Proceedings of the Symposium on Global and Environmental Monitoring: Proceedings of the Symposium on Global and Environmental Monitoring

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Persistent identifier:: 856665355

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts ; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856665355

Language:: English

Document type:: Multivolume work

Volume

Persistent identifier:: 856669164

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Scope:: XIV, 912 Seiten

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856669164

Illustration:: Illustrationen, Diagramme, Karten

Signature of the source:: ZS 312(28,7,1)

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: International Society for Photogrammetry and Remote Sensing, Commission of Photographic and Remote Sensing Data

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: [WP-1 ADVANCED COMPUTING FOR INTERPRETATION]

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: CONTEXTUAL BAYESIAN CLASSIFIER. Michal Haindl

Document type:: Multivolume work

Structure type:: Chapter

341 3 THE AUTOREGRESSIVE MODEL OF CLASS FREQUENCES Several different stochastic models can be used for the matic map class frequences modeling. However the com putational complexity is serious limiting factor, therefore the autoregressive model (7) was chosen. N Yt = X] AiYt-\ + A (7) >=i Where Y t E t are , A'—dimensional vectors, /1, are KxK ma trices of unknown model parameters and N is the order of model. E t is the white noise vector with following proper ties for t > N : 7 (t — 1) = *y(N) + t — 1 — N Ul = Yy(t-1) — Ky(t-l)K(t-l)^y(i-l) Yy(t-1) Ky(t-l) Vl_i Ky(t-i) Yz(t-1) T H«-.)= E YkYi k=N+1 E Z t Yl k=N+l k (1 -,i= E k=N+1 V/v is a positive definite matrix and l(N) > N(l + K) - 2 (18) (19) (20) (21) (22) (23) (24) £[£<] = 0 E[Ê t ÊJ_ x ] = 0 i J. 0 i < t (8) 4 NUMERICAL REALIZATION = 0 0 < i < t We assume, that probability density of E has multidimen sional normal distribution independent of previous data and is the same for every time t. E\È,ÈJ) = n (9) fi is a constant covariance A'—dimensional matrix. The task consist of finding the estimation Y (3) in dépendance of known process history. = (10) To construct estimator (3), we need to derive the condi tional probability density (ii) Using Bayesian estimation theory (Peterka,1981), we can express (11) in the form of Student’s distribution PWIU'-») = ir K > 2 T((i(t) -P+K + l)/2)/{r(( 7 (() -/» + 1)/2)(1 + ZjV^Z,)^ 2 |A,_,|'' 2 [1 + (Y, - Pl lZi f K-i(Y, -PLz,)H 1 + zfvr f !_ n z,)}"w-s+K + m ]{12) The predictor (13) can be evaluated using matrix V t (17) updating and its following inversion. Another pos sibility is direct updating of P t . According to work (Pe- terka,1981), to ensure the numerical stability of solution , it is advantageous to calculate (15) by the means of the square-root filter REFIL (Peterka,1981), which guarantees the positive definiteness of matrix (17). The filter REFIL updates directly the Cholesky square root of the matrix vr l • The numerical complexity of proposed classifier is larger than the conventional per-point Bayesian one. If we denote the number of arithmetic operations necessary to classify one pixel then the Bayesian classifier in its most effi cient version needs: h(*) = I<d(d + 3)/2 h{+) = I<(d - 1 )(d + 2)/2 + 2K The contextual Bayesian classifier is computationally more demanding: h(*) = Kd(d + 3)/2 + 3K 2 N + 2K 2 N 2 + SEN + 16A h{+) = K(d— l)(d+2)/2+K+3K 2 N+1.5K 2 N 2 +'2.5K N+n with conditional mean value ( 3) y; = PJ_ x z t Where n is the number of pixels in thematic map win dow. To avoid overflow problems the smallest possible sin- (13) gle class predictor value (13) was chosen to be 0.001. where P t -1 is estimation (15) of the Kx/3 matrix (14) P T = [Au- .., Ayv], (14) A-1 = v~i -l)Ezy(t—1) (15) Zt = [Y t T _ 1 ,. V’T ] T ■ ■ ? U-aJ (16) is the flxl data vector (/? = KN). The following notation was used in (12): vu = K_! + V N (17) 5 EXPERIMENTAL RESULTS The contextual classification algorithm was applied to agricultural type of Thematic Mapper subscene from North Moravia . The comparison was made by the Bayesian per- point classifier. The area studied is large cooperative farm situated in Vizovice Hills. The objective of the study was to determine its land-use, land-cover conditions. Ground areas of homogeneous landforms and land cover conditions

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