raph are at- 
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|| ERNEST. 
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tic network, 
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xY 
Figure 3: Parameters used to describe a line segment 
3 VALUATIONS 
The functions which evaluate the states of the analysis are 
very important since they are not only responsible for the 
efficiency of the search, but they are also decisive for the 
success or failure of the analysis. We relate the valuation 
of the search path to the valuation of the analysis goal in 
the given state of the analysis. The valuation of the goal 
is calculated considering the valuations of the instances and 
modified concepts already created and the estimates for the 
valuations of the instances and modified concepts which will 
be created in the path from the current node to the solution 
node. 
When an instantiation is performed, implicitly a hypothesis 
of match is established between the concept under instanti- 
ation and the chosen primitives from the database. Since we 
can not ultimately decide at the moment the instantiation 
is performed, if it is the correct one, we are working under 
uncertainty and we have to quantify our uncertainty. At the 
level of each concept in the semantic network we have a di- 
chotomous frame of discernment with the events: the chosen 
primitives 
e match 
e do not match 
to the concept (i.e. model). 
The valuations computed for the instances and modified con- 
cepts in each state of the analysis are measures of our sub- 
jective belief in these hypotheses. They take values between 
0 and 1 and we interpret them as basic belief masses in the 
framework of the Dempster-Shafer theory of evidence (Shafer, 
1976). The higher a valuation is, the stronger is our subjec- 
tive belief in the corresponding hypothesis. Using the meth- 
ods described in (Quint, 1995), the different valuations are 
combined and propagated in the hierarchy of the semantic 
network to result in the valuation of the analysis goal. 
We evaluate two aspects for our hypotheses of match: the 
compatibility and the model fidelity. The compatibility evalu- 
ates an analysis state considering the principles of perceptual 
grouping. It is calculated based on geometric, topologic and 
radiometric properties of the image primitives only. In this 
category belong for example the goodness of fit of several 
line segments extracted from the image data to form an edge 
of an object, the goodness of fit of several edges to form a 
polygon, the compatibility of the polarity of edges to form a 
polygon etc. 
The model fidelity measures the goodness of fit between the 
image primitives and the specific model gained through the 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
  
Figure 4: Neighbourhood function for the position of line 
segments 
analysis of the map. Portraying it in simplified terms, one 
can say that the compatibility is a measure for the ability of 
the chosen image primitives to form an object of the generic 
model, whereas the model fidelity is a measure for the ability 
to form exactly that object, which is predicted by the map. 
We present in this article measures used for the evaluation of 
the model fidelity. 
4 MODEL FIDELITY 
4.1 Model fidelity for line segments 
At the level of line segments we define the model fidelity 
with help of a distance function between the image primitives 
and the contours stored in the specific model. The distance 
function is part of a metric defined with help of a set of square 
integrable functions on a parametric space for line segments. 
We describe a line segment with help of the coordinates of 
its starting point, its length and the angle between the line 
and the positive z-axis (see Fig. 3). Thus, a line segment 
si is represented in the space S — (xz,y,1,0) by the point 
si = (zi, yi,li,0;). The coordinates of a line segment are in 
the domain (z,y) € R?, the length of a line is in | € R, 
and its angle is in 0 € (—5, 5]. The space (z, y, 1,0) is the 
Cartesian product of the enumerated domains and is different 
from IR". For this reason we do not use the Euclidean distance 
between two points in this space to calculate the distance 
between two line segments, but use instead a metric defined 
on an isomorphic space of functions. 
We define an isomorphism by attaching each point s; in the 
space S a function n;(x, y, l, 0) from the space of square inte- 
grable functions £2(S). We call this function neighbourhood 
function. As a distance between two line segments s; and s; 
we now use the distance defined on the family of functions 
ni. lt is well known that a distance function defined with the 
expression: 
1 
2 
dij = / (ni(z,y,1,0) — n(z, y,1,0)) dz dy di d 
s (1) 
satisfies the necessary properties for a metric on £?(S). 
we choose the functions n;(z, y, 1,0) such that their norm in 
the induced metric is equal to 1, i.e. 
| (este, v,1,0)) de dy dtas = 1. (2) 
S