# The two curves are characterized by scatterers whose

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TO APPEAR IN IEEE TRANS. GEOSCI. REMOTE SENS. 10 matrices are given in . We present their corresponding Kennaugh matrix forms using (3) as provided below, K I = 2 m +1 2 0 0 0 1 2 0 0 0 0 1 2 0 0 0 0 2 m - 1 2 0 m 1 , K II = 2 m +1 2 0 0 0 1 - 2 m 2 0 0 0 0 2 m - 1 2 0 0 0 0 2 m +1 2 0 m 0 . 5 , K III = 2 m +1 2 0 0 0 2 m - 1 2 0 0 0 0 2 m - 1 2 0 0 0 0 3 - 2 m 2 0 . 5 m 1 . (34) The curve I, which bounds the scatter plot from below, in particular, is called the azimuthal symmetry curve. We compute P GD GD values for these scatterers and trace the curves (shown in black) within the scatter plot plane in Fig. 8. The azimuthal symmetry curve fits tightly with the scatter plot as it is derived from a purely physical consideration. Nevertheless, the delimiting curve in P GD GD plane is distinct from that in the H/α plane. Firstly, the direction of the curve is reversed. This is because the physical depolarizers satisfying the Fry-Kattawar equation (21), which also includes coherent scatterers, all of which have a value of P GD = 1 . Secondly, the P GD has a lower bound for the physical depolar- izers, for which P GD = 0 . 25 . Thus, the zone with P GD < 0 . 25 is never realized. This lower bound is achieved for the endpoint of the curve I evaluated for m = 1 whose Kennaugh matrix is given as, K = 3 2 0 0 0 0 1 2 0 0 0 0 1 2 0 0 0 0 1 2 , for which the corresponding coherency matrix is given by T = 1 0 0 0 1 0 0 0 1 . Thus, it is the case of degenerate eigenvalues with eigenvalue 1 of multiplicity 3 . This also corresponds to the point of maximum entropy i.e., H = 1 in the H/α plane. This unique point in P GD GD scatter plot is characterized by P GD = 0 . 25 and α GD = 90 × cos - 1 (1 / 3) 54 . 7356 . B. Interpretation of the Classes In our interpretation of the classes, the scattering be- havior is determined by α GD , while P GD determines the purity/depolarizing nature of scattering. Table III identi- fies the classes with the segments from α GD and P GD . Under this classification scheme, each pair starting from (1 , 2) , (3 , 4) , (5 , 6) and (7 , 8) belongs to the same zone of α GD which is the proxy for scattering-type as given in Table II. (a) P GD α GD segmentation (b) P GD α GD segmentation (c) RS-2 segmentation map (d) ALOS-2 segmentation map Fig. 8: Unsupervised classification using P GD and α GD The even-numbered class within each pair is purer or less depolarizing than the odd-numbered class. Classes 1 and 2 discriminate the sea from land. Vegetation areas mostly belong to class 3 because it is characterized as a distributed scatterer, and hence majorly depolarizing. Urban areas oriented about the radar LoS and those perpendicular are identified in class 5 and 6 . Class 7 is practically absent because the corresponding α GD segment is very narrow, i.e., [80 , 90 ] and contains mostly pure scatterers viz., narrow dihedral and dihedral, hence, P GD > 0 . 5 . VI. A G ENERIC S CATTERING P OWER F ACTORIZATION F RAMEWORK In this section, we discuss a novel framework to obtain the scattering power components using the order of dominance of similarity to known scattering models in PolSAR literature.
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