We presented in this chapter many applications in image processing of the crack detection technique, based on the topological gradient. It provides an excellent frame for solving all these image processing problems. It has been successfully applied to image inpainting, restoration, classification and segmentation. In all these cases, we obtain excellent results and the computing time is very small.
We have also seen that this technique can be applied to color images as well as grey-level images, but also three-dimensional images, or movies, without any trouble. The theoretical complexity, confirmed by numerical experiments, allows us to process movies in nearly real time (on a dual-processor laptop, with a c++ code).
Another interesting point is that all these algorithms rely on the same kernel, as we always solve the same kind of PDE problems. This makes the implementation much more easy.
Several perspectives are currently under study. We can cite here the possibility of taking into account higher order differential operators, with the aim of a better reconstruction of the gradient of the image. For instance, in the case of inpainting problems, the inpainted image is piecewise affine. With the same kind of approach, we should be able to reconstruct more precisely the gradient of the image, and then the image itself.