
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 twoway 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.

