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We propose a generic Scattering Power Factorization Framework (SPFF) forPolarimetric Synthetic Aperture Radar (PolSAR) data to directly obtain $N$scattering power components along with a residue power component for eachpixel. Each scattering power component is factorized into similarity (ordissimilarity) using elementary targets and a generalized random volume model.The similarity measure is derived using a geodesic distance between pairs of$4\times4$ real Kennaugh matrices. In standard model-based decompositionschemes, the $3\times3$ Hermitian positive semi-definite covariance (orcoherency) matrix is expressed as a weighted linear combination of scatteringtargets following a fixed hierarchical process. In contrast, under the proposedframework, a convex splitting of unity is performed to obtain the weights whilepreserving the dominance of the scattering components. The product of the totalpower (Span) with these weights provides the non-negative scattering powercomponents. Furthermore, the framework along the geodesic distance iseffectively used to obtain specific roll-invariant parameters which are thenutilized to design an unsupervised classification scheme. The SPFF, the rollinvariant parameters, and the classification results are assessed using C-bandRADARSAT-2 and L-band ALOS-2 images of San Francisco.

A PolSAR Scattering Power Factorization Framework and Novel  Roll-Invariant Parameters Based Unsupervised Classification Scheme Using a  Geodesic Distance