ntly, accurate
| etc., can be
epipolar con-
erating hypo-
ation sources
994).
1emselves are
1 appearance
ological con-
: tastes, con-
c. Their ex-
js, weak con-
:s, loss of in-
sions and so
ective in cop-
using a vast
image under-
> background
nans possess.
-sense know-
or are forsee-
rental; we do
uch task und
r, 1993). Im-
gration of the
tor to achieve
motivates the
oaches to ob-
able to deliver
iser with con-
e accuracy. It
of the user be
| can be made
ccurate image
nands expert-
not without
rience, comes
DING
mated object
. model. Ob-
unctional and
rder to be in-
the presence,
s here on the
non objective,
including col-
rstner, 1993).
nodeling cap-
most, if not
ular, and (iii)
in of buildings
of object rep-
new modeling
ria.
leling is given
tric primitives
(i.e. fixed topology and variable geom etry) have been used for
reconstructing classes of simple buildings (Haala and Hahn,
1995; Lang and Schicker, 1993). While this representation
provides for volumetric modeling, it is not suitable for irregu-
lar or complex buildings. Moreover, constructing a complete
database of such models is unfeasible because the range of
building shapes is practically infinite.
Lin et al (1994) assume buildings to consist of union of rectan-
gular blocks. Herman and Kanade (1993) employ prismatic
models representing buildings by their height and a set of
closed polygons describing the ground plane. Buildings may
also be modeled (indirectly) as blob features in digital sur-
face models (DSMs) (Baltsavias et al, 1995). This coarse
representation can be employed as an approximation to re-
constructing buildings in the form of prismatic or parametric
models (Weidner and Forstner, 1995). All these three rep-
resentations generalise building shape to the extent that they
are inappropriate for precise building modeling, e.g. capturing
roof detail.
CAD systems employ representations such as the boundary
representation (BRep) and constructive solid geometry (CSG)
which are well-suited to and aimed at the construction of mod-
els of complex spatial objects. CAD models have been used
to reconstruct specific, a priori known buildings, e.g. “con-
trol houses" (Schickler, 1992) but due to their fixed topology
and geometry are inappropriate for unknown and complex
buildings. Generic building models, on the other hand, are
characterized by both variable topology and geometry. Fua
and Hanson (1991) reconstruct flat-roofed buildings from aer-
ial images using a generic model consisting of simple shapes
(rectlinear enclosures of edges) and photometric (planar in-
tensity within each building enclosure) components.
Mohan and Nevatia (1989) and this author in Baltsavias et al
(1995) hypothesized that generality in man-made object re-
construction may be achieved by having a not too large set of
common, regular geometrical shapes; any man-made shape in
the scene can be modeled by one of the shapes in the set or a
combination thereof. This suitability of this approach, which
we term composites of primitive surfaces (CPS) modeling,
for implementation in an operational building reconstruction
system is established below. Note that a similar concept has
been adopted by Braun et al (1995) in suggesting the recon-
struction of buildings as combinations of CSG primitives using
aspect representations.
3.1 Composites of Primitive Surfaces Modeling Scheme
CPS modeling is characterized by:
e A building is modeled by the reconstruction of its com-
ponent surfaces visible in the imagery. These surfaces,
when connected, produce a (partial) 3D description of
the building.
e CPS modeling enables a high degree of genericity: a
very large number of buildings can be modeled by com-
binations of a small set of geometrically-simple surface
primitives. Limiting assumption, such as flat roofs, 90?
angles, or simple rectangular shapes, typical of other
approaches, are avoided in CPS modeling.
e The modeling set is extensible to surface composites
which characterise typical geometries of building com-
ponents.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Class 1a in Figure 2 illustrates (some of) the core elements of
this set of surface primitives, i.e. primitive planar shapes. The
dimensions and 3D orientation of each primitive are variable.
For application in reconstruction, each primitive is represen-
ted in the computer as a set of criteria that extracted 3D sur-
faces fitting this model must fulfill. For example, the primitive
square is interpreted in the extraction procedure (see Sec. 4.3)
as a 4-sided polygon (4 lines, 4 corners) with 2 sets of par-
allel lines, all sides of equal length, 90 degree intersections.
Parallelity, intersection angles, line lengths and planarity can
be used as constraints in an adjustment of 3D lines hypottfes-
ized as a surface fitting the model (Sayed and Mikhail, 1990).
Image measurement inaccuracies must be accommodated in
formalizing these constraints. The planarity constraint must
be relaxed for curved surfaces, e.g. domes.
Class la Class 1b Class 2
Ero) ysis
Fog eqs
U Ken
Figure 2: Non-exhaustive classification of primitive surfaces
and composites for object modeling.
Class 1b contains closed planar surfaces with n-sides. Note
that the first primitive in this class permits non-orthogonal in-
tersections between the sides and is the generic representation
of all other primitives in classes 1a and 1b. A differentiation
is made, however, in order to take advantage of the added
constraints and checks the user is able to convey to the sys-
tem through the selection of more specific primitives, e.g. the
square primitive conveys provides the system with a greater
number of constraints than an n-sided polyface. The number
of primitives remains small and manageable.
This database of surface primitives is extended to include
commonly-occuring composities of the core (Class 1) prim-
itive surfaces. Each composite in Class 2 in Fig. 2 is sub-
ject to additional constraints and represents a subclass of
3D shapes. Further extensions are conceivable, with more
com plex com posites being formed to model increasingly more
specific cases. The parametric models of complete buildings
employed by Haala and Hahn (1995), Lang and Schickler
(1993), etc. can be seen as special cases of CPS modeling.
An example of the representational power of CPS is seen in
Fig. 3. The building can either be reconstructed using two
Class 1 primitives or two Class 2 composites.
= composite [77] : A }
or
= composite ATR ) —
Figure 3: Representing objects as composites of primitive
surfaces.
A number of features of CPS modeling may be seen as limit-
ations: (a) surface models cannot, in general, be uniquely
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