In this book, the design of two new planar patterns for camera calibration of intrinsic parameters is addressed and a line-based method for distortion correction is suggested. The dynamic calibration of structured light systems, which consist of a camera and a projector is also treated. Also, the 3D Euclidean reconstruction by using the image-to-world transformation is investigated. Lastly, linear calibration algorithms for the catadioptric camera are considered, and the homographic matrix and fundamental matrix are extensively studied. In these methods, analytic solutions are provided for the computational efficiency and redundancy in the data can be easily incorporated to improve reliability of the estimations. This volume will therefore prove valuable and practical tool for researchers and practioners working in image processing and computer vision and related subjects.

Treats automatic calibration and 3D reconstruction for structures light systems and catadioptric cameras Completely new approach to automatic calibration Presents an extensive study on the homography matrix and the fundamental matrix Includes supplementary material: sn.pub/extras

Inhalt

Chapter 1 Introduction.- 1.1 Vision Framework.- 1.2 Background.- 1.2.1 Calibrated Reconstruction.- 1.2.1.1 Static Calibration based methods.- 1.2.1.2 Dynamic Calibration based methods.- 1.2.1.3 Relative Pose Problem.- 1.2.2 Uncalibrated 3D reconstruction.- 1.2.2.1 Factorization-based method.- 1.2.2.2 Stratification-based method.- 1.2.2.3 Using Structured Light System.- 1.3 Scope.- 1.3.1 System Calibration.- 1.3.2 Plane-based Homography.- 1.3.3 Structured Light System.- 1.3.4 Omni-directional Vision System.- 1.4 Objectives.- 1.5 Book Structures.- Chapter 2 System Description.- 2.1 System Introduction.- 2.1.1 Structured Light System.- 2.1.2 Omni-directional Vision System.- 2.2 Component Modeling.- 2.2.1 Convex Mirror.- 2.2.2 Camera Model.- 2.2.3 Projector Model.- 2.3 Pattern Coding Strategy.- 2.3.1 Introduction.- 2.3.2 Color-Encoded Light Pattern.- 2.3.3 Decoding the Light Pattern.- 2.4 Some Preliminaries.- 2.4.1 Notations and Definitions.- 2.4.2 Cross Ratio.- 2.4.3 Plane-based Homography.- 2.4.4 Fundamental Matrix.- Chapter 3 Static Calibration.- 3.1 Calibration Theory.- 3.2 Polygon-based Calibration.- 3.2.1 Design of the planar pattern.- 3.2.2 Solving the vanishing line.- 3.2.3 Solving the projection of a circle.- 3.2.4 Solving the projection of circular point.- 3.2.5 Algorithm.- 3.2.6 Discussion.- 3.3 Intersectant-Circle-based Calibration.- 3.3.1 Planar Pattern Design.- 3.3.2 Solution for the circular point.- 3.4 Concentric-Circle-based Calibration.- 3.4.1 Some Preliminaries.- 3.4.2 The polynomial eigenvalue problem.- 3.4.3 Orthogonality-based Algorithm.- 3.4.4 Experiments.- 3.4.4.1 Numerical Simulations.- 3.4.4.2 Real Image Experiment.- 3.5 Line-based Distortion Correction.- 3.5.1 The distortion model.- 3.5.2 The correction procedure.- 3.5.3 Examples.- 3.6 Summary.- Chapter 4 Homography-based Dynamic Calibration.- 4.1 Problem Statement.- 4.2 System Constraints.- 4.2.1 Two Propositions.- 4.3 Calibration Algorithm.- 4.3.1 Solution for the Scale Factor.- 4.3.2 Solutions for the Translation Vector.- 4.3.3 Solution for Rotation Matrix.- 4.3.4 Implementation Procedure.- 4.4 Error Analyses.- 4.4.1 Errors in the Homographic matrix.- 4.4.2 Errors in the translation vector.- 4.4.3 Errors in the rotation matrix.- 4.5 Experiments Study.- 4.5.1 Computer Simulation.- 4.5.2 Real Data Experiment.- 4.6 Summary.- Chapter 5 3D Reconstruction with Image-to-World Transformation.- 5.1 Introduction.- 5.2 Image-to-World Transformation matrix.- 5.3 Two-Known-Plane based method.- 5.3.1 Static Calibration.- 5.3.2 Determining the on-line Homography.- 5.3.3 Euclidean 3D Reconstruction.- 5.3.4 Configuration of the two scene planes.- 5.3.5 Computational Complexity Study.- 5.3.6 Reconstruction Examples.- 5.4 One-Known-Plane based method.- 5.4.1 Calibration Tasks.- 5.4.2 Generic Homography.- 5.4.3 Dynamic Calibration.- 5.4.4 Reconstruction Procedure.- 5.4.5. Reconstruction Examples.- 5.5 Summary.- Chapter 6 Catadioptric Vision System.- 6.1 Introduction.- 6.1.1 Wide Field-of-View System.- 6.1.2 Calibration of Omni-directional Vision System.- 6.1.3 Test Example.- 6.2 Panoramic Stereoscopic System.- 6.2.1 System Configuration.- 6.2.2 Co-axis Installation.- 6.2.3 System Model.- 6.2.4 Epipolar geometry and 3D reconstruction.- 6.2.5 Calibration Procedure.- 6.2.5.1 Initialization of the Parameters.- 6.2.5.2 Non-linear optimization.- 6.3 Parabolic Camera System.- 6.3.1 System Configuration.- 6.3.2 System Modeling.- 6.3.3 Calibration with Lifted-Fundamental-matrix.- 6.3.3.1 The lifted fundamental matrix.- 6.3.3.2 Calibration Procedure.- 6.3.3.3 Simplified Case.- 6.3.3.4 Discussion.- 6.3.4 Calibration Based on Homographic matrix.- 6.3.4.1 Plane-to-mirror Homography.- 6.3.4.2 Calibration Procedure.- 6.3.4.3 Calibration Test.- 6.3.5 Polynomial Eigenvalue Problem.- 6.3.5.1 Mirror-to-mirror Homography.- 6.3.5.2 Constraints and Solutions.- 6.3.5.3 Test Example.- 6.4 Hyperbolic Camera System.- 6.4.1 System Structure.- 6.4.2 Imaging Process and Back Projection.- 6.4.3 Polynomial Eigenvalue Problem.- 6.5 Summary.- Chapter 7 Conclusions and Future Expectation.- 7.1 Conclusions.- 7.2 Future Expectations.- References.