This paper explains a new method of extracting polarimetric data from a Mueller matrix. Indeed, the main difficulty of this formalism lies in the extraction of the polarimetric coefficients and their relation to the physical properties of the medium observed. Therefore, a method enabling this extraction and optimizing the results in 1D as well as in imaging is proposed here. Each matrix can be decomposed into a product of three “optical properties matrices”. Due to the non-commutative matrices product, each matrix can be decomposed into several decompositions. The criteria for a general decomposition in 1D will first be examined before moving onto images showing that the commutation in the decomposition can be used to filter optical properties in 2D.