VISUAL RECONSTRUCTION

By ROBERT JONES

CONTENTS INTRODUCTION BACKGROUND ORGANIZATION FEATURES PART I FUNDAMENTAL ALGORITHMS FOR COMPUTER VISION ELLIPSE FITTING REPRESENTATION OF ELLIPSES LEAST-SQUARES APPROACH NOISE AND COVARIANCE MATRICES ALGEBRAIC METHODS ITERATIVE REWEIGHT RENORMALIZATION AND THE TAUBIN METHOD HYPER-RENORMALIZATION AND HYPERLS SUMMARY OF ALGEBRAIC METHODS GEOMETRIC METHODS GEOMETRIC DISTANCE AND SAMPSON ERROR FNS GEOMETRIC DISTANCE MINIMIZATION HYPER-ACCURATE CORRECTION ELLIPSE-SPECI?C METHODS ELLIPSE CONDITION METHOD OF FITZGIBBON ET AL METHOD OF RANDOM SAMPLING OUTLIER REMOVAL EXAMPLES SUPPLEMENTAL NOTE PROBLEMS REFERENCES FUNDAMENTAL MATRIX COMPUTATION FUNDAMENTAL MATRICES COVARIANCE MATRICES AND ALGEBRAIC METHODS RANK CONSTRAINT A POSTERIORI CORRECTION HIDDEN VARIABLES APPROACH EXTENDED FNS TRIANGULATION PERSPECTIVE PROJECTION CAMERA MATRIX AND TRIANGULATION TRIANGULATION FROM NOISY CORRESPONDENCE OPTIMAL CORRECTION OF CORRESPONDENCES 3D RECONSTRUCTION FROM TWO VIEWS CAMERA MODELING AND SELF-CALIBRATION EXPRESSION OF THE FUNDAMENTAL MATRIX FOCAL LENGTH COMPUTATION MOTION PARAMETER COMPUTATION 3D SHAPE COMPUTATION HOMOGRAPHY COMPUTATION HOMOGRAPHIES HYPERACCURATE CORRECTION PLANAR TRIANGULATION PERSPECTIVE PROJECTION OF A PLANE PROCEDURE OF PLANAR TRIANGULATION 3D RECONSTRUCTION OF A PLANE SELF-CALIBRATION WITH A PLANE COMPUTATION OF SURFACE PARAMETERS AND MOTION PARAMETERS SELECTION OF THE SOLUTION ELLIPSE ANALYSIS AND 3D COMPUTATION OF CIRCLES INTERSECTIONS OF ELLIPSES ELLIPSE CENTERS, TANGENTS, AND PERPENDICULARS PROJECTION OF CIRCLES AND 3D RECONSTRUCTION CENTER OF CIRCLE FRONT IMAGE OF THE CIRCLE PART II MULTIVIEW 3D RECONSTRUCTION TECHNIQUES MULTIVIEW TRIANGULATION TRILINEAR CONSTRAINT TRIANGULATION FROM THREE VIEWS OPTIMAL CORRESPONDENCE CORRECTION SOLVING LINEAR EQUATIONS EF?CIENCY OF COMPUTATION 3D POSITION COMPUTATION TRIANGULATION FROM MULTIPLE VIEWS BUNDLE ADJUSTMENT PRINCIPLE OF BUNDLE ADJUSTMENT BUNDLE ADJUSTMENT ALGORITHM DERIVATIVE COMPUTATION GAUSS-NEWTON APPROXIMATION DERIVATIVES WITH RESPECT TO 3D POSITIONS DERIVATIVES WITH RESPECT TO FOCAL LENGTHS DERIVATIVES WITH RESPECT TO PRINCIPAL POINTS DERIVATIVES WITH RESPECT TO TRANSLATIONS DERIVATIVES WITH RESPECT TO ROTATIONS EF?CIENT COMPUTATION AND MEMORY USE EF?CIENT LINEAR EQUATION SOLVING SELF-CALIBRATION OF AF?NE CAMERAS AF?NE CAMERAS FACTORIZATION AND AF?NE RECONSTRUCTION METRIC CONDITION FOR AF?NE CAMERAS DESCRIPTION IN THE CAMERA COORDINATE SYSTEM SYMMETRIC AF?NE CAMERA SELF-CALIBRATION OF SYMMETRIC AF?NE CAMERAS SELF-CALIBRATION OF SIMPLI?ED AF?NE CAMERAS PARAPERSPECTIVE PROJECTION MODEL WEAK PERSPECTIVE PROJECTION MODEL ORTHOGRAPHIC PROJECTION MODEL SELF-CALIBRATION OF PERSPECTIVE CAMERAS HOMOGENEOUS COORDINATES AND PROJECTIVE RECONSTRUCTION PROJECTIVE RECONSTRUCTION BY FACTORIZATION PRINCIPLE OF FACTORIZATION PRIMARY METHOD DUAL METHOD EUCLIDEAN UPGRADING PRINCIPLE OF EUCLIDEAN UPGRADING COMPUTATION OF X MODI?CATION OF KJ COMPUTATION OF H PROCEDURE FOR EUCLIDEAN UPGRADING 3D RECONSTRUCTION COMPUTATION SUPPLEMENTAL NOTES PART III MATHEMATICAL FOUNDATION OF GEOMETRIC ESTIMATION ACCURACY OF GEOMETRIC ESTIMATION CONSTRAINT OF THE PROBLEM ERROR ANALYSIS COVARIANCE AND BIAS BIAS ELIMINATION AND HYPER-RENORMALIZATION DERIVATIONS MAXIMUM LIKELIHOOD OF GEOMETRIC ESTIMATION MAXIMUM LIKELIHOOD SAMPSON ERROR BIAS ANALYSIS AND HYPER-ACCURATE CORRECTION THEORETICAL ACCURACY LIMIT KANATANI-CRAMER-RAO (KCR) LOWER BOUND STRUCTURE OF CONSTRAINTS DERIVATION OF THE KCR LOWER BOUND EXPRESSION OF THE KCR LOWER BOUND SOLUTIONS