  We propose a generic Scattering Power Factorization Framework (SPFF) for
Polarimetric Synthetic Aperture Radar (PolSAR) data to directly obtain $N$
scattering power components along with a residue power component for each
pixel. Each scattering power component is factorized into similarity (or
dissimilarity) 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 decomposition
schemes, the $3\times3$ Hermitian positive semi-definite covariance (or
coherency) matrix is expressed as a weighted linear combination of scattering
targets following a fixed hierarchical process. In contrast, under the proposed
framework, a convex splitting of unity is performed to obtain the weights while
preserving the dominance of the scattering components. The product of the total
power (Span) with these weights provides the non-negative scattering power
components. Furthermore, the framework along the geodesic distance is
effectively used to obtain specific roll-invariant parameters which are then
utilized to design an unsupervised classification scheme. The SPFF, the roll
invariant parameters, and the classification results are assessed using C-band
RADARSAT-2 and L-band ALOS-2 images of San Francisco.
