Numerical Simulation of Targets Deorientation and Its Application to Unsupervised Classification in Polarimetric SAR Images

Deorienation theory of polarimetric scattering targets is developed, which transforms the spatially oriented targets into a certain orientation or status, to show the prominence of the generic characteristics of scattering targets. A new set of the parameters u, v, w, ψ is defined and used to describe and classify different targets. Based on the vector radiative transfer (VRT) model of non-spherical particles above rough surface, numerical simulations illustrate the parameters u, v, w, ψ and the entropy H . These parameters are applied to the unsupervised classification in polarimetric images. An AirSAR polarimetric image over Canada’s Boreal district is classified into 8 classes and orientation-analyzed. Introduction In recent years, numerous methods of polarimetric scattering analysis are developed [1-3]. The target decomposition theory [3] proposed an unsupervised classification scheme for the terrain surfaces using the entropy H and target decomposition parameter α extracted from polarimetric SAR data. In this paper, we introduce the deorientation concept in order to reduce the influence of randomly fluctuating orientation and show the prominence of the characteristics of the scatter targets for surface classification. Based on our deorientated classification, a detailed target orientation, orderly or randomly, and classification of the scatter targets can be obtained. By transforming the target into a certain state with minimization of crosspolarization (min-x-pol), the angle ψ is extracted to indicate target’s orientation, and further a new parameterization is applied to the principal eigenvector of the coherency matrix, through which new parameters u, v, w are defined as well as the entropy H . Numerical simulations of polarimetric scattering of a single small non-spherical particle are analyzed to illustrate the relationships between the physical properties e.g. the Euler angles, shape, dielectricity etc. and the parameters u, v, ψ. As a vector radiative transfer (VRT) model, polarimetric scattering from a layer of random non-spherical particles above a rough surface is studied to show the effectiveness of the parameters u, v, ψ, H for classification of complex terrain surfaces. A new unsupervised classification scheme based on deorientation theory is applied to an AirSAR image over Canada Boreal forests and further orientation-analysis is conducted, through which further discrimination over some easily-confused surface types and detailed description of the terrain target orientations are achieved. Deorientation and Parameterization Consider a rotation of target’s orientation along the sight line by angle ψ, the Pauli vectorized [3] scattering vector kp become k′ p, which can be expressed as   cosα′ejφ ′ 1 sinα′ cosβ′ejφ ′ 2 sinα′ sinβ′ejφ ′ 3   =   cosα · e1 sin ( cos 2ψ cosβ + sin 2ψ sinβ · ej(φ3−φ2) ) · e2 sinα ( − sin 2ψ cosβ + cos 2ψ sinβ · ej(φ3−φ2) ) · e2   , (1) where the parameters with subscript x’ are the corresponding parameters after rotation. By applying the minimization of cross polarization (min-x-pol) to k′ p, i.e. min ψ ∣k′ p,3 ∣∣ ∣∣k′ p ∣∣∣∣ = min ψ ∣∣sinα ( − sin 2ψ cosβ + cos 2ψ sinβ · ej(φ3−φ2) ) · e2 ∣∣ . (2) Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 365 The deorientation angle ψm is obtained as ψm = [ sgn{(φ2 − φ3)} 2β − [2β]π + [tan−1{tan 2β| cos(φ2 − φ3)|}]π 4 ]

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