Algorithm

Next: Remarks Up: Inpainting Previous: Asymptotic expansion Contents

The inpainting algorithm is then the following:

$\bullet$

Calculation of

and

, solutions of the direct problems (2.11) and (2.12) respectively, without any inserted crack (unperturbed problem: $\sigma=\emptyset$ ).

$\bullet$

Calculation of

and

the two corresponding adjoint states, respectively solutions of equations (2.16) and (2.17).

$\bullet$

Computation of the matrix

defined by equation (2.19).

$\bullet$

Localization of the cracks: define

$\displaystyle \sigma=\{x\in\omega; \lambda_{min}(M(x)) < \delta < 0\},$

(2.20)

where $\delta$ is a negative threshold.

$\bullet$

Calculation of the solution of the Neumann problem (2.12) perturbed by the insertion of $\sigma$ .

This image is then equal to the original image in $\Omega\backslash\omega$ , and it has been reconstructed in $\omega$ .

Back to home page