MiHHHgini 
dui(e\, eo) < d w , 
d a (ei,e 2 ) < d Q , 
dc(ei. eo) < dc 
Figure 6: left: new definition of the ellipse border, right: tangent 
ellipses 
where d u} (ei, e 2 ) 
is the difference of the orientation 
¿Uj -f" Cü'y 7T 
of ellipses e\ and e2, and d a {e\,e2) = | a — ( —- H—) | 
2 ' 2' 
is a measure that checks that the ellipses are not shifted. Finally, 
dc(ei,e 2 ) =| d(ci, C2) — (&i + 62) |, where d(c\. c 2 ) stands for 
the Euclidian distance between the centers c\ and c 2 of the two 
ellipses e\ and 62 respectively. Then, we append a prior energy 
that promotes two tangent ellipses as follows: 
Uai(e u e 2 ) = 
S(dc(ei,eo),dc, r 
&{d a (ei,e 2 ), d c 
0 
if ei C2; (14) 
otherwise. 
Figure 7: Extraction results with modification of the data term: 
635 ellipses (/3 = 1000. = 11.95, s = 0.3, d Q = 6). 
where tu(x. i maI ) is a reward function, previously introduced in 
(Ortner et al., 2008) to favor aligned buildinss: 
configuration x: 
Xmax) — 
1 + x 2 
x I ^max ^ 
1 + X' 
V x < x 
'¿'max 
(15) 
7al 
y! Uai{ei,ej) 
l<i<j<n(x) 
(16) 
It is negative, when the measure x is below the threshold x max 
and zero, if the measure x equals x max . The weight Ô is de 
pendent on the distance between ellipses. It equals 1. when the 
ellipses are too close and is close to zero, otherwise. Finally, 
the prior energy of a configuration x. which corresponds to the 
alignment constraint is the sum over all the object pairs of the 
The weight 7 a i is likewise a parameter of our model and must be 
estimated by the SEM algorithm. The experience showed that a 
value of 7ai lower than leads to good results for boat detection. 
In our simulations, the initial value 7°/ used in the SEM algorithm 
for the parameter 7 a .i is set to 7„i=7d/3, where 7° is the initial 
value for -y d (see (Chatelain et al., 2009b) for more details on 
the numerical evaluation of 7®). The estimation procedure con 
verges after 1 h and 38 min and provides the following estimates: 
7d = 25.3426 and 7 a i = 10.535. The extraction results depicted 
in figure 8 show that the ellipses are better organized. However. 
Figure 8: Extraction results with an alignment constraint be 
tween ellipses: 715 ellipses (/3 = 1000, 7a = 25.34. 7 a i — 
10.53, s = 0.3, do = 6). 
Figure 5: top: photograph of vessels in France ©CNES, bottom: 
boat detection using an ellipse model 508 ellipses ©INRIA (/3 = 
1000, 7 d = 38.65, s = 0.3, do = 6). 
one can notice some false-detections standing for aligned ellipses 
that are placed on the same boat (the number of boats automati 
cally estimated is 715 while the hand-counted number of boats is 
570). Furthermore, introducing a repulsive energy that penalizes 
not aligned ellipses does not enhance boat extraction results and 
leads to several misdetections. Thus, in a similar way to (Perrin 
et al., 2005), we propose to promote aligned ellipses that have a 
particular orientation (which is denoted by u>n). since the ships of 
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