TO APPEAR IN IEEE TRANS. GEOSCI. REMOTE SENS.10matrices are given in . We present their correspondingKennaugh matrix forms using (3) as provided below,KI=2m+120001200001200002m-120≤m≤1,KII=2m+120001-2m200002m-1200002m+120≤m≤0.5,KIII=2m+120002m-1200002m-1200003-2m20.5≤m≤1.(34)The curve I, which bounds the scatter plot from below,in particular, is called the azimuthal symmetry curve. WecomputePGD/αGDvalues for these scatterers and trace thecurves (shown in black) within the scatter plot plane in Fig. 8.The azimuthal symmetry curve fits tightly with the scatter plotas it is derived from a purely physical consideration.Nevertheless, the delimiting curve inPGD/αGDplane isdistinct from that in theH/αplane. Firstly, the direction ofthe curve is reversed. This is because the physical depolarizerssatisfying the Fry-Kattawar equation (21), which also includescoherent scatterers, all of which have a value ofPGD= 1.Secondly, thePGDhas a lower bound for the physical depolar-izers, for whichPGD= 0.25. Thus, the zone withPGD<0.25is never realized. This lower bound is achieved for the endpointof the curve I evaluated form= 1whose Kennaugh matrixis given as,K=32000012000012000012,for which the corresponding coherency matrix is given byT=100010001.Thus, it is the case of degenerate eigenvalues with eigenvalue1of multiplicity3. This also corresponds to the point ofmaximum entropy i.e.,H=1in theH/αplane. Thisunique point inPGD/αGDscatter plot is characterized byPGD= 0.25andαGD= 90◦×cos-1(1/√3)≈54.7356◦.B. Interpretation of the ClassesIn our interpretation of the classes, the scattering be-havior is determined byαGD, whilePGDdetermines thepurity/depolarizingnatureofscattering.TableIIIidenti-fies the classes with the segments fromαGDandPGD.Under this classification scheme, each pair starting from(1,2),(3,4),(5,6)and(7,8)belongs to the same zone ofαGDwhich is the proxy for scattering-type as given in Table II.(a)PGD–αGDsegmentation(b)PGD–αGDsegmentation(c) RS-2 segmentation map(d) ALOS-2 segmentation mapFig. 8: Unsupervised classification usingPGDandαGDThe even-numbered class within each pair is purer or lessdepolarizing than the odd-numbered class.Classes1and2discriminate the sea from land. Vegetationareas mostly belong to class3because it is characterized asa distributed scatterer, and hence majorly depolarizing. Urbanareas oriented about the radar LoS and those perpendicular areidentified in class5and6. Class7is practically absent becausethe correspondingαGDsegment is very narrow, i.e.,[80◦,90◦]and contains mostly pure scatterers viz., narrow dihedral anddihedral, hence,PGD>0.5.VI. A GENERICSCATTERINGPOWERFACTORIZATIONFRAMEWORKIn this section, we discuss a novel framework to obtain thescattering power components using the order of dominance ofsimilarity to known scattering models in PolSAR literature.