Multi-compartment models (MCM) are increasingly used to characterize the brain white matter microstructure from diffusion-weighted imaging (DWI). Their use in clinical studies is however limited by the inability to resample an MCM image towards a common reference frame, or to construct atlases from such brain microstructure models. We propose to solve this problem by first identifying that these two tasks amount to the same problem. We propose to tackle it by viewing it as a simplification problem, solved thanks to spectral clustering and the definition of semi-metrics between several usual compartments encountered in the MCM literature. This generic framework is evaluated for two models: the multi-tensor model where individual fibers are modeled as individual tensors and the diffusion direction imaging (DDI) model that differentiates intra- and extra-axonal components of each fiber. Results on simulated data, simulated transformations and real data show the ability of our method to well interpolate MCM images of these types. We finally present as an application an MCM template of normal controls constructed using our approach.