COMPUTER AND ROBOT VISION

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1 VOLUME COMPUTER AND ROBOT VISION Robert M. Haralick University of Washington Linda G. Shapiro University of Washington A^ ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Wokingham, England Amsterdam Bonn Sydney Singapore Tokyo Madrid San Juan Milan Paris

2 CONTENTS H l Computer Vision: Overview ' 1.1 Introduction Recognition Methodology Conditioning Labeling Grouping Extracting Matching Outline of Book 8 Bibliography 11 Binary Machine Vision: Thresholding and Segmentation Introduction Thresholding Minimizing Within-Group Variance Minimizing Kullback Information Distance Connected Components Labeling Connected Components Operators Connected Components Algorithms An Iterative Algorithm The Classical Algorithm A Space-Efficient Two-Pass Algorithm That Uses a Local Equivalence Table An Efficient Run-Length Implementation of the Local Table Method 40 ix

3 X 2.4 Signature Segmentation and Analysis Summary 55 Exercises 55 Bibliography 55 Binary Machine Vision: Region Analysis Introduction Region Properties Extremal Points Spatial Moments Mixed Spatial Gray Level Moments Signature Properties Using Signature Analysis to Determine the Center and Orientation of a Rectangle Using Signature Analysis to Determine the Center of a Circle Summary 90 Exercises 91 Bibliography 93 Wmm Statistical Pattern Recognition Introduction Bayes Decision Rules: Maximum Utility Model for Pattern Discrimination Economic Gain Matrix Decision Rule Construction Prior Probability Economic Gain Matrix and the Decision Rule Maximin Decision Rule U2 4.6 Decision Rule Error: Misidentification/False Identification Reserving Judgement Nearest Neighbor Rule A Binary Decision Tree Classifier Decision Tree Construction Decision Rules Decision Rule Error Estimation Neural Networks Summary J43 Exercises 146 Bibliography 148

4 XI Mathematical Morphology Introduction Binary Morphology Binary Dilation Binary Erosion Hit-and-Miss Transform Dilation and Erosion Summary Opening and Closing Morphological Shape Feature Extraction Fast Dilations and Erosions Connectivity Separation Relation Morphological Noise Cleaning and Connectivity Openings, Holes, and Connectivity Conditional Dilation Generalized Openings and Closings Gray Scale Morphology Gray Scale Dilation and Erosion Umbra Homomorphism Theorems Gray Scale Opening and Closing Openings, Closings, and Medians Bounding Second Derivatives Distance Transform and Recursive Morphology Generalized Distance Transform Medial Axis Medial Axis and Morphological Skeleton Morphological Sampling Theorem Set-Bounding Relationships Examples Distance Relationships Summary 253 Exercises 253 Bibliography 255 HK^H Neighborhood Operators Introduction Symbolic Neighborhood Operators Region-Growing Operator Nearest Neighbor Sets and Influence Zones Region-Shrinking Operator Mark-Interior/Border-Pixel Operator Connectivity Number Operator Connected Shrink Operator 276

5 Xll Pair Relationship Operator Thinning Operator Distance Transformation Operator Radius of Fusion Number of Shortest Paths Extremum-Related Neighborhood Operators Non-Minima-Maxima Operator Relative Extrema Operator Reachability Operator Linear Shift-Invariant Neighborhood Operators Convolution and Correlation Separability 297 Exercises 299 Bibliography 300 Conditioning and Labeling Introduction Noise Cleaning A Statistical Framework for Noise Removal Determining Optimal Weight from Isotropie Covariance Matrices Outlier or Peak Noise K-Nearest Neighbor Gradient Inverse Weighted Order Statistic Neighborhood Operators A Decision Theoretic Approach to Estimating Mean Hysteresis Smoothing Sigma Filter Selecting-Neighborhood Averaging Minimum Mean Square Noise Smoothing Noise-Removal Techniques Experiments Sharpening Extremum Sharpening Edge Detection Gradient Edge Detectors Zero-Crossing Edge Detectors Edge Operator Performance Line Detection 352 Exercises 354 Bibliography 357 The Facet Model Introduction 371

6 xm 8.2 Relative Maxima Sloped Facet Parameter and Error Estimation Facet-Based Peak Noise Removal Iterated Facet Model Gradient-Based Facet Edge Detection Bayesian Approach to Gradient Edge Detection Zero-Crossing Edge Detector Discrete Orthogonal Polynomials Two-Dimensional Discrete Orthogonal Polynomials Equal-Weighted Least-Squares Fitting Problem Directional Derivative Edge Finder Integrated Directional Derivative Gradient Operator Integrated Directional Derivative Experimental Results Corner Detection Incremental Change along the Tangent Line Incremental Change along the Contour Line Instantaneous Rate of Change Experimental Results Isotropie Derivative Magnitudes Ridges and Ravines on Digital Images Directional Derivatives Ridge-Ravine Labeling Topographie Primal Sketch Introduction Mathematical Classification of Topographie Structures Topographie Classification Algorithm Summary of Topographie Classification Scheme 443 Exercises 445 Bibliography 449 H H Texture Introduction Gray Level Co-Occurrence Generalized Gray Level Spatial Dependence Models for Texture Strong Texture Measures and Generalized Co-Occurrence Spatial Relationships Autocorrelation Function and Texture Digital Transform Methods and Texture Textural Energy Textural Edgeness Vector Dispersion 470

7 xiv 9.9 Relative Extrema Density Mathematical Morphology Autoregression Models Discrete Markov Random Fields Random Mosaic Models Structural Approaches to Texture Models Texture Segmentation Synthetic Texture Image Generation Shape from Texture Summary 493 Exercises 493 Bibliography 494 Image Segmentation Introduction Measurement-Space-Guided Spatial Clustering Thresholding Multidimensional Measurement-Space Clustering Region Growing Single-Linkage Region Growing Hybrid-Linkage Region Growing Centroid-Linkage Region Growing Hybrid-Linkage Combinations Spatial Clustering Split and Merge Rule-Based Segmentation Motion-Based Segmentation Summary 548 Exercises 549 Bibliography 559 Are Extraction and Segmentation Introduction Extracting Boundary Pixels from a Segmented Image Concepts and Data Structures ' Border-Tracking Algorithm Linking One-Pixel-Wide Edges or Lines Edge and Line Linking Using Directional Information Segmentation of Ares into Simple Segments Iterative Endpoint Fit and Split Tangential Angle Deflection Uniform Bounded-Error Approximation 569

8 Breakpoint Optimization Split and Merge Isodata Segmentation Curvature Hough Transform Line Fitting Region-< Hough Transform Technique A Bayesian Approach to the Hough Transform Variance of the Fitted Parameters Principal-Axis Curve Fit 5f-Support Determination Robust Line Fitting Least-Square Curve Fitting Exercises Bibliography Gradient Descent Newton Method Second-Order Approximation to Curve Fitting Fitting to a Circle Variance of the Fitted Parameters Fitting to a Conic Fitting to an Ellipse Bayesian Fitting Uniform Error Estimation XV Q Appendix 639 A.l Properties of an Ellipse 639 A.2 Analytic Geometry of the Ellipse 639 A.3 Orientation and Axis Length 642 A.4 Tangent Lines and Extremal Points 647 A.5 Extremal Points 648 A.6 From Extremal Points to Characterization of the Ellipse 650 A.7 Moments of an Ellipse 654 A.7.1 Area 654 A.7.2 Second Moments 655 A.7.3 Second Moments and the Properties of the Ellipse 656 Appendix 659 B.l Linear Algebra Background 659 B.2 Discrete Least Squares Understood in Terms of Orthogonal Projection 663 Bibliography 665

9 xvi Appendix 666 C.l Experimental Protocol 666 Bibliography 667 Index 668

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