Synopsis:
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 their work.
Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today.
- Distills down a vast and complex world of information on optimization into one short, self-contained volume especially for computer graphics
- Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application
- Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments
Mathematical Optimization of Computer Graphics and Vision
Luiz Velho, Paulo Cezar Pinto Carvalho,
Jonas Gomes, Luiz Henrique de Figueiredo
Mathematical optimization is deeply pervasive in the vast majority of graphical applications. To study all available methodologies would be the work of a lifetime, however, there is a core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work.
This authoritative reference is a consolidated guide to the seminal techniques of mathematical optimization as applied to computer graphics and vision.
It provides a conceptual overview of the key problems in computer graphics and explains the core mathematical models that can be used to solve them, demonstrating their pivotal importance.
It aids readers in finding the right optimization technique for a specific application by providing combinatorial, continuous, variational, and global optimization methods for applications including:
Camera Calibration
Color Correction
Geometric Modeling
Animation
Visualization
Coding and Compression
Image Processing
Computer Vision
Image and Color Quantization
Level of Detail Computation
Interactive Visualization
Minimum Paths in Maps
Surface Reconstruction from Sections
Algorithms, such as Newton methods, linear programming, conjugate gradient and sequential quadratic programming, Dijkstra, and Branch-and-bound, are explained alongside strategies for devising good algorithms. Special emphasis is given to the subtle relationships between probability theory and mathematical optimization. Cutting-edge research is discussed in a section at the end of every chapter, accompanied by targeted references to further reading.
Professionals exploring computer vision, geometric modeling, visualization, animation, and image processing will all benefit from the insights of the authors, who are renowned researchers from IMPA, the Brazilian National Institute for Pure, and Applied Mathematics.
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