Information visualization Books

Book SynopsisPrevalent types of data in scientific visualization are volumetric data, vector field data, and particle-based data. Particle data typically originates from measurements and simulations in various fields, such as life sciences or physics. The particles are often visualized directly, that is, by simple representants like spheres. Interactive rendering facilitates the exploration and visual analysis of the data. With increasing data set sizes in terms of particle numbers, interactive high-quality visualization is a challenging task. This is especially true for dynamic data or abstract representations that are based on the raw particle data. This book covers direct particle visualization using simple glyphs as well as abstractions that are application-driven such as clustering and aggregation. It targets visualization researchers and developers who are interested in visualization techniques for large, dynamic particle-based data. Its explanations focus on GPU-accelerated algorithms for high-performance rendering and data processing that run in real-time on modern desktop hardware. Consequently, the implementation of said algorithms and the required data structures to make use of the capabilities of modern graphics APIs are discussed in detail. Furthermore, it covers GPU-accelerated methods for the generation of application-dependent abstract representations. This includes various representations commonly used in application areas such as structural biology, systems biology, thermodynamics, and astrophysics.Table of ContentsAcknowledgments.- Figure Credits.- Introduction.- History.- GPU-based Glyph Ray Casting.- Acceleration Strategies.- Data Structures.- Efficient Nearest Neighbor Search on the GPU.- Improved Visual Quality.- Application-driven Abstractions.- Summary and Outlook.- Bibliography.- Authors' Biographies.

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Book SynopsisThis open access book explores the role visual tools and graphical models play in safety management. It explains the importance of visualising safety, for teaching concepts, communicating ideas to peers, and raising awareness of potential threats through posters. Visualising Safety, an Exploration introduces graphical models which have been influential in promoting ideas of safety, and impacting the organisational design of safety mechanisms, including the Heinreich ‘safety pyramid’ and Reason’s ‘Swiss Cheese’. It analyses these models, as well as other forms of visualization, presenting viewpoints from academics and practitioners in the fields of safety science, history, ethnography and interface design.This brief will be of interest to anyone working in the field of safety management and design, including researchers, managers and students.Table of Contents1. Introduction.- 2. Screening Workplace Injury and Fatality: The Case of Only the Brave (2017).- 3. Anticipating Risk (and Opportunity): A Control Theoretic Perspective on Visualization and Safety.- 4. Visualization for the Safe Occupation of Workspaces.- 5. Visualizations, Metaphors and Slogans: Representations from Organizational Safety to Societal Resilience.- 6. Visualizing for Safety of Visualization of Safety?.- 7. Educating Nuclear Workers Through Images: the Work of Jacques Castan, Illustrator of Radiation Protection in the 1960s.- 8. Visualizing Complex Industrial Operations Through the Lens of Functional Signatures.- 9. Occupational Safety in Revamping Operations: Visualizing Spaces to Monitor Uncertainty.- 10. Drawings, Posters, Photos, and Metaphors in Safety and Safety Science, Some Historical Remarks.- 11. Network Visualization in Supply Chain Safety Culture Assurance of a Nuclear Power Plant Construction Project.- 12. Ways of Seeing (And Not Seeing) Safety.- 13. Conclusion.

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Book SynopsisFrom facial recognition to self-driving cars, the applications of computer vision are vast and ever-expanding. Geometry plays a fundamental role in this discipline, providing the necessary mathematical framework to understand the underlying principles of how we perceive and interpret visual information in the world around us. This text explores the theories and computational techniques used to determine the geometric properties of solid objects through images. It covers the basic concepts and provides the necessary mathematical background for more advanced studies. The book is divided into clear and concise chapters covering a wide range of topics including image formation, camera models, feature detection and 3D reconstruction. Each chapter includes detailed explanations of the theory as well as practical examples to help the reader understand and apply the concepts presented. The book has been written with the intention of being used as a primary resource for students on university courses in computer vision, particularly final year undergraduate or postgraduate computer science or engineering courses. It is also useful for self-study and for those who, outside the academic field, find themselves applying computer vision to solve practical problems. The aim of the book is to strike a balance between the complexity of the theory and its practical applicability in terms of implementation. Rather than providing a comprehensive overview of the current state of the art, it offers a selection of specific methods with enough detail to enable the reader to implement them. Table of Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Prodigy of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Low-level Computer Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Overview of the Boook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Fundamentals of Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Digital Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Thin Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Telecentric Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Radiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 The Pinhole Camera Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Pinhole camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Simplified Pinhole Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4 General Pinhole Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4.1 Intrinsic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4.1.1 Field of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4.2 Extrinsic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.5 Dissection of the Perspective Projection Matrix . . . . . . . . . . . . . . . . . 26 3.5.1 Collinearity Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.6 Radial Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Camera Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 The Direct Linear Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.3 Factorization of the Perspective Projection Matrix . . . . . . . . . . . . . . . 37 4.4 Calibrating Radial Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.5 The Sturm-Maybank-Zhang Calibration Algorithm . . . . . . . . . . . . . . 39 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5 Absolute and Exterior Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2 Absolute Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2.1 Orthogonal Procrustes Analysis . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3 Exterior orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.3.1 Fiore’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3.2 Procrustean Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.3 Direct Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6 Two-view Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 Epipolar Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.3 Fundamental Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.4 Computing the Fundamental Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.4.1 The 7-points Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.4.2 Preconditioning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.5 Planar Homography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.5.1 Computing the Homography . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.6 Planar Parallax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7 Relative Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.2 The Essential Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7.2.1 Geometric Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.2.2 Computing the Essential Matrix . . . . . . . . . . . . . . . . . . . . . . . 74 7.3 Relative Orientation from the Essential Matrix . . . . . . . . . . . . . . . . . . 75 7.3.1 Closed Form Factorization of the Essential Matrix . . . . . . . . 77 7.4 Relative Orientation from the Calibrated Homography . . . . . . . . . . . . 79 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Contents xv 8 Reconstruction from Two Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.2 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 8.3 Ambiguity of Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.4 Euclidean Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.5 Projective Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.6 Euclidean Upgrade from Known Intrinsic Parameters . . . . . . . . . . . . 89 8.7 Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 9 Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 9.2 Algebraic vs Geometric distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 9.3 Nonlinear Regression of the PPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 9.3.1 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 9.3.2 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 9.3.3 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 9.3.4 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 9.4 Nonlinear Regression of Exterior Orientation . . . . . . . . . . . . . . . . . . . 100 9.5 Nonlinear Regression of a Point in Space . . . . . . . . . . . . . . . . . . . . . . . 100 9.5.1 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 9.5.2 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 9.5.3 Radial Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 9.6 Regression in the Joint Image Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 9.7 Nonlinear Regression of the Homography . . . . . . . . . . . . . . . . . . . . . . 104 9.7.1 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 9.7.2 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 9.7.3 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 9.8 Nonlinear Regression of the Fundamental Matrix . . . . . . . . . . . . . . . . 107 9.8.1 Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 9.8.2 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9.8.3 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 9.9 Nonlinear Regression of Relative Orientation . . . . . . . . . . . . . . . . . . . 112 9.9.1 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 9.9.2 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 9.10 Robust Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 10 Stereopsis: geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 10.2 Triangulation in the Normal Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 10.3 Epipolar Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.3.1 Calibrated Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.3.2 Uncalibrated Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 11 Features points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 11.2 Filtering Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 11.2.1 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.2.1.1 Non-linear Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 11.2.2 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 11.3 LoG Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 11.4 Harris-Stephens Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 11.4.1 Matching and tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 11.4.2 Kanade-Lucas-Tomasi Algorithm . . . . . . . . . . . . . . . . . . . . . . 146 11.4.3 Predictive Tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 11.5 Scale Invariant Feature Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 11.5.1 Space-Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 11.5.2 SIFT Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 11.5.3 SIFT descriptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 11.5.4 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 12 Stereopsis: matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 12.2 Constraints and Ambiguities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 12.3 Local Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 12.3.1 Matching Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 12.3.2 Census Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 12.4 Adaptive Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 12.4.1 Multiresolution Stereo Matching . . . . . . . . . . . . . . . . . . . . . . . 166 12.4.2 Adaptive Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 12.5 Global Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 12.6 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 12.6.1 Reliability Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 12.6.2 Occlusions Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 13 Range sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 13.2 Structured Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 13.2.1 Active Stereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 13.2.2 Active Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 13.2.3 Ray-Plane Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 13.2.4 Scanning Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 13.2.5 Coded Light Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 13.3 Time-of-Flight Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 13.4 Photometric Stereo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.4.1 From Normals to Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . 188 13.5 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 14 Multiview Euclidean Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 14.1.1 Epipolar Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 14.1.2 The Case of Three Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 14.1.3 Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 14.2 Points-based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 14.2.1 Adjustment of Independent Models . . . . . . . . . . . . . . . . . . . . . 199 14.2.2 Incremental Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 14.2.3 Hierarchical Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 14.3 Frames-based Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 14.3.1 Synchronization of Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . 203 14.3.2 Synchronization of Translations . . . . . . . . . . . . . . . . . . . . . . . . 205 14.3.3 Localization from Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 14.4 Bundle Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 14.4.1 Jacobian of Bundle Adjustment . . . . . . . . . . . . . . . . . . . . . . . . 210 14.4.2 Reduced System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 15 3D Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 15.1.1 Generalised Procrustean Analysis . . . . . . . . . . . . . . . . . . . . . . . 218 15.2 Correspondence-less Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 15.2.1 Registration of Two Point-clouds . . . . . . . . . . . . . . . . . . . . . . . 220 15.2.2 Iterative Closest Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 15.2.3 Registration of Many Point-clouds . . . . . . . . . . . . . . . . . . . . . . 223 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 16 Multiview Projective Reconstruction and Autocalibration. . . . . . . . . . . 227 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 16.1.1 Sturm-Triggs Factorization Method . . . . . . . . . . . . . . . . . . . . . 227 16.2 Autocalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 16.2.1 Absolute Quadric Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . 231 16.2.1.1 Solution Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Linear Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Constant Intrinsic Parameters . . . . . . . . . . . . . . . . . . 233 16.2.2 Mendonça-Cipolla Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 16.3 Autocalibration via 퐻∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 16.4 Tomasi-Kanade’s Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 16.4.1 Affine Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 16.4.2 The Factorization Method for Affine Camera . . . . . . . . . . . . . 239 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 17 Multi-View Stereo Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 17.2 Volumetric Stereo in Object-space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 17.2.1 Shape from Silhouette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 17.2.2 Szeliski’s Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 17.2.3 Voxel Coloring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 17.2.4 Space Carving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 17.3 Volumetric Stereo in Image-space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Alignment of Epipolar Lines . . . . . . . . . . . . . . . . . . . 253 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Surface Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 17.4 Marching Cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 18 Image-based Rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 18.2 Parametric Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 18.2.1 Mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 18.2.1.1 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Synchronization of Homographies . . . . . . . . . . . . . . 261 18.2.1.2 Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 18.2.2 Image Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 18.2.3 Perspective Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 18.3 Non-parametric Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 18.3.1 Transfer with Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 18.3.2 Transfer with Disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 18.3.3 Epipolar Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 18.3.4 Transfer with Parallax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 18.3.5 Ortho-projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 18.4 Geometric Image Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Bilinear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 274 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 A Notions of linear algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A.2 Scalar Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A.3 Matrix Norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 A.4 Inverse Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 A.5 Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 A.6 Orthogonal Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 A.7 Linear and Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 A.8 Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 A.9 QR Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 A.10 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 A.11 Singular Values Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 A.12 Pseudoinverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 A.13 Cross Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 A.14 Kronecker’s Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 A.15 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 A.16 Matrices Associated with Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 B Matrix Differential Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 B.1 Derivatives of Vector and Matrix Functions . . . . . . . . . . . . . . . . . . . . . 299 B.2 Derivative of Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Axis/Angle Representation.. . . . . . . . . . . . . . . . . . . . 303 Euler Representation. . . . . . . . . . . . . . . . . . . . . . . . . . 303 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 C Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 C.2 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 C.2.1 Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 C.2.2 Nonlinear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 C.2.2.1 Gauss-Newton Method . . . . . . . . . . . . . . . . . . . . . . . 307 C.2.3 The Levenberg-Marquardt Method . . . . . . . . . . . . . . . . . . . . . . 308 C.3 Robust Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 C.3.1 Outliers and Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 C.3.2 M-estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 C.3.3 Least Median of Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 C.3.4 RANSAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 C.4 Propagation of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Propagation of Covariance in Least Squares. . . . . . 317 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 D Notions of Projective Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 D.2 Perspective Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 D.3 Homogeneous Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 D.4 Equation of the Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 D.5 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 E Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

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Book SynopsisDesign system for information design explained step by step How can you turn dry statistics into attractive and informative graphs? How can you present complex data sets in an easily understandable way? How can you create narrative diagrams from unstructured data? This handbook of information design answers these questions. Nicole Lachenmeier and Darjan Hil condense their extensive professional experience into an illustrated guide that offers a modular design system comprised of 80 elements. Their systematic design methodology makes it possible for anyone to visualize complex data attractively and using different perspectives. At the intersection of design, journalism, communication and data science, Visualizing Complexity opens up new ways of working with abstract data and invites readers to try their hands at information design New standard work for information design - Joseph Binder Award 2022, Winner Gold in the category "Information Design" Attractively designed and illustrated manual Innovative presentation solutions for analog and digital media Available in German and English (ISBN 9783035625042)

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Book SynopsisThis book provides users with cutting edge methods and technologies in the area of big data and visual analytics, as well as an insight to the big data and data analytics research conducted by world-renowned researchers in this field. The authors present comprehensive educational resources on big data and visual analytics covering state-of-the art techniques on data analytics, data and information visualization, and visual analytics. Each chapter covers specific topics related to big data and data analytics as virtual data machine, security of big data, big data applications, high performance computing cluster, and big data implementation techniques. Every chapter includes a description of an unique contribution to the area of big data and visual analytics. This book is a valuable resource for researchers and professionals working in the area of big data, data analytics, and information visualization. Advanced-level students studying computer science will also find this book helpful as a secondary textbook or reference.Table of ContentsInformation visualization.- Data analytics.- Visual analytics.- Intelligent information systems.- Business analytics,- Virtual data machine.- Big data architecture.- Security of big data.- Big data applications.- Tensor-based computation and modeling.- High performance computing cluster.- Big data technologies.

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Book SynopsisShape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between the areas geometric modeling and solid modeling. Apart from the differential geometry topics covered, the entire book is based on the unifying concept of recasting all shape interrogation problems to the solution of a nonlinear system. It provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, and geodesics.Trade ReviewFrom the reviews: "... Currently there are several excellent books in the area of geometric modeling and in the area of solid modeling. The major contribution of this book lies in its skilful manner of providing a bridge between these two areas that is guaranteed to make the target audience cry out aloud with delight. Apart from the differential geometry topics covered, the entire book is based on the unifying concept of recasting all shape interrogation problems to the solution of a nonlinear system. Indeed the book is quite compulsive; No study of shape interrogation can ignore Patrikalakis and Maekawa's. Nearly 460 references to the literature make the book widely welcomed. ..." Current Engineering Practice 2002-2003, Vol. 45, Issue 3-4 "... It provides a comprehensive coverage of the fundamental concepts that shape interrogation techniques rely on as well as of the various techniques and algorithms for interrogation of shape features. ... Containing 408 pages, the book can be an indispensable reference for anybody with interest in this field of computer aided geometric design and software development. Nick Patrikalakis and Takashi Maekawa, researchers at MIT, managed to presnet all related concepts in an insightful way. The careful arrangement of the topics and the endeavor of the authors to recast all shape interrogation problem to the numerical solution of a nonlinear system of equations impressed the reviewer. ..." I. Horváth, Structural and Multidisciplinary Optimization 2003, Vol. 24, Issue 6 "…this is a very detailed and complete book on topics that are important in both the theory and practice of geometric modeling. It is a welcome addition to the literature. Reading it and experimenting with the techniques it describes should be a rewarding experience." Luiz Henrique de Figueiredo, MATHEMATICAL REVIEWS "... This book by Patrikalakis and Maekawa is the first thorough, long overdue, look at this curicial area. The book presents an original and inclusive summary of advanced computational topics that relate to the geometry of freeform shapes. Research in these computational areas has matured to a point where such a compendium is no longer nice to have on one's shelf, but a necessity for the serious investigator. The book handles computational problems that represent fundamental components in any solid modeling environment, filling a vacuum in the literature. It will serve well any researcher, either in academia or industry, working in the area of freeform design or manusfacturing. This work continues from the point where the traditional geometric design and solid modeling books stop. ... Shape interrogation and computational geometry of freeform shapes have been a part of the geometric design and manufacturing community for a long time. This book makes efforts and is likely to become the 'Bible' for this area. As a high-quality produced book, it is a must reference for any advanced researcher or developer who works with splines and freeform representations. If you consider yourself one, this book should probably be on your bookshelf. I eagerly await what the first revision of this book may yield." Gershon Elber, Computer-Aided Design 35 (2003) 1053 "‘Shape Interrogation’ in general means the process of extracting information from a geometric model. … The aim of this text is to provide an exhaustive list of tools and algorithms useful for shape interrogation of freeform curves and surfaces. Their effectivity depends on the end user’s capability of solving systems of nonlinear equations, which is one reason for the author’s focus on robust polynomial solvers." (Johannes Wallner, Zentralblatt MATH, Vol. 1035, 2004) "‘Shape Interrogation’ is the process of extracting information from a geometric model. … This book provides a bridge between the areas of geometric modeling and solid modeling. Apart from the differential geometry topics covered, the entire book is based on the unifying concept of recasting all shape interrogations problems to the solution of a nonlinear system. … The book can serve as a textbook for teaching advanced topics of geometric modeling for graduate students as well as professionals in industry." (deslab. mit.edu, October, 2003) "This book gives a detailed description of algorithms and computational methods for shape interrogation … . The book can be used in a course for advanced graduate students and also as a reference text for researchers and practitioners in CAD/CAM. … is a very detailed and complete book on topics that are important in both the theory and the practice of geometric modeling. It is a welcome addition to the literature. Reading it and experimenting with the techniques it describes should be a rewarding experience." (Luiz Henrique de Figueiredo, Mathematical Reviews, 2003 a) "Shape interrogation and computational geometry of free-form shapes have been a part of the geometric design and manufacturing community for a long time. This book makes a first triumphant attempt at summarizing these research efforts and is likely to become the ‘Bible’ for this area. As a high-quality produced book, it is a must reference for any advanced researcher or developer who works with splines and freeform representations. If you consider yourself one, this book should probably be on your bookshelf." (Gershon Elber, Computer Aided Design, Vol. 35, 2003) "The book focuses on the topic of getting shape information from the geometric models of sculptured objects. … Containing 408 pages, the book can be an indispensable reference for anybody with interest in this field of computer aided geometric design and software development. … the text is sufficiently illustrated with figures and the production of the book is of good quality. … The book can be offered as a textbook for teaching advanced topics of geometric modeling for graduate students." (I. Horváth, Structural and Multidisciplinary Optimization, Vol. 24 (6), 2003) "This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces. … The book will inform and enlighten professionals in industry and therefore remains essential reading for them too." (Current Engineering Practice, Vol. 45 (3-4), 2002-03)Table of ContentsRepresentation of Curves and Surfaces.- Differential Geometry of Curves.- Differential Geometry of Surfaces.- Nonlinear Polynomial Solvers and Robustness Issues.- Intersection Problems.- Differential Geometry of Intersection Curves.- Distance Functions.- Curve and Surface Interrogation.- Umbilics and Lines of Curvature.- Geodesics.- Offset Curves and Surfaces.

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Book SynopsisThis work contains the proceedings of the "Mathematics and Culture" conference held in Venice in March 2002. The conference aims to act as a bridge across the various aspects of human knowledge. While keeping mathematics as its core, it is aimed at anyone endowed with cultural curiosity and interests, whether within or (even more so) outside mathematics. This volume therefore covers music, cinema, art, theatre and literature, with topics ranging from Tibet to comics.Trade ReviewFrom the reviews:“This is a collection of papers that highlight the relation between mathematics and culture in the broadest sense. … it is an eye-opener to many who might experience mathematics as an invention to terrorise children at school. … It is an excellent tool to raise public awareness of mathematics. It can be easily used by teachers or lecturers as a Trojan horse to conquer the fortress of the less mathematically inclined.” (A. Bultheel, The European Mathematical Society, October, 2012)Table of ContentsI Mathematicians: Open Your Eyes Through Mathematics by Emma Castelnuovo.- The Theory of Motion from Hellenism to the 20th Century by Giovanni Gallavotti.- How Mathematics Helps Us Avoid Biases by Aljoša Volcic.- II Mathematics and Music: Mathematical Modelling of Musical Sounds by Giovanni De Poli.- What Time-Frequency Analysis Can Do to Music Signals (and What It Can’t Do) by Monica Dörfler.- … Listen:… By Laura Tedeschini Lalli.- Being an Artist with Mathematics and a Computer by Stefano Busello.- Escher-Like Perspectives and Music Production by Claudio Ambrosini- III Mathematics and Art: Complexity in Art: Klee, Duchamp and Escher by Roberto Giunti.- Stayin’ Alive (Just Barely): The Fate of the Geometrical Fourth Dimension at Mid-Century by Linda Dalrypmple Henderson.- The pleasure of threads: The Visual Experience of Fred Sandback’s sculptures by Manuel Corrada.- Paladino’s Mathematicians by Enzo di Martino.- IV Mathematics and Cinema: Mathematics in the Movies: A Case Study by Harold W. Kuhn.- V Mathematics and Venice: Luca Pacioli and Venice by Giovanni Fazzini.- A Venetian Comic Book by Luca Boschi, Michele Emmer.- Labyrinths by Michele Emmer, Gian Marco Todesco.- The Romance of Double-Entry Bookkeeping by Anthony Phillips.- VI Peking 2002: Is Chinese Mathematics Chinese? by Jean-Claude Martzloff.- Why Mathematics in Ancient China? by Anjing Qu.- The "Lack of Grounding" of Chinese Astronomy: a Communis Opinio of XVII century Europe by Francesco D’Arelli.- A Mathematician in Lhasa by Michele Emmer.- VII Mathematics and Theatre: Infinity and the Search for Simplicity by Sergio Escobar.- VIII Mathematics and Comic Strips: Digital Character Construction in Walt Disney Pictures' Feature "Dinosaur" by Stewart Dickson.- Comics and MathMagic: Notes on Disney Numerology by Luca Boschi

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