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 × 4 real Kennaugh matrices. In standard model-based decomposition schemes, the 3 × 3 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.T ARGET decomposition (TD) theorems are an essential avenue of research in the study of Polarimetric Synthetic Aperture Radar (PolSAR) imagery. In this context, the study of light scattering by small anisotropic particles by Chandrasekhar [1] was the first instance of a TD. Later, Huynen [2] rigorously formulated this notion and laid the foundations of the modern day TDs.According to Huynen, the objective of TD is to identify the average scattering mechanism within the pixel in the form of a rank-1 covariance/coherency matrix. The interpretation of this information is achieved by obtaining a set of unique parameters often roll-invariant in nature for a description of the target under study. On the one hand, this approach is utilized in the eigenvalue/eigenvector based decomposition schemes. On the other hand, model-based decompositions interpret the observation as a weighted linear combination of specific scattering mechanisms. In the later, the scattering components can be rank-1 or distributed (rank ≥ 1, e.g. volume scattering models) targets [3].The extraction of a desirable rank-1 (pure or coherent) target is often synonymous with the most dominant scattering mechanism component from the observation [4]. However, retaining all the components (in decreasing order of dominance) is more useful for a complete and more realistic characterization of the target. This task is leveraged for better interpretation of the observation by model-based decompositions [5], [6], and for uniqueness, by the eigenvalue-eigenvector based decompositions [7], [8].Recently, Xu et al.[9] brought together rank-1 PolSAR decomposition, model-based decomposition, and image clustering under the single umbrella of image factorization...