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