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Topographic measurement: methods, which explicitly measure topographic details, such as local maxima or ridge 
lines, i.e. photogrammetric or terrestric measurement. 
Automated measurement: determination of object points by automatic processes, e.g. image correlation. 
Profiles: the object is scanned in various profiles, which can be arbitrary placed and shaped, located in parallel 
planes or symmetric to an axis of rotation. 
e Knowledge about the properties of lines on the original surface: lines impose topological and geometrical con- 
straints: breaklines indicate a C'-discontinuity, formlines indicate a high curvature across the line and borderlines 
determine the border of the surface. A special case are contourlines, because they usually represent a whole surface 
(or a big part of it) without other kinds of data. 
Knowledge about the measurement of lines 
e Knowledge about the way of modelling: the surface will be represented by a triangulation. The triangulation has 
to fulfil some conditions of validity (s. Hoschek and Lasser 1992), but it should also represent the surface in an op- 
timal way. 
e Knowledge about the modelling of lines: lines have to be included as series of constraint edges in the triangula- 
tion. 
e Additional knowledge: this includes information which is commonly not available, such as: surface normals in the 
data points (can be delivered through certain image matching techniques), Line-Of-Sight conditions (i.e. viewpoint 
for each point on the surface), fixed type of the surface (torus, plane, ...), etc. 
3 RULES 
After having identified all information that can be used for reconstruction, the next question is how to formulate this 
knowledge. A well studied approach for this purpose is the use of rules. 
3.1 Syntax of rules 
A rule is a single piece of knowledge, which has to be (according to Buchanan and Shortliffe 1985): 
elementary: the content of a rule has to be as simple as possible. 
primitive: a rule should perform only operations, as simple as possible - i.e. without sub-routines or loops. 
independent: a single rule must not be dependent from any other rule. 
not correlated: different rules must contain different statements. If two rules state the same thing, the result will be 
biased. 
The syntax of any rule can be defined as (Lucas and Gaag 1991, p. 102): 
<rule> = if <antecedent> then <consequent> 
<antecedent > <disjunction> | and <disjunction > ] 
<disjunction > <condition> | or <condition > ] 
<consequent > = <conclusion> | <conclusion > ] 
<condition > «predicate» ( «variable», «constant» ) 
«conclusion » «action» ( «variable», «constant» ) 
«predicate» same | not same | greater than ... 
«action» = add | remove ... 
Example: if a triangle 7; € S has an area smaller than all triangles 7; € S (i # j), than a certain evidence e can be assigned 
to 7;. e has to be a measure for the evidence that 7; belongs to the surface. This yields the following: 
antecedent. area(T;) < area(T)), V T; e S, T; eS, i 7 j. 
consequent: add(e;, E), where e; is the evidence of triangle 7; belonging to the surface and E some constant. 
3.2 probabilistic reasoning 
As can be seen in the example above, the statements, contained in the rules, are seldomly deterministic. This makes 
necessary the introduction of a system which allows the assessment, evaluation and propagation of uncertainties. In the 
field of Expert Systems, various approaches are in use. In this work three of them have been implemented and the so- 
called CF-method proved to be the most appropriate. The applied methods are: 
e Subjective Bayesian method, an extension of Bayes’ Theorem from classical Probability Theory (s. Lucas and 
Gaag 1991). 
e  Certainty-factor model (CF-model), which has been developed for the MYCIN-system, a system for medical diag- 
nosis (s. Buchanan and Shortliffe 1985). 
e A system, similar to the INTERNIST-model, which has also been developed for medical diagnosis (s. Puppe 1993). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 383