Summarising the types of iterations within the whole break-
line determination procedure, iterations per patch pair for
the robust estimation have to be distinguished from ad-
ditionally iterations per breakline. Robust estimation is
performed for each patch pair until the influence of all off-
terrain points is reduced as much as possible. On the other
hand the iterations per breakline, which perform a reclas-
sification of all ALS points into left and right points on the
basis of the refined breakline, lead to an iterative refine-
ment of the breakline. It is performed until no significant
change of the breakline can be recognised.
3.3 Integration of Additional Observations
A benefit of the proposed method is that additional infor-
mation within the breakline modelling procedure can be
introduced. Further observation equations can be easily
integrated in the adjustment for the determination of the
surface patches.
This extension allows the integration of both, high quality
2D breakline information (e.g. given by manual measure-
ment using image data) and high quality height informa-
tion from ALS data within one process. The influence of
the different observations can be easily controlled by an
additional weight factor that depends on the individual
observation accuracy. Furthermore the same additional
equations allow the consideration of the accuracy of the
2D approximation of the breakline.
4 AUTOMATISATION
As mentioned before, the method introduced for 3D break-
line modelling with the help of unclassified ALS data re-
lies on a 2D approximation of the breakline. Therefore the
following subsections concentrate on methods, which allow
the determination of this initial values. Basically, two ba-
sic concepts can be distinguished in the area of automated
breakline extraction.
The main group of algorithms tries to extract (generally in
2D) the whole breakline within one process (cf. section 2).
In contrast to these methods a different concept for the
automatic or at least semi-automatic breakline modelling
is presented in the following. It is based on 3D breakline
growing and tries to overcome the must of the modelling
method presented in section 3 of a entire 2D approxima-
tion of the breakline. For the start of the growing pro-
cedure the approximation of one breakline segment (one
point near the breakline and the approximative breakline
direction, cf. section 4.1) or just one point near the line (cf.
section 4.2) is necessary. The growing is performed with
the help of the ALS point cloud stored in a database.
4.1 3D Breakline Growing on the basis of a Start
Segment
This subsection presents the 3D breakline growing scheme
on the basis of a 2D start segment (e.g. manually digi-
tised). Based on this start segment the 3D breakline within
this segment, is determined with the help of robust surface
patches. Afterwards the growing into both directions on
1100
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Lots r
——— it lle
R^ r
+
Figure 6: Scheme for automated breakline growing (for-
ward and backward) with the help of à start segment
(L1/R1).
basis of the refined segment (forward and backward, cf.
figure 6) is performed. This growing method proceeds in
both breakline directions in the following way:
1. Compute the patch pair with the help of robust sur-
face patches (cf. section 3) and store the results. In
the first step the initial segment (L1/R;) and in the
following steps the extrapolated patch areas (Lin/Rib
and L;r/R;r) are used.
2. Compute the boundary for the next patch pair on the
basis of the previous line direction (extrapolation).
3. Export the unclassified ALS data within the new patch
boundary from the database.
This growing procedure (step 1 to 3) is continued until the
adjustment is unsuccessful or a certain break off point (e.g.
threshold for the intersection angle between both surface
pairs) is reached.
4.2 3D Breakline Growing on the basis of one
Start-Point
In à similar way breakline growing based on just one ini-
tial 2D point next to the breakline can be performed. For
this extension the breakline direction must be estimated
in à first additional step. For this aim a lot of different
approaches (e.g. determination of the maximum curvature
based on differential geometry in the surrounding of the
start point) can be considered. In the example, presented
in figure 7, an adjusting quadric, supported by the ALS
points near the start point, is used. 'The determination of
the breakline direction can be easily performed by an anal-
ysis of the main axis transformation. The approximation
of the breakline direction is given by the eigenvector of the
smallest eigenvalue (cf. figure 7). Afterwards the breakline
growing can be performed with the help of the procedure
presented in the previous section.
5 EXAMPLES
This section demonstrates the capabilities of the presented
methods for breakline modelling and growing. An addi-
tional section shows the improvement of the integration
of breaklines within the classification (filtering) process
for DTM generation using ALS data. Most of the re-
sults were obtained within a test project initiated by the
German federal agency for hydrology ("Bundesanstalt fiir
Gewässerkunde”).
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