nadir. Also, when the nadir point is close to the image 
centre (a usual situation in aerial photography), those 
horizontal line segments which generate buildings are 
either parallel or orthogonal within the building. 
These ideas are used in the line segment parser 
described below. 
The general procedure for reconstruction in object 
space is to start from a vertical line connected to 
several horizontal lines and introduce these into 
object space at an arbitrary datum. Vertical and 
horizontal lines connected to already introduced lines 
are then successively introduced. Logically weaker 
rules are introduced when no more lines can be 
introduced. As soon as a line has been found and 
introduced into object space, the procedure returns to 
the top level looking for more horizontal and vertical 
lines. A descending line of successively weaker rules 
used in this way are activated only when no stronger 
rule is applicable. 
The search for new lines is always made in order of 
numbering. As soon as a line has been introduced 
into object space, it can be used as a connection for 
new lines. The various steps are given below, most 
steps being illustrated in section 6 and figure 3. 
1) Generation of line drawing. Strip the 
segmentation of all line segments that cut the 
window boundary. The remaining structure is a 
bounded segmentation. 
2) Grouping. Sort the line segments of the 
segmentation into groups G;, i=1,..I, each group 
containing parallel line segments of a direction g,, 
i-1,.I-1, ojzo;, isj. The Eth group contains all line 
segments not parallel to any others. 
3) Vertical lines. Find the group of line segments 
pointing at the nadir point and call it group 1. This 
group can be empty. 
4) Search strategy. Sort the groups 2 to I-1 according 
to a predefined criterion. This criterion defines the 
search strategy, ie. it gives the order in which 
groups are searched in point 5). Several different 
search strategies will be used, the procedure 4) to 
15) running through each one in turn until the 
segmentation is accepted. Examples of search 
strategies are for instance sorting the groups 
according to decreasing size, first considering line 
segments that are orthogonal or parallel or sorting 
line segments according to length. 
Initial vertical line for parsing. Beginning with 
group 2 and proceeding to group I-1, look for two 
line segments belonging to the same group, both 
of which are connected to a line segment in group 
1. Avoid T-junctions. If no such pair is found, try 
the region segment parser. Introduce the three 
line segments found into object space. 
5) 
a) Assume that the altitude Z at the point closest 
to nadir of the line segment from group 1 is 
zero. Given the image coordinates (x,y), this 
point is given the point (X,Y,0) of object space 
using the transformation (1). The other point 
of this line segment is placed in (X,Y,h) of 
object space, where h is given by (2). 
731 
6) 
7) 
8) 
b) The other two line segments, both assumed to 
be horizontal, are connected to the end points 
of the line segment introduced in a). Their 
unconnected end points are ascribed altitudes Z 
according to the already known altitude of the 
connected end points. Both line segments are 
introduced into object space using the 
transformation (1). 
Connected horizontal and vertical line segments. 
Check all groups 1 to I for line segments connected 
to those already introduced in object space. 
a) If a line segment so found does not belong to 
group 1, is parallel or orthogonal in the line 
drawing to line segments already classified as 
horizontal, it is itself classified as horizontal 
and introduced into object space using the 
altitude Z of the connection point in the 
transformation (1). 
b) If a line segment so found does belong to group 
1, it is assumed to be vertical and introduced 
into object space using (2) to determine the 
altitude of the free end point. 
Line segments so found, but not qualifying 
under a) or b), are neglected. 
c) 
Do 6) until no more line segments qualifying 
under a) or b) are found. 
Sloping roof line segments. Look for two already 
classified line segments having the same height in 
object space and belonging to the same group. The 
two end points P,, P, should connect to two line 
segments L4 and L,, where the continued lines 
have a common point Ps. At least one of these line 
segments should be unclassified. The common 
point P5 should be on the continuation of a line 
segment Lj being either parallel or orthogonal to 
the horizontal line segments. 
The line segments L4 and L; are interpreted as 
sloping roof line segments. L; is interpreted as a 
roof line. L5 divides the roof into two roof parts to 
which L; and L, belong. If there exist line 
segments L; parallel to and belonging to the same 
segment as Ly, and L, parallel to and belonging to 
the same segment as L,, both of which have a 
common point on the continuation of L, at the 
other end point, the gable part defined by P;,P,,P, 
is assumed to be vertical. In this case, do a) else 
assume the roof to be symmetrical and do b). 
a) A line through P; and nadir cuts the line 
between P, and P, at P,. The line through P3,P, 
is considered vertical. The altitude of P4 and so 
of L5 is determined using the relation (2). 
Choose a point P,in the image, centred 
between P, and P;. A line through P, and nadir 
cuts a line colinear to L5 at Ps. The line segment 
P4,P5 is considered vertical. The altitude of P; 
and so of L4 is determined using the relation 
(2). 
L5 can now be introduced into object space using 
(1). L; and L, are introduced between the points P,, 
P, and the end point of L,. 
b)