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

TL;DR

This work introduces a Geodesic-Distance (GD) based Scattering Power Factorization Framework (SPFF) for PolSAR data, enabling direct, nonnegative decomposition of Span into multiple scattering powers by measuring similarity to elementary models via a unit-sphere Kennaugh distance. It also defines three roll-invariant parameters—$\alpha_{GD}$, $\tau_{GD}$, and $P_{GD}$—derived from GD, and demonstrates their utility for unsupervised classification and scattering-zone identification. The framework is shown to be flexible across data representations, invariant to Span and basis changes, and capable of integrating a generalized volume model; results on RS-2 and ALOS-2 San Francisco scenes illustrate improved discriminability for urban, vegetation, sea, and mixed zones and capture temporal-band differences. Overall, the approach provides a scalable, interpretable, and extensible toolkit for PolSAR target analysis and scene understanding with direct power partitioning and roll-invariant classification cues.

Abstract

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.

Figures (12)

• Figure 1: Pauli RGB images of RS-2 C-band (on left) and ALOS-2 L-band (on right) acquisition over San Francisco.
• Figure 2: Parameter values for proposed and existing parameters for RS-2 C-Band SF Image
• Figure 3: Parameter values for proposed and existing parameters for ALOS-2 L-band SF Image
• Figure 4: Profile of roll-invariant parameters computed along particular transects in the RS-2 and the ALOS-2 SF images
• Figure 5: Histograms for $\alpha_{GD}$ and $\tau_{GD}$ for different scattering zones for RS-2 and ALOS-2 SF images.