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Mathematical Optimization in Graphics and Vision: Paulo Cezar Pinto Carvalho, Luiz Henrique de Figueiredo, Jonas de Miranda
What is computer graphics?
The usual definition for computer graphics is the following: a set of models, methods and techniques to transform data into images that are displayed in a graphics device. The attempt to define an area is a difficult, if not impossible, task. Instead of trying to devise a good definition, perhaps the best way to understand an area is through a deep knowledge of its problems and the methods to solve them. From this point of view, the definition above has the virtue of emphasizing a fundamental problem of computer graphics, that is: the transformation of data into images.
In applied mathematics, the solution of problems is directly related with the mathematical models used to understand and pose the problem. For this reason, the dividing line between solved and open problems is more subtle than in the case of pure mathematics. In fact, in pure mathematics different solutions to the same problem, in general, do not constitute great innovations from the scientific point of view; on the other hand, in applied mathematics, different solutions to the same problem as consequence of the use of different models, usually bring a significant advance in terms of applications.
This book discusses the solution of various problems in computer graphics using optimization techniques. The underlying idea is to serve as a two-way channel: on one hand, stimulate the computer graphics community to study optimization methods; and on the other hand, call attention of the optimization community for the extremely interesting real world problems in computer graphics.
Since its origin, computer graphics is concerned with the study of models, methods and techniques that allow the visualization of information using a computer. Because, in practice, there is no limitation to the origin or nature of the data, computer graphics is used today by researchers and users from many different areas of human activity.