An attribute opening is an idempotent, anti-extensive and increasing operator that removes, in the case of binary images, all the connected components (CC) which do not fulfil a given criterion. When the increasingness property is dropped, more general algebraic thinnings are obtained. We propose in this paper, to use criteria based on the geodesic diameter to build algebraic thinnings for greyscale images. An application to the extraction of cracks is then given to illustrate the performance of the proposed filters. Finally, we will discuss the advantages of these new operators compared to other methods.