Magnetic resonance imaging and relaxation analysis are combined in a spatially resolved technique (relaxation tomography), which is able to quantify the parameters connected to the local structure in the internal regions of a porous material saturated by water, giving information on the pore space structure beyond the nominal instrumental resolution. Voxel-by-voxel longitudinal (T1) and transverse (T2) relaxation curves are acquired in order to obtain T1, T2 and S(0) maps, where S(0) is the extrapolation to zero time of the total equilibrium magnetization corrected for T2 decay. The proposed method permits evaluation of the porosity (ratio of pore space to total volume), at different length scales, from the sample to the voxel, not all achievable by traditional methods. More striking is its ability to describe how porosity is shared among different classes of surface-to-volume ratios of diffusion cells (the regions that the individual water molecules, starting at their particular positions, can experience by diffusion before relaxing). This is a consequence of the fact that relaxation times of water confined in a porous material can, under favorable circumstances, distinguish regions with the same local porosity but with different pore sizes and connections. So, parameters can be introduced, such as the microporosity fraction, defined as the fraction of the “micropore” volume with respect to the total pore volume, and several voxel average porosities, defined as the average porosities of the voxels characterized by particular classes of diffusion cells. Moreover, the imaging methods enable us to get all this information in a user-defined region of interest. The method has been applied to quantify changes in the structure of carbonate cores with wide distributions of pore sizes induced by repeated cycles of freezing and heating of the sample. With freezing, the microporosity fraction decreases significantly; the voxel average porosity of voxels with T1 shorter than for free water tend to decrease; and the distributions of porosity as functions of T1 show a trend, with much more signal with the T1 of free water, in accordance with the picture suggesting large vugs breaking, with fractures contributing to homogenizing the structure of the pore space and favoring coupling between neighboring pores. © 2001 American Institute of Physics.