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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
A set of hyperlines, {h':i=1,...,N}, are computed as P! is
intersected respectively by a set of line segments,
Ini... NI which is constructed by integrating the data-
driven and model-driven line cues. After setting up the
hyperline list, a process to partition P" with hyperlines
starts. This partitioning process consists of two procedure;
polygon classification and partition scoring.
pp me = 5
O
(a)
ris)
p ?
? zo )
Poh p
p P
best partition
Partition test and scoring Partitioning result BSP tree
© “open” or "pseudo-closed" polygon Q closed" or'empty' or "garbage polygon
Figure 7. Illustration of polygonal cue generation
43.1 Polygon classification
Polygon classification is a process to determine whether or
not the partitioning process is triggered over a given
polygon, P'. A polygon, P, is classified into a number of
polygon classes; "empty", "open", "closed", "pseudo-
closed”, “garbage” polygon. These polygon classes are pre-
determined depending on the labelling attributes of the
member points of P' or point density of the member points of
P or geometric property of P' as follows:
O
eee
o e Oo
(a) "empty" polygon (c) "closed" polygon
(b) “open” polygon
P i
n
| e P' a
| ® © ; = Ge” e if «lI, or A Xa,
(d) 'Pseudo-closed" polygon (e) “garbage” polygon
© non-building label Q building label
Figure 8. Polygon classification
* "Empty" polygon: P' is classified as “empty” polygon if
there is no member point within P (see figure 8 (a)).
* “Open” polygon: P is classified as "open" polygon if
the member points of P are attributed with both
building and non-building labels (see figure 8 (b)).
* "Closed" polygon: P is classified as "closed" polygon if
the member points of P' are attributed with only building
label (see figure 8 (c)).
* "Pseudo-closed" polygon: P' is classified as "pseudo-
closed" polygon if the member points of P* are attributed
with only building label, and the point density of P.
dp(P), is less than d;=0.1 (see figure 8 (d)), where
d, (P^) is determined by
NP
gl 0
where N,en(P) and A’ are the number of member points
and the area of P' respectively.
e "Garbage" polygon: P is classified as "garbage"
polygon if the member points of P are attributed with
both building and non-building labels, and any lateral
length or the area P is less than a certain threshold, i.e.,
l7 5 and a,5,750 respectively (see figure 8 (e))
The P' is partitioned with two child convex polygons if it is
classified as “open” or “pseudo-closed” polygon; otherwise
the partitioning over P' is terminated.
4.3.2 Polygon scoring
Once the partitioning of P is determined through the
polygon classification. The second step is partition scoring.
This process determines a hyperline, h', to generate the
“best” partitioning result of P' from the hyperline list. The
selection of /' is achieved by a partition scoring function.
That is, all the hyperlines are tested to obtain the "best"
partition of P' and the partitioning result generated by each
hyperline is evaluated by a partition scoring function. A
hyperline, h', with the highest partitioning score is finally
selected to partition P'. The partition scoring function, A,
over a polygon, P^, is given by
H (P^: l)e arg max (H(P^ WP gn #1) (2)
where P/* and P^ are child polygons produced by halving P”
with a hyperline, A’. In Eq 2, H assigns a maximum score to
A if it produces the best partitioning result, whereas a
minimum score for the worst partitioning result. Also, H
differently computes scores depending on the polygon class
of P^.
If P^ is classified as the “open” polygon, H computes
partitioning scores according to a bias degree of Ibe
distribution over P'* and P^ divided by h'; H for “open”
polygon computes higher partitioning score when a “closed”
polygon with larger area is produced by // (see figure 9 (a)).
The partition scoring function, 77, for *open" polygon can be
described by
P: =
P. I) (3)
(Pul) Nora
(rar) Nul
val? 5 ls NE (Psi. 3
(Pun) Gus
N on-bld
N on- bld
where A,,44 and Ny are functions to count numbers of
building labels and non-building labels belonging to a
corresponding polygon.
If. P is classified as the "pseudo-closed" polygon, 77
computes the partitioning score by an area ratio of child
“empty” polygon over P^ when either of P^ and P^ is