In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). 1APRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
Figure 4: Different types ol detection overlaps: (a) natural, (b) multiple detection, (c) false-false, (d) true-true and (e) true-false. 
Figure 5: Different situations while establishing pseudo one-to- 
one correspondence. Solid rectangles denote reference entity and 
dotted rectangles denote detection entity. The center of each en 
tity is either denoted by a dot or by a number. 
Two overlapping sets are obtained from B d and B r to facilitate 
establishing one-to-one correspondences. One is detection over 
lapping set Od = {od.,}. where 0 < i < m, of B d with respect 
to B T and another is reference overlapping set O r = { a r , 7 }, where 
0 < j < n, of B r with respect to Bd. Each entity o d . x in Od con 
tains a list of entities from B r which bd.i overlaps. If b d j over 
laps none from B r , o dd is empty. Similarly, each entity o r . v in 
O r contains a list of entities from B d which b r ,j overlaps. 
In order to obtain O d . a total of 16 points are considered on each 
rectangular entity b r ,j in B, \ 4 vertices and 3 points on each 
side at equal distant. All the entities b r . :/ in B r are tested against 
each entity b d j in B d . If at least 1 out of 16 points of b r j falls 
inside bd.i, b di j overlaps b r j. All b r .j which overlap each b d ,i are 
included into o d ,i. O r is obtained following the same procedure 
as that above. 
4.3 Pseudo One-to-One Correspondences 
In an approach similar to that of (Song and Haithcoat. 2005), a 
detected entity is counted as correct if any of its part overlaps a 
reference entity. Pseudo one-to-one correspondence means that 
each entity in one set has at most one correspondence in the other 
set. If a detected entity overlaps only one reference entity which 
is not overlapped by any other detected entity, then a true cor 
respondence is established between them. If a detected entity 
overlaps more than one reference entity, then the nearest refer 
ence entity (based on the distance between centres) is considered 
as a true correspondence for the detected entity. The same rule is 
applied when a reference entity is overlapped by more than one 
detected entity. As a consequence, there will be no correspon 
dence for false positive and false negative entities. 
Note that the definitions of true positive (TP), true negative (TN). 
false positive (FP) and false negative (FN) have been adopted 
from (Lee et al., 2003). In addition, a new term multiple de 
tection (MD), which indicates that for an entity presented in the 
reference set there are two or more entities in the detected set. 
has also been used. As shown in Fig. 4(b) there may be more 
than one detection of the same building. In order to establish the 
one-to-one correspondences it is important that only one of these 
detections is considered as a TP. The rests are counted as MDs 
and a new index named multiple detection rate is defined. Note 
that MD is counted for the detection set only and there will be no 
one-to-one correspondence for an MD. 
The iterative procedure below establishes the pseudo one-to-one 
correspondences between the detection and reference sets. 
1. If the overlapping entity o d . x corresponding to a detection 
entity b d ,i is empty, then b d . x is marked as an FP (Fig. 5(a)). 
Similarly, if the overlapping entity o i%7 corresponding to a 
reference entity is empty, then b r , is marked as an FN 
(Fig. 5(b)). 
2. For each overlapping entity o dd corresponding to a detec 
tion entity b d ,i, if b d ,i has not been marked yet: suppose the 
entities in o dd are sorted as {b r j 1 , b r .j 2 ,..., br, jk } (k > 1) 
in the ascending order of their center distances to the center 
of b d ,i. This means b r j 1 is the closest overlapped reference 
entity to bd.i- Further suppose the entities in o r . 7] are sorted 
as {bd.i,, b d ,i 2 , •••; } (/ > 1) in the ascending order of 
their center distances to the center of b r ,j,. If b ddl and b dd 
are the same entity, this means b dd is the closest overlapped 
detection entity to b r .j,. In this case, the following steps are 
followed: 
• Establish a one-to-one correspondence between b d . r 
and b r ,j 1 by marking both of them as TPs (Fig. 5(c)). 
• For each of the remaining entities b r .j s (2 < s < k) in 
o d ,i, b d .i is removed from the overlapping entity o r j s . 
In Fig. 5(d). since based on center distances reference 
2 is more close to the detection entity than reference 
1, reference 2 is a TP and reference 1 is an FP. 
• For each of the remaining entities b ddi (2 < t < l) 
in o r ,j], if the overlapping entity o ddi of b d . it con 
tains only one reference entity (which is obviously 
b r j 1 ) it is checked wdiether b ddi and bd.i overlap each 
other. If they overlap each other, then b d .i t is marked 
as an MD (Fig. 5(e)). If they do not overlap each 
other, then br.j, is removed from o ddt which becomes 
empty immediately (Fig. 5(f)). Otherwise, if o d . it 
contains more than one reference entities (including 
b r .ji), then brj, is removed from o d . lt . 
The above procedure continues until all the detection and refer 
ence entities are marked. Note that any of the overlapping entity 
which becomes empty in Step 2 of any iteration, the correspond 
ing detection or reference entity will be marked (as an FP or FN) 
in Step l of the next iteration. Since in practice, in most cases 
there will be only one overlap for each entity, the above iterative 
procedure converges quickly after a few iterations. 
4.4 Evaluation Indices 
Seven indices are used for object-based evaluation. Completeness 
C m , also known as detection rate (Song and Haithcoat, 2005) or 
producer's accuracy (Foody, 2002), correctness C r , also known 
as user’s accuracy (Foody, 2002) and quality Qi have been adopted 
from (Rutzinger et al., 2009). Multiple detection rate is the per 
centage of multiply and correctly detected entities in the detected 
set. Detection overlap rate is the percentage of overlap in the de 
tected set. Detection cross-lap rate, is defined as the percentage of 
detected entities which overlap more than one reference entities. 
Reference cross-lap rate is defined as the percentage of reference