The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
Transformed Divergence (TD) is one of the most used measures 
of separability which therefore may facilitate the estimation of 
total effort required by the KBS to reach high level recognition. 
It is determined for each pair of classes according to the 
following formula (Swain and Davis, 1978): 
TDij = 2(1 - (exp (- Dij/8))) (2) 
where 
Dij =0.5 tr (<q - Cj-xq -1 - Cj -1 )) + o.str ((q _1 - q -1 ) 
( Mi -Mj)( Mi ~Mj) T ) 
where: 
i and j = the two signatures being compared 
Ci = the covariance matrix of signature i 
i = mean vector of signature i 
tr = the trace function (matrix algebra) 
T = transposition function 
The technical advantage of using TD stems from the fact that it 
provides an expected threshold value for high separability 
(=2000). The recognition energy (Re) required by the expert 
system to resolve the existing level of inseparability 
(unresolved complexity) can be estimated by: 
Re = Yj (2000-TDj) (3 
Where i is the index for pairs of classes. 
Similarly, the effort needed or actually invested in producing an 
expert system for resolving the existing level of inseparability 
at a certain level of expected / obtained accuracy (Ue) may be 
estimated by: 
While it is possible to estimate the work/ effort invested in 
extracting evidence (Kw ) or in constructing procedural 
mechanisms of inference (Iw), it is impossible to determine 
directly the 'effort' made by deduction/ induction/ abduction. 
Equation 9 suggests that it might be estimated in productive 
recognition energy (Re ' Ue ) units when it is treated as an 
element of the overall work invested in building the recognition 
system. 
Shoshany and Cohen,(2007) implemented this approach by 
assessing the efforts in constructing the evidential basis and the 
recognition results obtained for a simple Rule Based system 
(DDI) and for Dempster- Shafer based KBS (DII). This 
assessment was conducted within the framework of a crop 
mapping task in Mediterranean region where in evidences were 
derived for one study area and then the two expert systems 
were implemented for another study area which was not trained. 
Figure 1 shows that Rule based systems may have an advantage 
when workloads area high and when there is no differentiation 
in efforts required for constructing thematic type of evidence 
(implicit evidence) and continuous type of evidence (explicit 
evidence). As the differences in evidence production between 
explicit and implicit increases the advantage of the DII is 
enhanced. 
Figure 1: Gain from Dempster Shafer Type Inference as 
obtained for different work loads (efforts required for 
constructing evidence). 
C Y(K W + Iw + Gw)~ Re Ue (4) 
Where Kw and Iw are the work/efforts invested in producing the 
KB and formalizing the procedural inference mechanism, 
respectively (i.e., working hours, manpower units etc.); c is a 
scaling/calibration coefficient translating effort units to 
productive recognition energy (Re ' Ue ); and, Gw is the 
productive recognition / information gain from using the 
inference without investing effort in developing it: either by 
using DII or by using previously developed DDI. Different 
combinations of Kw , Iw and Gw facilitating the same 
recognition targets thus represent the relative sophistication 
embedded in each of the inference mechanisms. 
6. DISCUSSION AND CONCLUSIONS 
This study presented one of the fii-iti attempts ever made in 
comparing the gain from evidence versus that from inference, 
which are two central elements in the reasoning the remote 
sensing recognition process. Assessment of relationships 
between them is extended when considering implicit versus 
explicit evidence and domain-dependent versus independent 
inference. Domain-independent inference (DII) represents one 
of the common intelligence capabilities founded on general 
principles of induction, deduction or abduction. The highest 
level of expert system 'intelligence' is gained in resolving most 
complex problems from a most redundant data/information of 
the implicit type. The bottom line suggests that DII may have 
significant gain when the production of implicit evidence 
requires a third or less effort than that required for producing 
hard explicit evidence. However, it must be emphasized that the 
gain identified here for DII in general terms must be attributed 
specifically to the Dempster-Shafer theory of evidence. In our