Remote Sensing Digital Image Analysis

__Remote Sensing Digital Image Analysis__ provides a comprehensive treatment of the methods used for the processing and interpretation of remotely sensed image data. Over the past decade there have been continuing and significant developments in the algorithms used for the analysis of remote sensing imagery, even though many of the fundamentals have substantially remained the same. As with its predecessors this new edition again presents material that has retained value but also includes newer techniques, covered from the perspective of operational remote sensing. The book is designed as a teaching text for the senior undergraduate and postgraduate student, and as a fundamental treatment for those engaged in research using digital image analysis in remote sensing. The presentation level is for the mathematical non-specialist. Since the very great number of operational users of remote sensing come from the earth sciences communities, the text is pitched at a level commensurate with their background. The chapters progress logically through means for the acquisition of remote sensing images, techniques by which they can be corrected, and methods for their interpretation. The prime focus is on applications of the methods, so that worked examples are included and a set of problems conclude each chapter. Preface Contents 1 Sources and Characteristics of Remote Sensing Image Data Abstract 1.1 Energy Sources and Wavelength Ranges 1.2 Primary Data Characteristics 1.3 Remote Sensing Platforms 1.4 What Earth Surface Properties Are Measured? 1.4.1 Sensing in the Visible and Reflected Infrared Ranges 1.4.2 Sensing in the Thermal Infrared Range 1.4.3 Sensing in the Microwave Range 1.5 Spatial Data Sources in General and Geographic Information Systems 1.6 Scale in Digital Image Data 1.7 Digital Earth 1.8 How This Book Is Arranged 1.9 Bibliography on Sources and Characteristics of Remote Sensing Image Data 1.10 Problems 2 Correcting and Registering Images Abstract 2.1 Introduction 2.2 Sources of Radiometric Distortion 2.3 Instrumentation Errors 2.3.1 Sources of Distortion 2.3.2 Correcting Instrumentation Errors 2.4 Effect of the Solar Radiation Curve and the Atmosphere on Radiometry 2.5 Compensating for the Solar Radiation Curve 2.6 Influence of the Atmosphere 2.7 Effect of the Atmosphere on Remote Sensing Imagery 2.8 Correcting Atmospheric Effects in Broad Waveband Systems 2.9 Correcting Atmospheric Effects in Narrow Waveband Systems 2.10 Empirical, Data Driven Methods for Atmospheric Correction 2.10.1 Haze Removal by Dark Subtraction 2.10.2 The Flat Field Method 2.10.3 The Empirical Line Method 2.10.4 Log Residuals 2.11 Sources of Geometric Distortion 2.12 The Effect of Earth Rotation 2.13 The Effect of Variations in Platform Altitude, Attitude and Velocity 2.14 The Effect of Sensor Field of View: Panoramic Distortion 2.15 The Effect of Earth Curvature 2.16 Geometric Distortion Caused by Instrumentation Characteristics 2.16.1 Sensor Scan Nonlinearities 2.16.2 Finite Scan Time Distortion 2.16.3 Aspect Ratio Distortion 2.17 Correction of Geometric Distortion 2.18 Use of Mapping Functions for Image Correction 2.18.1 Mapping Polynomials and the Use of Ground Control Points 2.18.2 Building a Geometrically Correct Image 2.18.3 Resampling and the Need for Interpolation 2.18.4 The Choice of Control Points 2.18.5 Example of Registration to a Map Grid 2.19 Mathematical Representation and Correction of Geometric Distortion 2.19.1 Aspect Ratio Correction 2.19.2 Earth Rotation Skew Correction 2.19.3 Image Orientation to North–South 2.19.4 Correcting Panoramic Effects 2.19.5 Combining the Corrections 2.20 Image to Image Registration 2.20.1 Refining the Localisation of Control Points 2.20.2 Example of Image to Image Registration 2.21 Other Image Geometry Operations 2.21.1 Image Rotation 2.21.2 Scale Changing and Zooming 2.22 Bibliography on Correcting and Registering Images 2.23 Problems 3 Interpreting Images Abstract 3.1 Introduction 3.2 Photointerpretation 3.2.1 Forms of Imagery for Photointerpretation 3.2.2 Computer Enhancement of Imagery for Photointerpretation 3.3 Quantitative Analysis: From Data to Labels 3.4 Comparing Quantitative Analysis and Photointerpretation 3.5 The Fundamentals of Quantitative Analysis 3.5.1 Pixel Vectors and Spectral Space 3.5.2 Linear Classifiers 3.5.3 Statistical Classifiers 3.6 Sub-classes and Spectral Classes 3.7 Unsupervised Classification 3.8 Bibliography on Interpreting Images 3.9 Problems 4 Radiometric Enhancement of Images Abstract 4.1 Introduction 4.1.1 Point Operations and Look Up Tables 4.1.2 Scalar and Vector Images 4.2 The Image Histogram 4.3 Contrast Modification 4.3.1 Histogram Modification Rule 4.3.2 Linear Contrast Modification 4.3.3 Saturating Linear Contrast Enhancement 4.3.4 Automatic Contrast Enhancement 4.3.5 Logarithmic and Exponential Contrast Enhancement 4.3.6 Piecewise Linear Contrast Modification 4.4 Histogram Equalisation 4.4.1 Use of the Cumulative Histogram 4.4.2 Anomalies in Histogram Equalisation 4.5 Histogram Matching 4.5.1 Principle 4.5.2 Image to Image Contrast Matching 4.5.3 Matching to a Mathematical Reference 4.6 Density Slicing 4.6.1 Black and White Density Slicing 4.6.2 Colour Density Slicing and Pseudocolouring 4.7 Bibliography on Radiometric Enhancement of Images 4.8 Problems 5 Geometric Processing and Enhancement: Image Domain Techniques Abstract 5.1 Introduction 5.2 Neighbourhood Operations in Image Filtering 5.3 Image Smoothing 5.3.1 Mean Value Smoothing 5.3.2 Median Filtering 5.3.3 Modal Filtering 5.4 Sharpening and Edge Detection 5.4.1 Spatial Gradient Methods 5.4.1.1 The Roberts Operator 5.4.1.2 The Sobel Operator 5.4.1.3 The Prewitt Operator 5.4.1.4 The Laplacian Operator 5.4.2 Subtractive Smoothing (Unsharp Masking) 5.5 Edge Detection 5.6 Line and Spot Detection 5.7 Thinning and Linking 5.8 Geometric Processing as a Convolution Operation 5.9 Image Domain Techniques Compared with Using the Fourier Transform 5.10 Geometric Properties of Images 5.10.1 Measuring Geometric Properties 5.10.2 Describing Texture 5.11 Morphological Analysis 5.11.1 Erosion 5.11.2 Dilation 5.11.3 Opening and Closing 5.11.4 Boundary Extraction 5.11.5 Other Morphological Operations and Applications 5.12 Object and Shape Recognition 5.13 Bibliography on Geometric Processing and Enhancement: Image Domain Techniques 5.14 Problems 6 Spectral Domain Image Transforms Abstract 6.1 Introduction 6.2 Image Arithmetic and Vegetation Indices 6.3 The Principal Components Transform 6.3.1 The Mean Vector and the Covariance Matrix 6.3.2 A Zero Correlation, Rotational Transform 6.3.3 The Effect of an Origin Shift 6.3.4 Example and Some Practical Considerations 6.3.5 Application of Principal Components in Image Enhancement and Display 6.3.6 The Taylor Method of Contrast Enhancement 6.3.7 Use of Principal Components for Image Compression 6.3.8 The Principal Components Transform in Change Detection Applications 6.3.9 Use of Principal Components for Feature Reduction 6.4 The Noise Adjusted Principal Components Transform 6.5 The Kauth-Thomas Tasseled Cap Transform 6.6 The Kernel Principal Components Transform 6.7 HSI Image Display 6.8 Pan Sharpening 6.9 Bibliography on Spectral Domain Image Transforms 6.10 Problems 7 Spatial Domain Image Transforms Abstract 7.1 Introduction 7.2 Special Functions 7.2.1 The Complex Exponential Function 7.2.2 The Impulse or Delta Function 7.2.3 The Heaviside Step Function 7.3 The Fourier Series 7.4 The Fourier Transform 7.5 The Discrete Fourier Transform 7.5.1 Properties of the Discrete Fourier Transform 7.5.2 Computing the Discrete Fourier Transform 7.6 Convolution 7.6.1 The Convolution Integral 7.6.2 Convolution with an Impulse 7.6.3 The Convolution Theorem 7.6.4 Discrete Convolution 7.7 Sampling Theory 7.8 The Discrete Fourier Transform of an Image 7.8.1 The Transform Equations 7.8.2 Evaluating the Fourier Transform of an Image 7.8.3 The Concept of Spatial Frequency 7.8.4 Displaying the DFT of an Image 7.9 Image Processing Using the Fourier Transform 7.10 Convolution in Two Dimensions 7.11 Other Fourier Transforms 7.12 Leakage and Window Functions 7.13 The Wavelet Transform 7.13.1 Background 7.13.2 Orthogonal Functions and Inner Products 7.13.3 Wavelets as Basis Functions 7.13.4 Dyadic Wavelets with Compact Support 7.13.5 Choosing the Wavelets 7.13.6 Filter Banks 7.13.6.1 Sub Band Filtering, and Downsampling 7.13.6.2 Reconstruction from the Wavelets, and Upsampling 7.13.6.3 Relationship Between the Low and High Pass Filters 7.13.7 Choice of Wavelets 7.14 The Wavelet Transform of an Image 7.15 Applications of the Wavelet Transform in Remote Sensing Image Analysis 7.16 Bibliography on Spatial Domain Image Transforms 7.17 Problems 8 Supervised Classification Techniques Abstract 8.1 Introduction 8.2 The Essential Steps in Supervised Classification 8.3 Maximum Likelihood Classification 8.3.1 Bayes’ Classification 8.3.2 The Maximum Likelihood Decision Rule 8.3.3 Multivariate Normal Class Models 8.3.4 Decision Surfaces 8.3.5 Thresholds 8.3.6 Number of Training Pixels Required 8.3.7 The Hughes Phenomenon and the Curse of Dimensionality 8.3.8 An Example 8.4 Gaussian Mixture Models 8.5 Minimum Distance Classification 8.5.1 The Case of Limited Training Data 8.5.2 The Discriminant Function 8.5.3 Decision Surfaces for the Minimum Distance Classifier 8.5.4 Thresholds 8.5.5 Degeneration of Maximum Likelihood to Minimum Distance Classification 8.5.6 Classification Time Comparison of the Maximum Likelihood and Minimum Distance Rules 8.6 Parallelepiped Classification 8.7 Mahalanobis Classification 8.8 Non-parametric Classification 8.9 Table Look Up Classification 8.10 kNN (Nearest Neighbour) Classification 8.11 The Spectral Angle Mapper 8.12 Non-parametric Classification from a Geometric Basis 8.12.1 Linear Classification and the Concept of a Weight Vector 8.12.2 Testing Class Membership 8.13 Training a Linear Classifier 8.14 The Support Vector Machine: Linearly Separable Classes 8.15 The Support Vector Machine: Overlapping Classes 8.16 The Support Vector Machine: Nonlinearly Separable Data and Kernels 8.17 Multi-category Classification with Binary Classifiers 8.18 Applying the Support Vector Classifier 8.18.1 Initial Choices 8.18.2 Grid Searching for Parameter Determination 8.18.3 Data Centering and Scaling 8.18.4 Examples 8.19 Committees of Classifiers 8.19.1 Bagging 8.19.2 Boosting and AdaBoost 8.20 Networks of Classifiers: The Artificial Neural Network 8.20.1 The Processing Element 8.20.2 Training the Neural Network—Backpropagation 8.20.3 Choosing the Network Parameters 8.20.4 Example 8.21 The Convolutional Neural Network 8.21.1 The Basic Topology of the Convolutional Neural Network 8.21.2 Detecting Spatial Structure 8.21.3 Stride 8.21.4 Pooling or Down-Sampling 8.21.5 The ReLU Activation Function 8.21.6 Handling the Outputs of a CNN 8.21.7 Multiple Filters in the Convolution Layer 8.21.8 Simplified Representation of the CNN 8.21.9 Multispectral and Hyperspectral Inputs to a CNN 8.21.10 A Spectral-Spatial Example of the Use of the CNN 8.21.11 Avoiding Overfitting 8.21.12 Variations 8.22 Recurrent Neural Networks 8.22.1 Multi-temporal Remote Sensing 8.22.2 Importance of Memory 8.22.3 The Recurrent Neural Network (RNN) Architecture 8.22.4 Training the RNN 8.23 Context Classification 8.23.1 The Concept of Spatial Context 8.23.2 Context Classification by Image Pre-processing 8.23.3 Post Classification Filtering 8.23.4 Probabilistic Relaxation Labelling 8.23.4.1 The Algorithm 8.23.4.2 The Neighbourhood Function 8.23.4.3 Determining the Compatibility Coefficients 8.23.4.4 Stopping the Process 8.23.4.5 Examples 8.23.5 Handling Spatial Context by Markov Random Fields 8.24 Bibliography on Supervised Classification Techniques 8.25 Problems 9 Clustering and Unsupervised Classification Abstract 9.1 How Clustering is Used 9.2 Similarity Metrics and Clustering Criteria 9.3 k Means Clustering 9.3.1 The k Means Algorithm 9.4 Isodata Clustering 9.4.1 Merging and Deleting Clusters 9.4.2 Splitting Elongated Clusters 9.5 Choosing the Initial Cluster Centres 9.6 Cost of k Means and Isodata Clustering 9.7 Unsupervised Classification 9.8 An Example of Clustering with the k Means Algorithm 9.9 A Single Pass Clustering Technique 9.9.1 The Single Pass Algorithm 9.9.2 Advantages and Limitations of the Single Pass Algorithm 9.9.3 Strip Generation Parameter 9.9.4 Variations on the Single Pass Algorithm 9.9.5 An Example of Clustering with the Single Pass Algorithm 9.10 Hierarchical Clustering 9.10.1 Agglomerative Hierarchical Clustering 9.11 Other Clustering Metrics 9.12 Some Alternative Clustering Techniques 9.12.1 Histogram Peak Selection 9.12.2 Mountain Clustering 9.12.3 k Medians Clustering 9.12.4 k Medoids Clustering 9.13 Clustering Large Data Sets 9.13.1 The K Trees Algorithm 9.13.2 DBSCAN 9.14 Cluster Space Classification 9.15 Bibliography on Clustering and Unsupervised Classification 9.16 Problems 10 Feature Reduction Abstract 10.1 The Need for Feature Reduction 10.2 Approaches to Feature Reduction 10.3 Feature Reduction by Spectral Transforms 10.3.1 Feature Reduction Using the Principal Components Transform 10.3.2 Feature Reduction Using the Canonical Analysis Transform 10.3.2.1 Within-Class and Among-Class Covariance 10.3.2.2 A Separability Measure 10.3.2.3 The Generalised Eigenvalue Equation 10.3.2.4 An Example 10.3.3 Discriminant Analysis Feature Extraction (DAFE) 10.3.4 Non-parametric Discriminant Analysis (NDA) 10.3.5 Decision Boundary Feature Extraction (DBFE) 10.3.6 Non-parametric Weighted Feature Extraction (NWFE) 10.4 Feature Reduction by Block Diagonalising the Covariance Matrix 10.5 Feature Selection 10.5.1 Measures of Separability 10.5.2 Divergence 10.5.2.1 Definition 10.5.2.2 Divergence of a Pair of Normal Distributions 10.5.2.3 Using Divergence for Feature Selection 10.5.2.4 A Problem with Divergence 10.5.3 The Jeffries-Matusita (JM) Distance 10.5.3.1 Definition 10.5.3.2 Comparison of Divergence and JM Distance 10.5.4 Transformed Divergence 10.5.4.1 Definition 10.5.4.2 Transformed Divergence and the Probability of Correct Classification 10.5.4.3 Use of Transformed Divergence in Clustering 10.5.5 Separability Measures for Minimum Distance Classification 10.6 Distribution Free Feature Selection—ReliefF 10.7 Improving Covariance Estimates Through Regularisation 10.8 Bibliography on Feature Reduction 10.9 Problems 11 Image Classification in Practice Abstract 11.1 Introduction 11.2 An Overview of Classification 11.2.1 Supervised Classification 11.2.1.1 Selection of Training Data 11.2.1.2 Feature Selection 11.2.1.3 Classifier Outputs and Accuracy Checking 11.2.2 Unsupervised Classification 11.2.3 Semi-supervised Classification and Transfer Learning 11.3 Effect of Resampling on Classification 11.4 A Hybrid Supervised/Unsupervised Methodology 11.4.1 Outline of the Method 11.4.2 Choosing the Image Segments to Cluster 11.4.3 Rationalising the Number of Spectral Classes 11.4.4 An Example 11.4.5 Hybrid Classification with Other Supervised Algorithms 11.5 Cluster Space Classification 11.6 Assessing Classification Accuracy 11.6.1 Use of a Testing Set of Pixels 11.6.2 The Error Matrix 11.6.3 Quantifying the Error Matrix 11.6.4 The Kappa Coefficient 11.6.5 Number of Testing Samples Required for Assessing Map Accuracy 11.6.6 Number of Testing Samples Required for Populating the Error Matrix 11.6.7 Placing Confidence Limits on Assessed Accuracy 11.6.8 Cross Validation Accuracy Assessment and the Leave One Out Method 11.7 Decision Tree Classifiers 11.7.1 CART (Classification and Regression Trees) 11.7.2 Random Forests 11.7.3 Progressive Two-Class Decision Classifier 11.8 Image Interpretation Through Spectroscopy and Spectral Library Searching 11.9 End Members and Unmixing 11.10 Is There a Best Classifier? 11.10.1 Segmenting the Spectral Space 11.10.2 Comparing the Classifiers 11.11 Bibliography on Image Classification in Practice 11.12 Problems 12 Multisource Image Analysis Abstract 12.1 Introduction 12.2 Stacked Vector Analysis 12.3 Statistical Multisource Methods 12.3.1 Joint Statistical Decision Rules 12.3.2 Committee Classifiers 12.3.3 Opinion Pools and Consensus Theory 12.3.4 Use of Prior Probabilities 12.3.5 Supervised Label Relaxation 12.4 The Theory of Evidence 12.4.1 The Concept of Evidential Mass 12.4.2 Combining Evidence with the Orthogonal Sum 12.4.3 Decision Rules 12.5 Knowledge-Based Image Analysis 12.5.1 Emulating Photointerpretation to Understand Knowledge Processing 12.5.2 The Structure of a Knowledge-Based Image Analysis System 12.5.3 Representing Knowledge in a Knowledge-Based Image Analysis System 12.5.4 Processing Knowledge—The Inference Engine 12.5.5 Rules as Justifiers of a Labelling Proposition 12.5.6 Endorsing a Labelling Proposition 12.5.7 An Example 12.6 Operational Multisource Analysis 12.7 Bibliography on Multisource Image Analysis 12.8 Problems Appendices Appendix A: Satellite Altitudes and Periods Appendix B: Binary Representation of Decimal Numbers Appendix C: Essential Results from Vector and Matrix Algebra C.1 Matrices and Vectors, and Matrix Arithmetic C.2 The Trace of a Matrix C.3 The Transpose of a Matrix or a Vector C.4 The Identity Matrix C.5 The Determinant C.6 The Matrix Inverse C.7 The Eigenvalues and Eigenvectors of a Matrix C.8 Diagonalisation of a Matrix Appendix D: Some Fundamental Material from Probability and Statistics D.1 Conditional Probability and Bayes’ Theorem D.2 The Normal Probability Distribution D.2.1 The One Dimensional Case D.2.2 The Multidimensional Case Appendix E: Penalty Function Derivation of the Maximum Likelihood Decision Rule E.1 Loss Function and Conditional Average Loss E.2 A Particular Loss Function Index