Mathematical Optimization in Graphics and Vision - Luiz Velho - Impa

1.2. MATHEMATICAL MODELING AND ABSTRACTION PARADIGMS 9
of the y-axis, and take the cartesian product of both partitions to obtain the grid of
points
(x i , y j ), i = 1, . . . , n, j = 1, . . . , m
in the plane as depicted in Figure 1.6. In each vertex (x i , y j ) of the grid, we
take the value of the function z ij = f(x i , y j ) and the terrain representation if
defined by the height matrix (z ij ). This representation is called representation by
uniform sampling because we take the vertices of a uniform grid and we sample
the function at these points. The implementation can be easily attained using a
matrix as a data structure.
Figure 1.6: A grid on the function domain.
1.2.2 Image representation
Now we will consider the problem of image modeling. We will take a photograph
as the image model in the real world. This physical image model is characterized
by two properties:
• it has a support set (a rectangular piece of paper);
• there is a color attribute associated to each point of the support set.