计算机视觉几何基础

本书主要讲解计算机视 觉的几何基础（核心数学基 础），包括图像处理与模式 识别的几何视角、三维射影 几何学、摄像机模型、摄像 机标定、立体视觉、三维视 觉重构等。本书提供了具体 且有趣的案例，并配有方便 读者实践、颇具实用性的原 创展示代码，让读者从实际 问题与实践中学习计算机视 觉几何基础。 本书可作为理工科学生 的计算机视觉、深度学习等 相关课程教学用书，也可作 为科研用书供从事视觉智能 感知相关工作的科技人员、 工程师阅读参考。

李颢，青飞智能科技有限公司首席技术官（CTO），前为上海交通大学副教授、博士生导师。自幼迍蒙，然承庭训慈养、长尊泽润，乃不至于冥顽，且登于教化，曷胜忻幸。笃志破万卷于琅嬛，神交圣贤；冀望行万里于四海，广阅人生。及长，负笈求学于南洋浦畔，深造留学于法兰西国，先学后工，徜徉北法南法近十载。归国，先续缘母校，矢志传道授业，将平素所知、所行、所经、所历之感触寓诸教学。后重返业界，并故交同道共驰骋，亦不辍探赜索隐、钩深致远。恒秉格物致知、格心致德、知行合一之理念。

Preface Chapter 1 Introduction 1.1 Vision systems 1.2 Image representation and two-dimensional geometry analysis 1.3 Computer vision and three-dimensional geometry analysis 1.4 Scope preview 1.5 Code demonstration for practice Chapter 2 Image Processing for Feature Extraction 2.1 Image coordinates system 2.1.1 From discrete indices to continuous coordinates 2.1.2 Linear interpolation 2.1.3 Quadratic interpolation 2.1.4 Image resolution enhancement 2.2 Feature points 2.2.1 Thresholding: pixel-wise point extraction 2.2.2 Application of image thresholding: watermark removal 2.2.3 Adaptive thresholding 2.2.4 Non-maximum suppression: extremum point extraction 2.2.5 Dilation and erosion: contour extraction 2.3 Edge points 2.3.1 Gradient image 2.3.2 Directional non-maximum suppression 2.3.3 Double thresholding 2.3.4 Canny edge detection 2.4 Corner points 2.5 Scale-space feature extraction 2.5.1 Scale space: filtered images associated with various filtering-scale parameters 2.5.2 Gaussian pyramid 2.5.3 Scale-invariant Laplacian 2.5.4 Difference-of-Gaussian 2.6 Scale invariant feature transform (SIFT) 2.6.1 Feature point localization 2.6.2 Local image orientation assignment 2.6.3 Local image descriptor generation 2.7 Post-SIFF features 2.7.1 Fast filtering: example of SURF 2.7.2 Fast feature detection: example of FAST 2.7.3 Simplified feature description: example of BRIEF 2.7.4 Oriented FAST and Rotated BRIEF (ORB) 2.8 Machine learning based features 2.8.1 Pre-deep learning methods 2.8.2 Deep learning methods 2.8.3 Learn for feature extraction 2.9 Note Chapter 3 Computational Geometry 3.1 Distance 3.1.1 Euclidean distance 3.1.2 Minimum-distance-path perspective 3.1.3 Point-to-line distance 3.1.4 Point-to-plane distance 3.2 Generalized distances and measures 3.2.1 Lp-norm distance 3.2.2 City-block distance 3.2.3 Mahalanobis distance 3.2.4 Distance, area, volume, and fractal measures 3.3 Graph 3.3.1 Topological abstraction 3.3.2 Planar graphs and Euler formula 3.3.3 Planar straight-line graphs 3.3.4 Point-location problem 3.4 Convex geometry 3.4.1 Convex polygon 3.4.2 Point-inclusion problem 3.5 Closest point problems 3.5.1 Find the closest pair among points 3.5.2 Voronoi diagram Chapter 4 Projective Geometry and Camera Model 4.1 Projective geometry 4.2 Camera model 4.2.1 Pinhole camera model 4.2.2 Extrinsic and intrinsic parameters 4.2.3 Perspective mapping 4.2.4 Revisit common sense of projective geometry 4.3 Homography 4.3.1 Bijective mapping between two-dimensional planes 4.3.2 Homography calibration 4.3.3 Inverse perspective mapping 4.4 Image distortion 4.4.1 Distortion-considered camera model 4.4.2 Inverse distortion model and distortion rectification 4.5 Stereo vision 4.5.1 Why stereo vision is \\\"natural\\\" ? 4.5.2 Epipolar constraint: fundamental and essential matrices 4.5.3 Rectified stereo vision 4.5.4 Binocular disparity Chapter 5 Camera Calibration 5.1 Camera intrinsic calibration 5.1.1 Exploitation of known homography 5.1.2 Chessboard pattern for camera intrinsic calibration 5.1.3 Initial estimate of camera intrinsic parameters 5.2 Refined estimate of camera intrinsic parameters 5.2.1 Three-dimensional rotation and Rodrigues formula 5.2.2 Lie group interpretation of three-dimensional rotation 5.2.3 Estimate refinement via optimization 5.3 Image distortion calibration 5.4 Camera-X calibration 5.4.1 Fundamental matrix calibration 5.4.2 Essential matrix calibration 5.4.3 Stereo camera calibration 5.4.4 Camera-range sensor cal