Revisiting the generalized polar decomposition of Mueller matrices

Mueller polarimetry is a powerful imaging modality that has been successfully applied to various application fields. Decomposition of Mueller matrices in elementary components is classically considered in order to unfold complex physical phenomena taking place in probed samples or scenes. In this context, the generalized polar decomposition, also known as Lu and Chipman decomposition, plays a prominent role. In this paper, we show that the set of candidate generalized polar decompositions is richer than the set used so far. Negative-determinant Mueller matrices are naturally addressed in the proposed framework. We show that taking into account those supplementary polar decompositions addresses issues raised in the literature. Application is carried out on synthetic and on measured Mueller matrices.