For most issues encountered in materials sciences and in geosciences, X-ray microtomography is an efficient technique to obtain morphological, structural, and topological information on complex multiphasic materials. However the seg-mentation of three-dimensional images of these materials is rarely straightforward. For instance, the segmentation processes that are used are strongly dependant on the quality of the images, the samples and the objects or phases of interest to extract. In this study a variational method which is a versatile technique enabling to segment a lot of three-dimensional images of geomaterials has been developed. This technique is illustrated with two case studies belonging to two distinct fields of research in earth sciences. In one case the crack network of a weathered granite sample is considered, while, in the other, the distributions of the mineralogical phases on an ore sample are investigated.