
Laplace and Poisson 109
This system can be solved by using a sparse linear solver, such as
the ones discussed in Chapter 6.
As you have probably noticed, the linear equation system we
have described above has no notion of the fact that the missing
values all lie on scattered lines. That is, the same system also
solves the image completion problem described in Equation (7.5).
Image operations by Poisson equations
After we saw the usage of the Laplace equation for image comple-
tion, in this section we will examine several more applications of
the Laplace and Poisson equations in the image domain.
Poisson image editing. In many situations, we would like ...