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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
[| Topology | Regularization | Generalization | Description |
| | Constructed: — skeleton. of | — No. roof faces | Regular DSM, ground plans. Hypothesize-and-test
ground plan. bounded by ground | using skeleton. Result strongly coupled to ground
plan edges. plans.
2 Constraints derived | Controlled by mini- | Regular DSM. Segmentation of planes but no topol-
automatically. mum region size. ogy built. Automatic derivation of constraints.
3 | Relaxation to connect points
from weakly structured cloud.
Constraints, snap.
Manually by operator.
Stereo images. Manual measurement of weakly
structured point cloud. relaxation to derive topol-
ogy, adjustment using constraints. snapping to correct
topology. Semiautomatic.
4 | CSG: Primitives and Boolean
operations.
CSG primitives, snap.
Manually by operator.
Mono images. Selection of primitives by operator,
measurement of primitive parameters supported by
image matching. Semiautomatic.
5 | Find and connect edges be-
tween extracted planar faces.
Outlines and jump
edges follow main ori-
entation. Constraints
proposed.
Controlled by mini-
mum region size.
Original laser scan data. Hough based region extrac-
tion, detection of edges. connected edges form topol-
ogy.
6 | CSG: Primitives and Boolean
operations.
CSG primitives, snap
(limited to height).
Influenced by ground
plan and buffer param-
eter.
Regular DSM. ground plans. Subdivision of ground
plan into rectangles, reconstruct individually, and
merge.
7 | Constrained tree search to find
topology between extracted
Constraints proposed.
Influenced by ground
plan and acceptance
planar faces. rules.
Regular DSM, ground plans. Extract planes. ac-
cept/reject on the basis of rules, global search for
topology. Weakly coupled to ground plans.
8 | Find and connect edges be- | —
tween extracted planar faces.
Influenced by ground
plan and split & merge
parameters.
Original laser scan data. Subdivide building area ac-
cording to ground plan, extract faces using Hough
transform, split & merge. Detection and connection
of edges.
9 | Find and connect edges be-
tween extracted planar faces.
Automatic constraint
detection and global
adjustment proposed.
Controlled by mini-
mum region size.
Regular DSM for segmentation, original laser scan
points for estimation. Extraction of roof planes.
merge, detection and connection of edges.
Table 1: Comparison of different modelling approaches: How is the topology obtained, how are regularities enforced?
I (Haala and Brenner, 1997), 2 (Weidner, 1997), 3 (Griin and Wang, 1998), 4 (Gülch et al., 1999), 5 (Vosselman, 1999),
6 (Brenner, 1999), 7 (Brenner, 2000a), 8 (Vosselman and Dijkman, 2001), 9 (Rottensteiner and Briese, 2003).
extrusions. Thus, the generalization level can be con-
trolled, but is of course tied closely to the ground plan.
(Brenner, 2000b) extracts planar faces from a regularized
DSM using a random sampling consensus (RANSAC) ap-
proach. Faces are accepted or rejected based on a set
of rules, which express relationships between faces and
ground plan edges. The final topology of the roof is ob-
tained from all accepted regions by a global search proce-
dure. The introduction of constraints and a least squares
adjustment to enforce regularity is described in (Brenner,
2000a). Generalization is linked to the ground plan and the
set of rules.
(Vosselman and Dijkman, 2001) and (Vosselman and Su-
veg, 2001) is an approach similar to (Vosselman, 1999),
however to prevent spurious roof faces, ground plans are
introduced as additional information. Concave ground
plan corners are extended to cut the building area into
smaller regions. The Hough-based plane extraction is con-
strained to those regions. Split-and-merge is used to obtain
the final faces. By using ground plans, generalization is
tied to the ground plan generalization, but also depends on
the parameters during split-and-merge.
(Rottensteiner and Briese, 2003) extract roof races using
seed regions and region growing in a regularized DSM.
Similar to (Vosselman, 1999), intersection and step edges
are detected and a polyhedral model is derived. It is pro-
posed to detect regular structures automatically and to in-
troduce them as constraints into a global adjustment. Gen-
eralization is controlled by parameters governing the plane
extraction process.
1087
2.2 Conclusions Drawn
From the presented approaches, one can conclude that
building the correct topology, enforcing geometric regu-
larities and ensuring a given generalization level are major
problems that have not been solved yet in a satisfactory
manner.
The easiest way to ensure a correct surface topology is to
construct the boundary representation directly. However,
this is only true as long as no subsequent processes (snap-
ping, parameter estimation) lead to a geometric change
which affects topology. Also, adjacent buildings should
not be modelled individually. Constructive algorithms like
CSG Boolean operations or building the skeleton yield the
correct topology, provided no numerical instabilities arise
(de Berg et al., 2000). When using CSG, the primitive
parts from which an object is built must be aligned prop-
erly, which is often a problem when the parameters of the
primitives are determined from measurements.
Enforcing constraints has been proposed by several au-
thors, however it has not been used to a larger extend.
The practical problem with constraints is that their num-
ber increases quickly with scene complexity. For exam-
ple, similar to the 2D case outlined below, a simple box
in 3D space can be described by its position (3), orienta-
tion (3) and dimensions (3), for a total of 9 parameters,
or degrees of freedom (DOF). However, considering this
box as a general polyhedral surface, we obtain 24 DOF
for the 8 points, 18 DOF for the 6 planes, and 33 con-
straints which enforce regularity, so that again 9 DOF re-
main. Thus, even if one had a modeler capable of identi-
