The retrieval of a volumetric defect (singly- or multiply-connected) affecting the wall of a hollow metal tube is investigated from measurements of variations of impedances of an inner probe. Both non-ferromagnetic and ferromagnetic materials are taken into account in view of potential applications. This inverse problem is modeled as the estimation of the shape of a volumetric void defect and then becomes a binary one, solved by properly adapted techniques, two of them analyzed herein: a conjugate-gradient-type one, and a level-set-type one, the performances of which are illustrated by simulations in various configurations.