Mathematical optimization in computer graphics and vision
Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in th...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier / Morgan Kaufmann Publishers
c2008.
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| Edición: | 1st edition |
| Colección: | The Morgan Kaufmann Series in Computer Graphics
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627633206719 |
Tabla de Contenidos:
- Front Cover; Mathematical Optimization in Computer Graphics and Vision; Copyright Page; Table of Contents; List of Figures; Preface; Acknowledgments; Chapter 1. Computer Graphics; 1.1 What is Computer Graphics?; 1.1.1 Related Areas; 1.1.2 Is There Something Missing?; 1.2 Mathematical Modeling and Abstraction Paradigms; 1.2.1 Terrain Representation; 1.2.2 Image Representation; 1.3 Graphical Objects; 1.3.1 Revisiting the Diagram; 1.4 Description, Representation, and Reconstruction; 1.4.1 Description; 1.4.2 Representation; 1.4.3 Reconstruction; 1.4.4 Semantics and Reconstruction
- 1.5 Comments and ReferencesBibliography; Chapter 2. Optimization: An Overview; 2.1 What is Optimization?; 2.1.1 Classification of Optimization Problems; 2.2 Classification Based on the Nature of Solution; 2.2.1 Continuous Optimization Problems; 2.2.2 Discrete Optimization Problems; 2.2.3 Combinatorial Optimization Problems; 2.2.4 Variational Optimization Problems; 2.3 Other Classifications; 2.3.1 Classification Based on Constraints; 2.3.2 Classification Based on the Objective Function; Linear Programs; 2.4 The Problem of Posing Problems; 2.4.1 Well-Posed Problems; 2.4.2 Problem Reduction
- 2.5 How to Solve It?2.5.1 Global Versus Local Solutions; 2.5.2 NP3-Complete Problems; 2.6 Comments and References; Bibliography; Chapter 3. Optimization and Computer Graphics; 3.1 A Unified View of Computer Graphics Problems; 3.1.1 The Classification Problem; 3.2 Geometric Modeling; 3.2.1 Model Reconstruction; 3.3 Visualization; 3.4 Computer Vision; 3.5 The Virtual Camera; 3.5.1 Camera Specification; 3.6 Image Processing; 3.6.1 Warping and Morphing; 3.7 Image Analysis; 3.7.1 Edge Detection; 3.7.2 Character Recognition; 3.8 Animation and Video; 3.9 Comments and References; Bibliography
- Chapter 4. Variational Optimization4.1 Variational Problems; 4.1.1 Solve the Variational Problem Directly; 4.1.2 Reduce to a Continuous Optimization Problem; 4.1.3 Reduce to a Discrete Optimization Problem; 4.2 Applications in Computer Graphics; 4.2.1 Variational Modeling of Curves; 4.3 Comments and References; Bibliography; Chapter 5. Continuous Optimization; 5.1 Optimality Conditions; 5.1.1 Convexity and Global Minima; 5.2 Least Squares; 5.2.1 Solving Least Squares Problems; 5.3 Algorithms; 5.3.1 Newton's Method; 5.3.2 Unidimensional Search Algorithms; 5.3.3 Conjugate Gradient
- 5.3.4 Quasi-Newton Algorithms5.3.5 The Levenberg-Marquardt Algorithm; 5.4 Constrained Optimization; 5.4.1 Optimality Conditions; 5.4.2 Least Squares with Linear Constraints; 5.4.3 Algorithms; Penalty and Barrier Methods; Projected Gradient Methods; 5.5 Linear Programming; 5.5.1 Simplex Algorithm for Linear Programs; 5.5.2 The Complexity of the Simplex Method; 5.6 Applications in Graphics; 5.6.1 Camera Calibration; 5.6.2 Registration and Color Correction for a Sequence of Images; 5.6.3 Visibility for Real-Time Walk-Through; 5.7 Comments and References; Bibliography
- Chapter 6. Combinatorial Optimization
