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David Heitzinger
categories of knowledge, which have been introduced in chapter 2, some important rules will be presented (current
amount of rules: about 40).
5.1 Knowledge about the properties of the original surface
Self-Touching Rule
Description | It will be tested, if the candidate triangle 7; touches the already ex- ka
tracted surface, or not. Self-touching or intersection is not allowed ^
(all terms are explained in Figure 4).
Antecedent | (P; belongs to surface) and (P lies not on the border) or ((k; ; be-
longs to surface) and (k; ; lies not on the border)) or ((k; » belongs to
surface) and (k; ; lies not on the border))
Consequent | The evidence e, that T; belongs to the surface, is set to zero.
ki 1
Figure 4, a candidate 7;, with its
elements.
Intersection Rule
Description | Due to the incremental strategy, it can occur, that extracted triangles
are overlapping (s. Figure 5). To test the overlapping, a spatial crite-
rion, according to Mencl and Miiller (1997a), is used.
Antecedent | The currently extracted triangle 7; overlaps a triangle 7; of the sur-
face
Consequent | The evidence e, that T; belongs to the surface, is set to zero.
Figure 5, the triangle 7; overlaps
the triangle 7;.
52 Knowledge about the measurement of the surface
Minimum Area Rule
Description | According to the Sampling Theorem, it can be stated, that points lying close together (small Euclidean
distance) are more likely to be neighbours on the surface than points lying far away from each other.
Hence, triangles with small areas should be enforced.
Antecedent | The triangle T; has the smallest area of all candidate triangles
Consequent | The evidence e, that T; belongs to the surface, is increased by a certain value
Scanner Rule mx x X
Description | Scanner data (e.g. from laser scanning) is generally arranged in an x x x T
array: there are scan-lines /;, ..., /, and m points per scan line. x j
Antecedent | One edge of the triangle 7; connects two consequent points of a 3 x (=
scan-line. 2x x K x
Consequent | The evidence e, that 7; belongs to the surface, is increased by a cer- 1 = X X x
tain value. l; l,
Figure 6, Scanner Data: the trian-
gle 7; is much more likely than
the triangle 7;.
5.3 Knowledge about the properties of lines on the original surface
A lot of knowledge can be used, when the object has been sampled with contourlines. The reconstruction has to solve
two questions:
l. Determination of the neighbourhood relations between all contourlines.
2. Determination of the surface (in our case the triangulation) between two neighbouring lines.
ad 1
It can be shown, that three types of neighbourhood-relations are sufficient (s. Figure 7): vertical neighbours, horizontal
neighbours and lines which are related over their endpoints (gaps in the data).
Hı H3
gap
l vertical neighbours
H5 y
| vertical neighbours
Hi
Figure 7, the three types of neighbourhood relation, which are sufficient for modelling a surface with contourlines.
horizontal
neighbours
Hj
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 385
