recognized as an “empty” polygon, otherwise the null value
is assigned as the partitioning score for P^ by H. The "best"
partition of P^ can be obtained when an "empty" polygon
with the largest area is produced by // (see figure 9 (b)).
The partition scoring function, H, for "pseudo-closed"
polygon can be described by
A(P*
H(P' Wu) ) if P" ="empty" polygon
A(P”)
A(P!
jte 0) = E if P z"empty" polygon “@
[re NU ) =0 if P" #"empty" polygon
IE HL) =0 if P" #"empty" polygon
where A() is the area of corresponding polygon. In fact, the
partition functions defined in Eq. 3 and Eq. 4 generate
polygons according to their level-of-detail forming a
building object; the most "significant" building part is
generated first and less "significant" one is later.
lower partitioning score higher partitioning score
(a) “open” polygon
lower partitioning score higher partitioning score
(b) “pseudo-closed” polygon
Q non-building label Q building label
Figure 9. Illustration of partition scoring functions
Once the partitioning scores for h' are computed by Eq. 3 or
Eq. 4, remaining hyperlines are sequentially selected from
the hyperline list and their partitioning scores are measured
by H. In figure 7(b), a hyperline, 4”, with the maximum
partitioning score is finally selected to partition P^. Then,
geometric information of P^ and A" are stored as a root node
of BSP tree, which is expanded as new child nodes with
vertices of P'* and P^ are added to the root node for further
recursive partitioning. The same method used for the
partition of P^ is applied to P'* and P^ respectively, but to
only an “open” or “pseudo-closed” polygon. This process
continues until no leaf node of the BSP tree can be
partitioned by hyperlines (see figure 7 (c)).
4.4 Polygonal cue grouping
Figure 10 (a) — (c) shows an example how the BUS space
with a set of convex polygons is generated by the recursive
partition of an initial polygon as described in the previous
section.
Once the BUS space is generated by expanding a BSP tree,
final leaves of the BSP tree are collected. A heuristic
filtering is applied to them so that only "building" polygons
remain (see figure 10(d)). A convex polygon of final leaves
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
of the BSP tree is verified as the "building" polygon by
following rules:
e A polygon, P, is verified as the “building” polygon If it
is classified as "closed" polygon, satisfying following
conditions:
N, (P) » n, and d, (P) » yxd,; P 5 "closed" polygon(5)
where Nye» is the number of member points of P^. n,
(75) is a member point threshold; d,, is the point density
of P' computed by Eq. 1; y (70.6) is a control parameter
(0€ y €1); dj, (70.1) is a point density threshold.
e A polygon, P, is verified as the “building” polygon if it
is classified as "open" polygon, satisfying following
conditions:
N ULP!
Pp» (P) = IU > Pns P* ="open" polygon (6)
where py; is a point ratio of building labels over the total
number of member points of P and its threshold is pil
(70.6); Ny, and N,,,,, are functions to count numbers of
building labels and non-building labels belonging to P'.
(a) initial partitioning (b) intermediate partitioning
(c) final BSP partitioning (d) “open” polygon filtering
Figure 10. Polygonal cue generation and grouping
5S. BUILDING EXTRACTION RESULT
Figure 11(a) shows a building extraction result over the
Greenwich dataset (referred as the UCL building map)
generated by the proposed technique. The overall success of
the technique was evaluated in comparison with the ground
plan vectors of MasterMap® provided by the Ordnance
Survey (see figure 11(b)).
Although the OS MasterMap® provides a high-level of detail
and accuracy, there are distracting features of the OS
MasterMap® that causes difficulties in the quality
assessments. The OS data does not contain some buildings
even though they are obviously apparent in the Ikonos image
and lidar. This is because the OS data was constructed at a
different time to the acquisition of the Ikonos image and
lidar data, from which the UCL building map was generated.
In addition, the scale of the features in the OS MasterMap”
has been compiled at a larger scale than the one of Ikonos
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