From the numerical point of view, cracks are modeled by a very small conductivity instead of considering real holes in the domain. The previous algorithm has a complexity of
, where 
is the size of the image, i.e. the number of pixels, as explained in section 2.7.
The main advantage of this algorithm is that the reconstruction is done in only one iteration of the topological gradient algorithm, which consists of 
resolutions of a PDE (the two direct and two adjoint unperturbed problems, and then one direct perturbed problem) in the domain 
representing the image. Several numerical results are presented in [26] and show the quality and efficiency of the reconstruction.
The only control parameter of this method is the negative threshold: below a given value, the pixels are considered as being part of the edge set, whereas it is not the case beyond the threshold. The reconstructed image is provided by the resolution of the direct perturbed problem (2.12), and the quality of the image relies on the connexity of the identified edges. If a given identified edge is not connex, the Laplacian indeed produces a blurred zone. Then, the threshold is usually set such that the main identified edges are connex. Of course, it may lead to the wrong identification of edges. But the various numerical experiments have shown that the threshold can be fixed to an a priori value, as the optimal threshold is almost independent of the images.
Another solution to this problem is presented in section 2.8.