David Heitzinger
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Due to the limited types of neighbourhood, there is also a limited amount of possible valid triangles between these lines
(only seven types are allowed).
The facts about neighbourhood of contourlines and the triangles between can easily be formulated in a set of rules.
5.4 Knowledge about the way of modelling
The triangulation has to fulfil certain conditions of validity. Furthermore it should represent the surface in an optimal
sense. For this optimisation different criterions are possible:
Delaunay Rule
Description | The Delaunay criterion in 2D is equivalent to the maximisation of the minimum angle in each triangle.
In 3D it is also desirable to gain equally shaped triangles.
Antecedent | T; is the triangle of all candidates with the biggest minimum angle.
Consequent | The evidence e, that T; belongs to the surface, is increased by a certain value.
Crease angle Rule
Description | To gain a smooth surface, triangles with crease angles near to 71/2
are enforced s. Figure 8).
Antecedent | T;is the triangle of all candidates with the biggest crease angle ß.
Consequent | The evidence e, that T; belongs to the surface, is increased by a cer- Figure 8, crease angle f between
tain value. the triangle 7; and the already
extracted triangle T;.
The evidence, assigned to T;, is composed from two aspects: at first
the importance of the symptom f itself in regard of the diagnosis
(part of the surface, or not). Secondly, the actual value of P: a short
value produces a low evidence, a value near to 7/2 a high evidence.
The diagram of Figure 9 shows the evidence of p (the evidence
ranges from 0.0 to 1.0) in a histogram. In this example Bis used in
favour of and against a membership to the surface, i.e. a value of B
between 0? and 100? votes against a membership, a value between
100* and 180? votes pro. TS EN
The user can manipulate the evidences and according histograms, to 0 2 4
trim the extraction in respect to the current data set. The program
offers the user a training-mode, where a given triangulation is ana-
lysed and suggestions for the evidences are determined.
Figure 9, evidence of the angle A, depending on
its value.
6 EXAMPLES
The presented method has been implemented and tested with various data sets. Some of these examples will be shown.
The three presented methods for probabilistic reasoning have been implemented. In the following examples, always the
certainty-factor model has been used.
6.1 Torus
This data set has been provided by Ernst P. Miicke (it is available - together with other data sets - under:
http://www.geom.umn.edu/software/cglist/GeomDir/data 1.1.tar.gz). Due to the homogeneous point distribution, the
surface could be reconstructed without any problems - Figure 10.
6.2 Bust
This data set is also one of E. P. Mücke. The point distribution is also homogeneous (s. Figure 11). Some points on the
ears could not be inserted.
386 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
