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Rules of Class 
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One of the simplest example is a Markov chain, where 
transitional probability is determined only by the previous 
class. In addition the probability also can be affected by 
combination of classes in the neighborhood. In this study, 
we assume a model at which transitional probability is 
determined by the combination of classes in the 
neighborhood. And landcover data with five classes is used 
as test data. 
In an example model which we used in an 
experiment, spatial and temporal relations affect the 
transitional probability in three ways as shown in the 
Figure.2. The first one can be called "spatial continuity", 
based on the assumption that the same class data tends to 
continue in spatial dimension. Second one is called temporal 
continuity. This is an extension of spatial continuity to 
temporal domain. The third aspect is expansion-contraction 
relations based on the assumption that some class data has 
high possibility to expand its area at next time-slice, while 
others tend to contract. The temporal change in the pixel 
with un-contractible class type will be determined by the 
pixels class itself. And the temporal landuse change in the 
pixel with contractible type will be determined by class of 
the pixel and classes of its expansible neighborhood. 
  
  
    
  
   
TEMPORAL; 
CONTINUITY ! 
Figure.2 3D Spatial- Temporal Relation of 
Pixel-based Class Variable Data 
3.3.2 Definition and Computation of Fitness of an 
Individual 
Fitness of an individual is defined by the combination 
of behavioral fitness and observational fitness. Behavioral 
fitness is defined as combined probability of change events 
of nominal variables under the condition that these changes 
follow a given probabilistic behavioral model or rule. 
Observational fitness can be defined as combined probability 
that the observational nominal values occur under 
probabilistic functions of observational errors/uncertainties. 
Observational probability can be determined by accuracy, 
resolution and frequency of observation. By multiplying 
behavioral fitness and observational fitness, overall fitness 
can be computed. Behavioral/structural models and 
observational data can be integrated by optimizing the 
overall fitness. 
805 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
1)Behavioral Fitness: As showing in Figure.2, let 
PAC Cp pu) 85 the probability of changes from 
landuse class C,, to landuse class C, considering the 
expansion-contraction effect of its neighbourhood, and 
Esc (C, - C, ) as the probability of spatial continuity. If we 
assume that P_{(C,.C.Y% and PB IC ~C ) are 
independent, we can compute behavioral fitness of each 
individual according to following formula: 
Np N, 
FITNESS 7 [1 4, Il B Cho Corn?! 
(behavioralfitness) P1 =] 
Np N; 
= i { H Pr (C... e ECC, e e Cor Ci) j 
where N, : is the pixel number in 2D space, 
N, : is the temporal slice number, 
C, , : is the landuse class of the cell on the 
Pth pixel at the T time slice; 
For the class change probability with spatial 
continuity, E (Ca 7 C,,), we set values according to 
following five neighboring pixel's statues along the spatial 
dimension, which form a set of behavioral rules: 1)If or 
not classes in all neighbouring pixels are equal; 2) If or not 
classes in 4 neighbouring pixels are equal; 3) If or not classes 
in 3 neighbouring pixels are equal; 4) If or not classes in 2 
neighbouring pixels are equal; 5) If all classes in 5 pixels 
are unequal. 
To calculate the probability of class changes under 
the temporal continuity/expansion-contradiction effect, 
B, (C,,. C.) , three possible changing patterns of landuse 
classes in spatial-temporal distribution are picked up and 
listed in the Figure.3. They will be determined based on 
the probability integrating class changes in Markov chain, 
P, (C, C.) , and expansion speed of class-types into 
neighboring pixels. Their behavioral rules can be reckoned 
from tables similar to Table.1. 
2) Observational Fitness: Observational fitness can 
be computed with the following formula. Observational 
probability can be determined mainly by the accuracy of 
  
  
  
  
  
  
ESO f Cu Cu Ca = Ce: |; Others 
= + = > ~ 
une dr (c care, cp Cy Pi €) 
Yes | Yes : 
(Oc. Ni. 3 0 0 Invasion 0 
Yes No d ; 
( oc, | (1-00, | Invasion 0 Invasion 0 
No | Yes 4 xv 
ao do.) 0 Invasion | Invasion 0 
No No | Markov | Markov | Markov | Markov 
(1-0) (1-2) Chain Chain Chain Chain 
  
  
  
  
  
  
  
  
Notice: 1> Supposed C,;, and C,, are expansible (il, i2 21 — 4); 
2» 0c, and Oc, are defined as expansion speed of C, , and C,,; 
Table.1 Behaviors of Class Changing in Case3