genetics. They combine survival of the fittest among string 
structures with a structured but randomized gene exchange 
to form a search algorithms with some of innovative flair 
of human search (D.E.Goldberg, 1989). 
Genetic algorithms are computationally simple and 
powerful in their search without restrictive assumptions 
about search spaces. In a simple genetic algorithm, five basic 
aspects should be considered; the representation or coding 
of problem, the initialization of population, the definition 
of evaluation function, the definition of genetic operators, 
and the determination of parameters. 
2.2 Optimization Scheme for Nominal Variable 
Interpolation 
Most natural properties seems to vary continuously: 
Spatial continuity and temporal continuity are intuitive 
assumptions which provides rationale for interpolating 
observational data (M.A.Olover, 1990). However, 
knowledge and rules governing spatio-temporal patterns and 
behavior of geographic objects (e.g. environmental systems) 
are now being rapidly accumulated and represented by many 
simulation models. They can provide more robust and 
quantitative basis for interpolating observational data, 
though many of the models still may not be accurate and 
reliable enough. On the other hand, it can be said that not 
very reliable results estimated from model simulation can 
be improved by combining observational data. Actually, 
integration of observational data and models (GCM etc.) 
are conducted in meteorology as daily routine. There are 
not no such attempt to extend the idea of integration to more 
generic geographic objects. 
It is reasonable to assume that spatio-temporal events 
or "voxel-field" of nominal variables which are estimated 
should maximize likelihood under given observational data 
and behavioral models, if we suppose that observation is a 
probabilistic event and behavioral models are structured and 
probabilistic a priori knowledge on behavior of the object 
phenomenon. Observational data and behavioral models/ 
rules can be integrated in the process of maximizing 
likelihood of spatio-temporal events, 
By the way, spatial-temporal data can be divided into 
two types: continuous variables and nominal variables. 
Although relatively more interpolation methods have been 
developed for continuous variables even from multi-source 
data (e.g. R.Shibasaki et al.(1993) etc.), few interpolation 
methods have been proposed for nominal data. 
In this article we propose a spatio-temporal 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
interpolation of nominal variables which allows integration 
of observational data with behavioral/structural models/ 
rules. Since searching for the most likely spatio-temporal 
voxel-field of nominal data is typical combinatorial 
optimization problem, we introduce the genetic algorithm 
as a optimization scheme for class variable data to get 
optimized interpolated time-slice data. The likelihood is 
computed based on the fitness of interpolation results both 
to observational data and to behavioral/structural models/ 
rules. 
3.APPLICATION OF GA FOR INTEGRATING 
BEHAVIORAL MODELS AND OBSERVATIONAL 
DATA TO CLASS VARIABLE INTERPOLATION 
3.1 3D Representation of an Individual (coding) 
In the following sections, three dimensional array is 
defined to represent the individual(see Figure.1). While, 
the horizontal surface is used to represent 2D space and 
vertical dimension is used to represent temporal dimension. 
  
  
  
  
  
  
  
  
  
  
  
Figure.1 Representation of Individual 
3.2 Initialization of Population 
An initial population for a genetic algorithm is 
usually chosen at random; one random trial is made to 
produce each individual. All members of initial population 
are chosen automatically by same procedure so that the 
expected value of each member of initial population is same. 
In addition we use cubes of 1*1*1, 2*2*2 and 3*3*3 pixels 
as the initial unit for the initialization of population to 
increase the efficiency of procedure. 
3.3 Definition and Computation of Individual's Fitness 
3.3.1 Spatio-temporal Behavioral Models/Rules of Class 
Variable Data 
Any types of behavioral/structural models/rules can 
be used for the GA-based interpolation if they can determine 
the probability of every possible behavior/transition of 
nominal or "class" variables. For nominal variable data, 
possible changes of a class at one pixel is basically defined 
by the probability of the changes from one class to another. 
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