)-
NA
—" — |
On
t
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vel XXXV, Part B2. Istanbul 2004
l. Extraction of Linear Local Context Objects and as-
signment to ATKIS Carriageway Object-Segments (de-
pending on the quality of extracted Linear Local Con-
text Objects and its modeled topologic relation to AT-
KIS).
2. Definition of ROI for each ATKIS Carriageway Ob-
Ject-Segment, depending on the assumed quality of
Extracted Road Objects. Subsequent extraction of
road objects in the ROI.
3. Assessment ofthe ATKIS segment using Hint-Theory:
To what degree do the extracted objects support the
existence/nonexistence of the ATKIS segment? The
given certainties and precisions assigned to the ob-
jects are considered and are reflected in the degree of
support.
4. Linkage ofthe assessment results of all segments from
one ATKIS object in order to achieve an object-wise
assessment.
The sequence concerning the assignment of Extracted Road
Objects to the ATKIS segment (step 2) depends on the road
extraction strategy. If the road extraction algorithm uses
input information from AKTIS (as done e.g. in (Gerke et
al., 2004)) the definition of a ROI before road extraction is
reasonable, whereas if it does not use such information the
road extraction is independant from the ROI (similar to the
procedure for Linear Local Context Objects).
4.1 Assignment of Extracted Linear Local Context Ob-
jects to ATKIS Segments
The decision if a Linear Local Context Object is assigned
to a certain ATKIS segment depends on a) the width of the
extracted object, b) the quality measures of both objects
and c) the modeled topologic relation. The ROI in which
an extracted local context object must be situated is a buffer
with the radius »r_ROI = A + wo + d_max around the
respective segment of the ATKIS Carriageway. The value
A is the sum of all certainty values given for the ATKIS-
Segment and the extracted Linear Local Context Object:
À = A, + An, with A4 - AA T Apa and Ap =
Awo Appo t Apao + 20,0. Note that the precision o is
here converted to a certainty measure by means of the 20
calculus as the ROI can be interpreted as a 95%-confidence
area of the two segments.
4.0 ROI-Definition and Extraction of Road Objects
The calculation of r ROI for the subsequent extraction of
road objects is similar to the definition above: r ROI —
À = A4 + wo + Âo with Ao — Avo + Apao + 290.
As the width of the extracted objects is unknown a priori
a predefined value can be used, keeping in mind its impact
to the assessment result. If however a road extraction was
performed independently of ATKIS data no assumptions
have to be made.
4.3 Assessment of ATKIS Segments Using Hint- Theory
In the relationship model the topologic and geometric rela-
tionship between an ATKIS segment and the segments of
Linear Local Context Objects (resp. the Extracted Road
Objects) are defined. It is now desirable to exploit this
knowledge in the assessment phase. This means two frames
805
of discernment can be defined: a) OG — (G, 5G] which
includes the hypothesis G expressing that the segment of
the extracted object and the ATKIS segment coincide with
respect to geometric relations, respectively its negation 3G
and b) Oz — (TT) including hypothesis 7' which refers to
the topologic relations. Note that the complementary hy-
pothesis regarding topology (—T7') is not included. This is
motivated by the fact that it is already assured in the as-
signment phase that a considered extracted road or context
object has an impact to the respective ATKIS object. Thus
it is clear that it supports 7'. The question is to what degree
it does support this hypothesis.
The focal sets are not completely disjoint: any object just
gives as much evidence for the hypotheses that an ATKIS
segment and this object coincide regarding the modeled re-
lation as justified by the respective measures and quality
values. Here the advantage over traditional probability the-
ory or a Baysian approach is exploited: the formulation of
ignorance is possible.
4.3.1 Hints Regarding Topologic Relations For the ex-
amination of the topologic relations between two objects
the approach presented in (Winter, 1996, Winter, 1998) is
applied. In that work the topologic relations between im-
precise and uncertain regions are assessed. Winter shows
that all eight topologic relations two objects may undergo
(divided in two relation clusters C, and C5, refer to Tab. 1)
can be derived from the minimum and maximum distance
between so called certain zones. Winter proves that if two
objects undergo the relation touch (considering their uncer-
tainty) it is impossible that they undergo relations beyond
overlap (C3) and vice versa. The decision whether C, or
C^ applies is made based on an overlapping factor. Certain
zones are then defined depending on the relation cluster: in
C the area not being covered by the two objects is certain,
in C» this area is uncertain. The signed distance function
between the certain zones is introduced as ? and derived
from the morphologic distance transform along the zonal
skeleton of the uncertain zone. Winter introduces the sign
of Ÿ being dependant on the object the zonal skeleton inter-
sects. The definition of range classes V5 — (v. ,v9, v4)
allows to represent the topologic relations by means of the
min. and max. value of #*. For this work the definition of
the range classes have to be extended in order to consider
the side conditions din ANd dax for the relation disjoint:
VE%_,ifŸ < dmin
V mm {v_, Vo, V4) with Ü € Wo, if dinin = Ü = daz
Üec Vy, if Ÿ > Amex
The assignment of 2,,;,, and 2,,,, to these classes leads
to ,,;4 and Wax Which can be transferred to the topo-
logic relations (ref. to Tab. 1). Note that the modeled
relation contains is supported by the original relations con-
tains, covers, equal as it is allowed that the boundaries of
the respective objects are identical. Special attention has
to be paid if the side condition identical width is given for
contains. This side condition can not be checked by means
3 Winter uses the term € for the range classes. In order to avoid con-
fusion with the terms used for the Hint-Theory here the expression V is
introduced.
