Supervised Baysian SAR iage Classification Using The Full Polarietric Data (1) () Ziad BELHADJ (1) SUPCOM, Route de Raoued 3.5 083 El Ghazala - TUNSA () ENT, BP. 37, 100 Tunis Belvedere, TUNSA Abstract Supervised classification procedures are developed and applied to synthetic aperture radar (SAR) in order to identify their various earth terrain coponents. An ipleentation of the axiu a posteriori (MAP) and the axiu likelihood (ML) algoriths are presented. These two techniques need a statistic odel for the conditional distribution of the polarietric coplex data. Many previous studies used the classical Rayleigh distribution to characterize the earth terrain, but this odel doesn t yield a good result for heterogeneous backscattering edia. This study applies a new odel based on the -distribution. This distribution, based on the physical definition of the texture and its atheatical representation, will be shown as rigorous odel to describe aplitudes and intensities of the backscattering signal. We also use Markov fields to enhance the results of the classifications. These classification procedures have been applied to the Flevoland site (Holland) and Landes forest (France) SAR iages, supplied by the Jet Propulsion Laboratory. ey-words : SAR ages, Supervised Classification, -distribution, Markov Rando Field. ntroduction Classification of earth terrain in SAR iage is one of the any iportant applications of polarietric data. We will present a survey on the different techniques of classifications of polarietric data: the axiu a posteriori (MAP) and the axiu likelihood (ML) algoriths. The first stage of the classification is the odeling of the radar echo. t consists of finding distribution laws that describe well the aplitudes and the absolute intensities of the backscattering signal. Certainly Gaussian odels are often used to characterize the observed regions, however, they are not always able to represent the reality of the land for heterogeneous regions: forest, heat... The distribution, based on the physical definition of the texture and its atheatical representation, will be shown as rigorous odel to describe aplitudes and the absolute intensities of the backscattering signal, that can fitto the hoogeneous and heterogeneous regions at the sae tie. n a second level, we will present the distribution and we will prove the good odeling of this distribution in the different regions of iaged scene. n any situations, radar polarietric data are provided under shape of atrix of Muller or ulti look covariance to reduce the volue of data or to iniize the presence of the speckle. We will spread the distribution laws fro one look to ulti look case, as well as the notion of the equivalent nuber of views. At the end of this work, we will present a technique of iproveent of results of the classification. t is about the iproveent by Markov fields n this paper, both MAP and ML classification techniques will be used in classification of fully polarietric synthetic aperture radar iage. Two iages are used: The first was collected at P band fro Flevoland forest (Holland). They are 186 pixels in the range and 56 in the aziuth with a 5 by 5- resolution by pixel. The second is a C band iage representing Land forest (France) they are 445 pixels in the range and 1970 in the
aziuth. The first iage is 4 look iage; the second is one look iage.. Classification procedures Our paper deals with the supervised techniques of classification. We will present the Bayes classifier and the axiu likelihood classification. The first stage of the application of these algoriths is the choice of the odel characterizing the land. n the statistical approach of the supervised classification, each pixel is considered as the realization of a certain vector. The distribution of this vector is defined as characteristic of the density function of the class to which it belongs. ndeed, every class of the land is described by a law of probability that describes the possibility that a given pixel belongs to this class or no. Consequently, the description of the picture derives fro paraeters of the law that odels the land. We will copare the yields results with using Gaussian odel and the distribution The characteristic vector of the atrix of diffusion of a pixel is given: HH X = HV where HH = HH exp(iφhh ) (.1) VV HH and φ HH are respectively the aplitude and the phase of the electroagnetic return at the HH polarization..1 Bayes classifier MAP (axiu a prior) Bayes defined the general criteria that perits to optiize the probability of success in the classification of the radar iage: - w i ) is the probability of occurrence of the class i - X/ w i ) the conditional probability of the vector X, held account that the class i is kept a priori. - w i / X ) the conditional probability of the class i, held account that X is kept a priori. This probability is also called Likelihood []. - X ) the probability so that X occurs A vector X belongs to class wi if the probability of X belongs to wi is bigger than the probability that X belongs to the other classes. wi / X ) w j / X ) for all j i (.3) While applying the Bayes law: X / wi) w ) X / w ) w ) i j j for all j i (.4) X ) X ) nowing w i ) and X/ w i ) we can apply the algorith of classification pixel by pixel.. Maxiu Likelihood (ML) classification The axiu Likelihood classification consists in axiizing the probability X/w i ). Says otherwise, a pixel possessing a polarietric vector X is classified in class wi if only: X/ω i ) = ax { X/ω j ) j = 1, N} (.5) N is the total nuber of classes t is necessary to note that this technique of classification is a particular case of MAP classification. ndeed, while supposing that all classes have the sae probability of occurrence, MAP classification becoes the ML classification. For our survey, we chose two distributions to characterize the polarietric vector X = [HH HV VV]: the Gaussian distribution and the distribution. We present in the next section the statistic odel of the distribution and we will deonstrate that it can characterize the polarietric SAR data. 3. Statistic Model For - Distribution The aplitude of the radar signal can be described by a Rayleigh distribution. However, any recent studies showed that this representation is valid only for the hoogeneous regions and often fails for heterogeneous backscattering edia [1].Several other odels have been experiented to represent the land cover. Aong these odels, the distribution sees to be very efficient to characterize the different types of lands: hoogeneous and heterogeneous. The distribution has been applied for the first tie in order to odel the radar echo by Jao in 1984. The choice of this distribution rests on a atheatical basis and assigning it a physical signification. ndeed, it is the result of the presence of the speckle and the texture in the radar iage []. t can be given by two ways: by a rando coherent anner of while supposing that the
nuber of distributor in a cell follows a negative binoial law [4], or in supposing that it is the product of a gaa distribution characterizing the texture and a Gaussian distribution characterizing the speckle. n one look case, the distribution of the aplitude of a signal is given by: b ba p( A) = ( ) 1( ) ( ) Γ ba (3.1) A represents the aplitude of every coponent of the polarietric vector, HH, HV, and VV. is the second order odified Bessel function with paraeter -1. b = where < A² is the intensity of the signal < A² n the case of a picture intensity iage, while putting =A²: b b p() = ( ) 1(b ) (3.) The expression of the aplitude noralized is: p 1+ 4 = ( An) An 1 ( An), An = A < A² (3.3) We notice that when the value of alpha increases, the curve of the distribution is confounded with the Rayleigh distribution. Fro this fact, we can say that the distribution of Rayleigh is a particular case of the distribution for the big values of alpha. Noralized aplitude < A = + 0 A A) da (3.5) These oents are given by [4]: + < A² / < A = ( ) ( / )! (3.6) The noralized aplitudes oent is: + ( ) A ( / )! = (3.7) / and the noralized intensity oent is: ( ) + = ( )! (3.8) Practically, noralized intensities oents are given by: ( ) E( HH ) HH = (3.9) E( HH ²) The order oent constitutes the siplest eans to appraise alpha, it is given by: () 1 1 = (1 + ) so = (3.10) () 1 The paraeter alpha is appraised for every polarietric channel. t is bound strongly to the nature of the constituent of the scene: age, density. () For values toward the infinity, tend to what corresponds at the two-order oent of the exponential distribution. Thus, For the hoogeneous regions ( big), the distribution tends toward Gaussian distribution. This affirs that the distribution doesn't characterize well that the hoogeneous regions and that the distribution is a ore general case that describes well all types of land [1]. Fig 1 PDF of the distribution for different values of copared to the Rayleigh distribution. The paraeter alpha of the distribution is esteeed fro oents of aplitudes or intensities noralized.
Fig. Adjustent of theoretical PDF of the - distribution to the experiental histogra. n the figue, the PDF of noralized aplitudes are plotted and copared to the experiental histogra of the Landes forest (=5.4) For ulti-look iages, the expression of noralized intensity is [1]: L+ L+ 1 = ( L Ln ) LN Γ Γ L ( L Ln ) ( ( L) (3.11) L Ln = < where L represents the nuber of look and Γis the gaa function. and the oent order are related by [1]: ( ) + L + L = (3.1) M L L) t is known that NASA/JPL ulti-look polarietric data are over sapled to get a size of the pixel finer than the spatial resolution. This situation produces an interrelationship between the neighbor pixels and generates a istake of evaluation paraeter [3]. We deonstrated by siple graphic visualization that the applied data histogras fit to the theoretical curves of the distribution better for a different nuber of looks (figure 3). This nuber will be naed equivalent nuber of looks (ENL). Fig.4 Results of ML classification using HH channel and Rayleigh distribution Fig.5 Results of ML classification using HH channel and -distribution ML MAP HH Vect HH Vect Water 60. 70.5 85 75. Forest 6, 67 83 85 Gras 60,6 90 90 79 Table1 probability of good classification using Gaussian distribution (Flevoland). ENL=4 ENL=3.1 Fig.6 Results of MAP classification using HH channel and -distribution Fig. 3 Adjustent of the PDF of noralized aplitudes 4. Results the experiental And Analysis histogra for two ENL ( Flevoland site)
Fig.7 Results of MAP classification using full polarietric data and -distribution ML MAP HH VECT HH Vect Water 80. 95.3 85.3 91.5 Forest 60 86.3 7.3 77.6 Gras 95 100 85.3 90.1 Table Probability of good classification using - distribution (Flevoland). classification in presence of a doinant or rare class. To illustrate the effect of fully polarietric data, supervised classifications were perfored using various polarietric channel and full polarietric data. t clearly appears, on coparing results of the classification that results obtained fro full polarietric data are better than the ones obtained fro one channel data. This shows the value of the inforation contained in full polarietric data. On the other hand, the distribution yields good results of classification. The yield iages are ore legible than those yielded by Gaussian odel. The probability of good classification is raised for the hoogeneous and heterogeneous zones. t affirs the good choice of the distribution that takes its origins fro the physical definition of the texture. 5. Enhanceent Of Classification By Markov Field: Fig.8 Results of ML classification using full polarietric data and -distribution. Gaussian distribution HH VECT HH VECT Tree 33-46 years 60. 77.5 75 90 Tree 1-5 years 57. 78.6 79.6 89. Table.3 Coparison of the probability of good classification using Gaussian distribution and - distribution (Land forest). Tables 1 and show that the error of Bays classification is saller than the ML classification, this is du to the fact that the ML technique does not account the probability of different class occurrences. This is can introduce istakes of The results of the classification aren t good in certain zones. These istakes are owed to the presence of the speckle in the radar iages and to the heterogeneity of the scene. Several techniques of iproveent of results of classification have been developed: contribution ulti frequency, fuzzy logic, Markov fields We chose the Markov fields ethod because it represents the atheatical interaction between the neighboring pixels. This inforation is rarely used in classification algoriths. t constitutes a suppleentary contribution to the inforation extracted fro the radar pictures. To iprove results of the classification of a pixel s, we can replace the conditional distribution of the polarietric vector Xs of s by the product of the conjoined conditional laws of whole polarietric vector restrained in a Ns neighborhood of s: X 1,..., X N s. This supposes that vectors are independent. This independence in law is due to the non-correlation of these vectors. Supposing in addition that a MxM window containing the window of Ns size is hoogeneous (all pixels have one sae label). The conditional law of X of all the window knowing that the region is L is:
p ( X / L = l) = p( Xi / L = l ) (5.1) s s i N s s reote sensing'' Anales des télécounications, toe 51 no 11-1 1996. [3] J.S LEE,.J RANSON H.LANG, ''distribution for ultilook processed polarietric SAR iagery'' 199 [4] E.JACMAN, P.N.PUSEY ''A odel for non Rayleigh echos'' EEE transaction on antenna and propagation, vol 4 no 6 1976. Fig.9 Results of the enhanceent using full polarietric data and -distribution Water Gras Soil Beet Water 98.6 0.46 0 0 Gras 0 100 0 0 Soil 0 0 100 0 Beet.7 0 0 97.7 Table.4 probability of good classification using Results of the enhanceent. The classification accuracy ranged between 97% and 100%. 6. Conclusion A supervised classification technique has been presented in this paper. Coparisons of results using single and full polarietric data indicates the utility of full polarietric data. The -distribution sees to be a good odel for characterizing area. Further work is necessary to develop -distribution for other types of area. References [1] Z.Belhadj, ''apport de la polariétrie ultifréquences pour la classification en télédétection radar'' PHD these, REST, Nante, 1995 [] Z.Belhadj, J.SALLARD and S.EL ASSAD ''Polarietric observation of forest cover in radar