundancy .......................................362
Contents XXIII
13.2.3 The Need for Calibration ............................364
13.2.4 The Problem of Dimensionality:
The Hughes Phenomenon ............................364
13.3 Data Calibration Techniques .................................366
13.3.1 Detailed Radiometric Correction ......................366
13.3.2 Data Normalisation .................................367
13.3.3 Approximate Radiometric Correction ..................368
13.4 Interpretation Using Spectral Information ......................368
13.4.1 Spectral Angle Mapping .............................368
13.4.2 Using Expert Spectral Knowledge
and Library Searching ...............................369
13.4.3 Library Searching by Spectral Coding .................371
13.4.3.1 Binary Spectral Codes ......................371
13.4.3.2 Matching Algorithms .......................373
13.5 Hyperspectral Interpretation by Statistical Methods ..............373
13.5.1 Limitations of Traditional
Thematic Mapping Procedures .......................373
13.5.2 Block-based Maximum Likelihood Classification ........375
13.6 Feature Reduction .........................................377
13.6.1 Feature Selection ...................................378
13.6.2 Spectral Transformations ............................379
13.6.3 Feature Selection from Principal Components
Transformed Data ..................................381
13.7 Regularised Covariance Estimators ...........................381
13.8 Compression of Hyperspectral Data ...........................382
13.9 Spectral Unmixing: End Member Analysis .....................385
A Missions and Sensors ........................................ 389
A.1 Weather Satellite Sensors ...................................389
A.1.1 Polar Orbiting and Geosynchronous Satellites ...........389
A.1.2 The NOAA AVHRR
(Advanced Very High Resolution Radiometer) ..........390
A.1.3 The Nimbus CZCS (Coastal Zone Colour Scanner) ......390
A.1.4 GMS VISSR (Visible and Infrared Spin Scan Radiometer)
and GOES Imager ..................................391
A.2 Earth Resource Satellite Sensors
in the Visible and Infrared Regions ...........................391
A.2.1 The Landsat System ................................391
A.2.2 The Landsat Instrument Complement ..................393
A.2.3 The Return Beam Vidicon (RBV) .....................393
A.2.4 The Multispectral Scanner (MSS) .....................394
A.2.5 The Thematic Mapper (TM)
and Enhanced Thematic Mapper + (ETM+) .............396
A.2.6 The SPOT HRV, HRVIR, HRG, HRS and Vegetation
Instruments ........................................397