An attribute opening is an idempotent, anti-extensive and increasing operator, which removes from an image connected components which do not fulfil a given criterion. When the increasingness property is dropped, we obtain a - more general - attribute thinning. In this paper, we propose efficient grey scale thinnings based on geodesic attributes. Given that the geodesic diameter is time consuming, we propose a new geodesic attribute, the barycentric diameter to speed up the computation time. Then, we give the theoretical error bound between these two attributes, and we note that in practice, the barycentric diameter gives very similar results in comparison with the geodesic diameter. Finally, we present the algorithm with further optimisations, to obtain a 60× speed up. We illustrate the use of these thinnings in automated non-destructive material inspection: the detection of cracks. We discuss the advantages of these operators over other methods such as path openings or the supremum of openings with segments.