Polarization imaging and Mueller polarimetry provide powerful tools for probing the microstructure of complex anisotropic media, which is a core task in material science, biomedical diagnosis and many research fields. However, Mueller matrix elements and many polarization parameters are sensitive to the spatial orientation of the sample and experimental configurations, hindering the effectiveness for distinguishing different sources of anisotropies. In this paper, we propose a set of rotation invariant parameters and corresponding orientation parameters, which are explicit functions of the Mueller matrix elements. They are valid under the condition that the illumination and detection directions are collinear with the rotation axis of the sample. More detailed examinations show that these parameters have potential applications for fast analyzing different anisotropy contributions in the media, such as birefringence, dichroism, and their coexistence. The conclusions are validated with Monte Carlo simulations and the experimental results of transparent tape samples.