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CONTEXTUAL BAYESIAN CLASSIFIER 
Miclial Haindl 
Institute of Information Theory and Automation 
Czechoslovak Academy of Sciences 
Pod vodarenskou vezi 4, 182 08 Prague 8 
Czechoslovakia 
ISPRS Commission VII 
Abstract 
A new type of Bayesian classifier is introduced to recognize remote sensing image data. The classifier uses 
contextual information about the classified pixel surrounding based on autoregression model prediction. 
Key Words: Bayesian Classifier 
1 INTRODUCTION 
The conventional approach to remote sensing picture data 
classification is to perform test on unknown pixel against 
all classes using a spectral feature subset and then assign 
the unknown pixel to one of these classes, not taking re 
specting the large spatial correlation (Tubbs,2). The inter 
pretation of picture element - pixel does not depend upon 
any relationship with any other pixel, so we do not use all 
available information. Not using context has fundamental 
limitation influence on classification accuracy for machine 
recognition. On the other hand the use of all context in 
formation is paid in unsolvable increase of computational 
demands. Possible solution is a compromise. 
The developed decision rule is the optimal contextual 
Bayesian classifier with several simplifications. We assume 
local neighbour pixels to be conditionaly statisticaly inde 
pendent, their class conditional density to be independent 
on neighbour labels and we neglect the space arrangement 
of local neighbour labels. In the first step the thematic map 
as the output from per-point Bayesian classifier is created. 
The second step consists of Bayesian classifier in which 
formula the apriori class probabilities are replaced by non- 
causal frequency predictor. This predictor is based on the 
autoregressive model of class frequences estimated from the 
first step classification. 
2 CONTEXTUAL CLASSIFIER 
Let us chose some direction of movement on the image 
plane, for example row scanning from left to right and top 
to bottom. According to this choice the following index is 
used throughout this paper: 
t = (i-l)N , + j (1) 
where i,j = 1,2,..., N' is row and column index, respec 
tively. N' x !\ rl is the size of classified image. Let us de 
note X t (multidimensional pixel) in time t of scanning. u>, 
i = 1,..., A class indicator,Y t the A—dimensional vector, 
which i-th compound is the occurence frequency of u t in 
a window D t .D t window is defined as the set of thematic 
map entries within a given region centered around the class 
indicator corresponding X t . The window is defined to be 
perpendicular with odd number of class indicators in both 
directions, so that each frequency vector Y can be assigned 
to the center pixel of its respective window. 
Let us denote the set of past thematic map windows 
D (t) = {£> t , A-i, • • •, Di) (2) 
and Lflb the set of all pixel indexes from D. We have 
chosen the noncausal frequency predictor: 
Y t = E[Y t \D (t ~ l) ] (3) 
Let us denote 
Mi(Xt) = (Xt - - ta) (4) 
where /q, E, are mean value vectors and covariance ma 
trices (in practise their estimators) of single classes. Now, 
the modified Bayesian decision rule using the context in 
formation abont the class membership of surrounding, can 
be put in the form: 
Assign feature vector X t into class uq if 
Mi(X t ) + In |£i| - 2 In Y t (i) 
= min {A/ J (A'«) + ln|E J |-21nV;(i)} (5) 
The thematic map for prediction construction is as 
sumed to be the output from per-point Bayesian classifier 
. then the relation (3) can be put in the form (6) 
Y t = E[Y t | min {Mj(X m ) + In |Ej| 
- 2 In Pj} : m e £) (t-1) ] (6) 
where P 3 are some prior class probabilities estimations.