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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
In (Kohlas and Monney, 1995) it is shown that the Bayesian
approach can be represented by E-T, whereas a represen-
tation of E-T by Bayes Theory is not feasible. One inte-
resting difference to the Bayesian approach is the possi-
bility to formulate ignorance: in the Bayesian framework
the evidence must be allocated completely to the possible
hypotheses, thus a priori probabilities are selected in order
to calculate conditional probabilities from found evidence.
In E-T it is allowed to explicitely formulate ignorance and
therefore a specification of a priori knowledge is not re-
quired.
In this work the Hint-Theory is preferred to a Bayesian ap-
proach because assumptions about a priori probability dis-
tributions concerning the quality of an individual ATKIS
object can not be made. One could take into account to ob-
tain this information from experience but this could lead to
a distortion of results. The main reason for this is that the
influences to the data quality of ATKIS are manifold and
can not be modeled a priori.
3 RELATIONSHIP MODEL
The assessment of ATKIS objects by means of extracted
objects or by means of objects of a higher quality requires
a model describing the properties of all involved object
classes and their relations. The model used here has two
major properties: a) the attributes and the attributive and
positional certainties can be assigned in an uniform man-
ner and b) a separation between objects to be assessed, ob-
jects which directly give evidence and context objects is
given. These properties are important because a) assures
that the model is extensible with new object classes and b)
allows to apply this approach even without having infor-
mation about context objects.
The relationship model (ref. to Fig. 1) contains three ma-
jor classes: ATKIS objects, context objects and extracted
road objects. Additionally the topologic and geometric re-
lations are described. Such models are called relationship
models, because the main intention is to illustrate the re-
lations between the objects of interest. It can also be un-
derstood as an extension to so called local context models
as introduced in (Mayer, 1998). The main extension con-
sists in the insertion of the GIS objects which have to be
assessed. Moreover the geometric subelements of a line
object (segments) are explicitely contained.
Objects are geometrically described by a concatenation of
segments consisting of two points (thus resulting in a line-
string). The decision to choose this representation (e.g. in
contrast to a polynomial one) is based mainly on computa-
tional considerations. If necessary the conversion from any
representation to a line-string representation is done by a
quantization (accepting a certain amount of loss of accu-
racy). In the assessment phase each segment of an object
is analysed separately. By means of combining the assess-
ment results of all object’s segments it is possible to obtain
an assessment result for the whole object.
The relationship model is independent of global context,
ie. the appearance of objects in different environments.
This knowledge must be considered by the respective ob-
ject extraction algorithm.
803
Linear Local Context Object (Line-string)
W,; width
Aw,; certainty width | |
App, certainty position projection |
N
° Apa,: certainty position algorithm
E Op, precision position
© p_con: confidence
L od
x
o9
x»
o
o Row of Buildings | Row of Trees Convoy of Vehicles
e e ©
|
Row of Buildings- Row of Trees- Convoy of Vehicles |
Segment Segment Segment |
0 ; ;
£ is parallel is parallel is parallel
9 disjoint with disjoint with contains
S d min-3m, d min-1m, identical width: no
o d max-15m d max-10m
e
Nn
Pd
o i
$ ATKIS Carriageway (Line-string) |
Oo ATKIS Carriageway :
o Object-Segment e w,: Width |
e Aw: certainty width |
E Ap,: certainty position |
is_parallel
contains
identical width: yes
Extracted Road Object-Segment
e
Extracted Road Object
(Line-string) Types of
connection
w_: width |
Pu ; d p> generalization i
Aw. certainty width !
Apa,: certainty position algorithm @ composition |
Op, precision position association |
Extracted Road Objects Relations
p. con: confidence
Figure 1: Relationship Model
3.1 Object Classes
Three groups of attributes for the specification of the qua-
lity are used (refer to Fig. 1):
1. certainty A: The certainty represents the range in which
a variable is defined. Certainty can be understood as
an equipartition. For example if an attribute width is
5m and the certainty of this value is 2m than it is as-
sumed that width-[3 . . . 7m].
2. precision a: The precision is a measure in the sense
of a standard deviation (Gaussian). If in the above
example the precision is 2m then the probability that
width-|1 . .. 9m] would be about 95% (20).
3. confidence Pcon: Many object extraction algorithms
apply an internal evaluation of the results. This mea-
sure should be used in the assessment phase and is
therefore also part of the attributes. The confidence is
defined in [0, 1].
