Modern estimation of rock properties combines imaging with advanced numerical simulations, an approach known as digital rock physics (DRP). In this paper we suggest a specific segmentation procedure of X-ray micro-computed tomography data with two different resolutions in the µm range for two sets of carbonate rock samples. These carbonates were already characterized in detail in a previous laboratory study which we complement with nanoindentation experiments (for local elastic properties). In a first step a non-local mean filter is applied to the raw image data. We then apply different thresholds to identify pores and solid phases. Because of a non-neglectable amount of unresolved microporosity (micritic phase) we also define intermediate threshold values for distinct phases. Based on this segmentation we determine porosity-dependent values for effective P- and S-wave velocities as well as for the intrinsic permeability. For effective velocities we confirm an observed two-phase trend reported in another study using a different carbonate data set. As an upscaling approach we use this two-phase trend as an effective medium approach to estimate the porosity-dependent elastic properties of the micritic phase for the low-resolution images. The porosity measured in the laboratory is then used to predict the effective rock properties from the observed trends for a comparison with experimental data. The two-phase trend can be regarded as an upper bound for elastic properties; the use of the two-phase trend for low-resolution images led to a good estimate for a lower bound of effective elastic properties. Anisotropy is observed for some of the considered subvolumes, but seems to be insignificant for the analysed rocks at the DRP scale. Because of the complexity of carbonates we suggest using DRP as a complementary tool for rock characterization in addition to classical experimental methods.