Ali Akbar Abkar 
  
2 DESCRIPTION OF THE METHOD 
In this paper a framework is developed that allows a formal integration of information derived about objects and 
processes in the analysis procedure. This is graphically represented in Fig. 1. In the developed framework, the data 
and/or knowledge contained in a GIS about terrain objects and processes (e.g. growth, harvest, and development) can be 
combined with the sensor model and the atmospheric model to optimize information extraction from RS data. The 
proposed model is based on the probability theory, which enable combining information from different sources with the 
purpose of classifying each pixel and making probabilistic assessments about the model “parameters” (Fig. 1). The 
Bayesian probability theory is used to describe the uncertainties in the relationship between the observed RS data d, the 
hypothetical class label ay, and the model parameters p, modeled by the combined probability prob(d, «x, p) of all 
relevant factors in both the data domain and model domain. Here d is the collection of remotely sensed multi-spectral 
data at a fixed time and «y are the radiometric classes with k as the number of classes defined by the users (map 
categories) and p is the parameter vector of the pattern model (ie. the combined atmosphere, scene, and 
sensor. ..efects). Therefore, for our purpose, we define Pattern — prob(d, «y, p); see Abkar (1999). 
We use the Bayes rule, to find maximum probability prob(oyld, p) over [(x; yj] and [exx; yj). pl from (RS) data given 
the GIS under certain conditions of independency, i.e., separable into a radiometric model and a geometric model. 
prob(d, «y, p) - prob(o, ld, p)prob(d, p) — prob(dloy, p)prob(oy, p) 
Thus, we have 
prob(d|o, , p)prob(a, . p) 
prob(gy d. p) = X | (1) 
Y. prob(d|o, . p)prob(o, . p) 
k=1 
  
The application of (1) in classification and parameter estimation requires knowledge of the combined probabilities 
prob(w,, p). However, a form can be obtained through the application of the law of conditional probability 
prob(oy, p) - prob(oylp)prob(p) 
since prob(p) cancels from the numerator and denominator of (1) after substitution, we have 
prob(d|o, ,p)prob(w, Ip 
dp=-= (2) 
X prob(d|o, p)prob(o, I 
kzl 
  
  
prob(w, 
which is the basis for calculation of the maximum probability values for model parameters Abkar (1999). 
The method developed for making use of the information/knowledge about objects and processes stored in GIS and 
other information (sensor) in the analysis procedure is called Likelihood-Based Segmentation and Classification 
(LBSC) of remotely sensed data (Abkar, 1999) and comprises three main processes (Fig. 1): 
l. a radiometric likelihood generator, which generates likelihood vectors (probability for radiometry given 
radiometric class) from multi-spectral RS data and a radiometric model for subsequent analysis by segmentation 
and classification. Store the likelihood vectors in radiometric evidence maps. 
As was noted that for the proper application of the refined Bayes formula (2), an estimate of prob(dloy, p) was 
needed in order to find the probability (2), which are estimated from the training sample set. For a given p the set of 
posteriori probabilities prob(ayld) can be arranged to form the K-dimensional vector E which we referred to as 
radiometric likelihood vectors or radiometric evidence vectors E = [prob(mld)  prob(a»ld) ui prob(oxld)]/. 
2. a geometric hypothesis generator, which generates geometric hypotheses for image partitioning given initial 
parameters and with geometric constraints. Current GIS is used as the source of object models to generate 
geometric hypotheses (Fig. 1). Include the signal mixture model as defined by a sensors point-spread function. 
Store each iteration over the geometric parameter space in a probability for class vector hypothesis map. 
  
10 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
thi 
se: 
sai 
the 
lik 
sh 
3. E? 
The L 
locate 
31 € 
The d 
The g