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 T V ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Wokingham, England Amsterdam Bonn

2 CONTENTS K ^ Illumination Introduction Radiometry Bidirectional Reflectance Function Photometry Torrance-Sparrow Model Lens Collection Image Intensity Photometrie Stereo Shape from Shading Shape from Focus Polarization Representation of Light Using the Coherency Matrix Representation of Light Intensity Fresnel Equation Reflection of Polarized Light A New Bidirectional Reflectance Function Image Intensity Related Work Perspective Projective Geometry Introduction 13.2 One-Dimensional Perspective Projection m

3 IV 13.3 The Perspective Projection in 3D Smaller Appearance of Farther Objects Lines to Lines The Perspective Projections of Convex Polyhedra are Convex Vanishing Point Vanishing Line D Lines-2D Perspective Projection Lines D to 3D Inference Using Perspective Projection Inverse Perspective Projection Line Segment with Known Direction Cosines and Known Length Collinear Points with Known Interpoint Distances N Parallel Lines N Lines Intersecting at a Point with Known Angles N Intersecting Lines in a Known Plane Three Lines in a Plane with One Perpendicular to the Other Two Point with Given Distance to a Known Point Point in a Known Plane Line in a Known Plane Angle Parallelogram Triangle with One Vertex Known Triangle with Orientation of One Leg Known Triangle Determining the Principal Point by Using Parallel Lines Circles Range from Structured Light Cross-Ratio Cross-Ratio Definitions and Invariance Only One Cross-Ratio Cross-Ratio in Three Dimensions Using Cross-Ratios Hl Analytic Photogrammetry Introduction Nonlinear Least-Squares Solutions The Exterior Orientation Problem Standard Solution Auxiliary Solution Quaternion Representation 140

4 v 14.4 Relative Orientation Standard Solution Quaternion Solution Interior Orientation Stereo D-2D Absolute Orientation D-3D Absolute Orientation Robust M-Estimation Modified Residual Method Modified Weights Method Experimental Results Error Propagation Implicit Form Implicit Form: General Case Summary 178 Motion and Surface Structure from Time Varying 187 Image Sequences 15.1 Introduction The Fundamental Optic Flow Equation Translational Motion Focus of Expansion and Contraction The Moving Line Segment Optic Flow Acceleration Invariant Rigid Body Motion Linear Algorithms for Motion and Surface Structure from Optic Flow The Planar Patch Case General Case: Optic Flow-Motion Equation A Linear Algorithm for Solving Optic Flow-Motion Equations Mode of Motion, Direction of Translation, and Surface Structure Linear Optic Flow-Motion Algorithm and Simulation Results The Two View-Linear Motion Algorithm Planar Patch Motion Recovery from Two Perspective Views: A Brief Review General Curved Patch Motion Recovery from Two Perspective Views: A Simplified Linear Algorithm Determining Translational Orientation Determining Mode of Motion and Relative Depths 219

5 vi A Simplified Two View-Motion Linear Algorithm Discussion and Summary Linear Algorithm for Motion and Structure from Three Orthographie Views Problem Formulation Determining r 3 3,s 3 3, Solving a Unique Orthonormal Matrix R Linear Algorithm to Uniquely Solve R, S, a s Summary Developing a Highly Robust Estimator for General Regression Inability of the Classical Robust M-Estimator to Render High Robustness Partially Modeling Log Likelihood Function by Using Heuristics Discussion MF-Estimator Optic Flow-Instantaneous Rigid-Motion Segmentation and Estimation Single Rigid Motion Multiple Rigid Motions Experimental Protocol Simplest Location Estimation Optic Flow-Rigid-Motion Segmentation and Estimation Motion and Surface Structure from Line Correspondences Problem Formulation Solving Rotation Matrices R',R" and TranslationsT'.T" Solving Three Dimensional Line Structure Multiple Rigid Motions from Two Perspective Views Problem Statement Simulated Experiments Rigid Motion from Three Orthographie Views Problem Formulation and Algorithm Simulated Experiments Further Research on the MF-Estimator Literature Review Inferring Motion and Surface Structure Computing Optic Flow or Image Point Correspondences 274 f Image Matching 16.1 Introduction Image Matching and Object Reconstruction

6 Vll The Principle of Image Matching Image Matching Procedures Intensity-Based Matching of One-Dimensional Signals The Principle of Differential Matching Estimating an Unknown Shift Estimating Unknown Shift and Scale Compensation for Brightness and Contrast Estimating Smooth Deformations Iterations and Resampling Matching of Two Observed Profiles Relations to Cross-Correlation Techniques Intensity-Based Matching of Two-Dimensional Signals The Principle and the Relation to Optical Flow Estimating Constant-Shift Parameters Estimating Linear Transformations Invariant Points An Interest Operator Introduction Estimating Corner Points Evaluation and Classification of Selected Windows Selection of Optimal Windows Uniqueness of Selected Points Robust Estimation for Feature-Based Matching The Principle of Feature-Based Matching The Similarity Measure Heuristics for Selecting Candidate Pairs Robust Estimation for Determining the Spatial Mapping Function Evaluating the Final Result Structure from Stereo by Using Correspondence Epipolar Geometry Generation of Normal Images Specializing the Image-Matching Procedures Precision of Three-Dimensional Points from Image Points 362 The Consistent-Labeling Problem Introduction Examples of Consistent-Labeling Problems The TV-Queens Problem The Latin-Square Puzzle The Edge-Orientation Problem The Subgraph-Isomorphism Problem The Relational-Homomorphism Problem 382

7 viii 17.3 Search Procedures for Consistent Labeling The Backtracking Tree Search Backtracking with Forward Checking Backtracking with Discrete Relaxation Ordering the Units Complexity The Inexact Consistent-Labeling Problem Continuous Relaxation Vision Applications Image Matching Using Continuous Relaxation Characterizing Binary-Relation Homomorphisms The Winnowing Process Binary-Relation Homomorphism Characterization Depth-First Search for Binary-Relation Homomorphisms 420 Object Models and Matching Introduction Two-Dimensional Object Representation Global Feature Representation Local Feature Representation Boundary Representation Skeleton Representation Two-Dimensipnal Part Representation Three-Dimensional Object Representations Local Features Representation Wire Frame Representation Surface-Edge-Vertex Representation Sticks, Plates, and Blobs Generalized Cylinder Representation Superquadric Representation Octree Representation The Extended Gaussian Image View-Class Representation General Frameworks for Matching Relational-Distance Approach to Matching Ordered Structural Matching Hypothesizing and Testing with Viewpoint Consistency Constraint View-Class Matching Affine-Invariant Matching Model Database Organization 479

8 IX Knowledge-Based Vision Introduc ;tion Rnowlec Ige Representations Feature Vectors Relational Structures Hierarchical Structures Rules Frames and Schemes Control Strategies Hierarchical Control Heterarchical Control Information Integration Bayesian Approach Dempster-Shafer Theory A Probabilistic Basis for Evidential Reasoning Exampli Summai Legal Court Paradigm Degree of Belief as Chance Probability of Being Inferred Belief Calculus Examples z Systems VISIONS ACRONYM SPAM MOSAIC Mulgaonkar's Hypothesis-Based Reasoning SCERPO Ikeuchi's Model-Based Bin-Picking System Jain's Evidence-Based Recognition System ABLS Accuracy Introduction Mensuration Quantizing Error Automated Position Inspection: False Alarm and Misdetection Rates Analysis Discussion Experimental Protocol Determining the Repeatability of Vision Sensor Measuring 554

9 X The Model Derivation Determining the Positional Accuracy of Vision Sensors The Model Derivation Performance Assessment of Near-Perfect Machines The Derivation Balancing the Acceptance Test Lot Assessment Summary 568 Glossary of Computer Vision Terms The Image Photometry and Illumination Photogrammetry Image Operators Point Operators Spatial Operators Morphological Operators Hough Transform Digital Geometry 2D Shape Description Curve and Image Data Structures Texture Segmentation Matching Localization General Image Processing Vision Pattern Recognition Index of Terms Index 621

COMPUTER AND ROBOT VISION

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