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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
construction of the KBS. We conclude with the results and 
conclusions. 
2. STUDY AREA 
Two agricultural areas in Israel, which comprise 33% of the 
overall cultivated areas in the country, were investigated. The 
southern area lies along the Coastal Plain. It covers 700 km? 
and is characterized by topographic fluctuations between sea 
level and 240 m. Annual precipitation ranges between 400 and 
500 mm and over 60% of the soils are suitable for agriculture. 
Agriculture is the main land use (over 50%), and developed 
areas form approximately one-third of the total. There are 
relatively wide natural habitats on both the eastern and western 
sides of the study area. The northern area covers 1600 km“, and 
there are steep west-east topographic and climatic gradients. 
The height of the Jordan Valley on the east is 300 m below sea- 
level, and 17 km to the west of the valley the Gilbo'a 
Mountains rise to 570 m above sea level. In addition, to the 
west, the proximity of the Yizra'el Valley to the Carmel 
Mountains creates enormous height differences over limited 
horizontal distances. The annual average rainfall decreases 
along this gradient from approximately 650 mm/year in the 
west to less than 200 mm/year in the east. Soil types vary 
between Terra-Rossa, brown and light rendzina, groumosoils, 
red-loam, dark-brown soils and sandy soils. Cultivated areas 
form 50% of this study area, in which the environmental 
variations cause wide variability in natural vegetation types, 
crop types, and in the crop seeding and harvesting periods. 
3. METHODOLOGY 
3.1 KBS and the Dempster-Shafer Theory of Evidence 
KBSs as a type of expert systems address real-life problems 
and, therefore, they must deal with uncertain data, information, 
and knowledge. During the mid-1970s Shafer (1976) 
crystallized and formalized the mathematical theory of evidence 
based on earlier ideas of Art Dempster, which since then has 
been known as the *Dempster-Shafer Theory of Evidence" (D- 
S ToE). D-S ToE and its Gordon and Shortliffe approximation 
(GSA) (Gordon and Shortliffe, 1985), when applied to a body 
of evidence, have domain-independent inference capabilities to 
combine evidence while representing some levels of ignorance, 
bias and conflicts. The fundamental aspects of the D-S ToE will 
be described here in most general terms, with reference to its 
application to crop recognition in remote sensing images, 
following the work of Gordon and Shortliffe (1985) and Cohen 
(2000). 
3.1.1 Frame of Discernment 
Suppose an interpreter needs to analyze a satellite image of an 
agricultural site. To his knowledge, this area contains only two 
summer crops: cotton (cn) and sunflower (cf); and two winter 
crops: wheat (wh) and pea (pe). The set of possible hypotheses, 
which is called a Frame of Discernment (FoD) is defined as: 
© = (en, sf, wh, pe} Where each compatible possibility (crop) 
in O is called a singleton. Since the hypotheses in || are 
exhaustive the empty set, ", is considered as a false hypothesis 
in ®. In addition to the singletons there are subsets of © 
representing hypothetical possibilities of combinations such as 
summer crops or (cn, sf] in our example. The set of all subsets 
of © is denoted 2°, and a set of size n has 2"-1 true hypotheses. 
9017 
3.1.2 Basic Probability Assignment 
Suppose that there is a body of evidence in support of the non- 
empty subset A of 29. A function m{A}, called the Basic 
Probability Assignment (BPA), assigns to hypothesis A, a 
degree, denoted m, to which the evidence supports the 
hypothesis. Degrees of support are numbers in the range of 
[0,1] and must sum to 1 over all possible hypotheses. 
3.1.3 Combination of Belief Functions 
Dempster’s rule of belief functions combination enables the 
computation of the degree of support gained by combining 
multiple belief functions that refer to a set of possible 
hypotheses A of 29. Suppose that one piece of evidence 
supports summer crops and one supports cotton to degrees of 
0.4 (m,) and 0.7 (m;) respectively. Three new BPAs' are 
defined by the D-S combination rule, denoted m;®m, 
calculated by means of the following table: 
  
  
m (cn (0.7) | (0.3) 
m» UNE : 
{ ~ 
br gh {cn} (0.4%0.7)=(0.28) fcn, sf1(0.4*0.3)-(0.12) 
(0.6) {cn}(0.6*0.7)=(0.42) Q(0.6*0.3)-(0.18) 
  
  
  
  
where: m,€m; (cnj = 0.28+0.42 = 0.7; m;®m, {cn,sf} = 
0.12; m®m, {®} = 0.18. 
Suppose m, was attached to wheat, i.e., my{wt} = 0.7. In such 
cases of conflicting evidence, the support in each hypothesis is 
raised by 1/(1-k), where k is the support committed to ©: 
m;€m, (wtj — 0.58; m,Om;(en,sf] = 0.16; m;®m, {O} = 
0.25. 
A pairwise addition of the following form allows more than two 
BPAs' to be combined: 
m,®Dmz >>> (m,®m3) O m; »»» ((m,&m;) ® m3) 8 m4... 
3.1.4 Cumulative Belief Value (CBV) 
Integration of all applicable rules (evidence) for each pixel 
provides the formal basis for the calculation of cumulative 
belief values (CBV) of each class (hypothesis). In this way, 
each pixel initially has a CBV for each class. Final recognition 
requires application of decision criteria for selecting the most 
probable class, i.e., the class with the highest CBV is selected. 
3.2 Knowledge-based crop 
Construction and Implementation 
recognition system: 
An evidential reasoning mechanism based on the Gordon- 
Shortliffe Algorithm was realized in C++. The operation of the 
GSA is carried out on the basis of three input files, which 
represent the knowledge base: Database, Rule-Base and 
Hierarchic Representation. In each operation of the GSA 
program, the evidential values of all applied rules for each 
class, for each pixel, are combined in order to calculate the 
class convergent belief value (CBV). Each pixel is then 
classified into the most probable class, i.e., the class with the 
highest CBV. 
3.2.1 | Database construction 
Information layers required for the database formation were 
derived from three main sources: imagery data, Israeli GISs, 
and existing maps. The spatial database comprised a total of 
nine layers: 
« 5 multi-temporal NDVI layers generated from Landsat TM 
images (Table 1);