îptember 1-3, 2010 
ln: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds), 1APRS. Vol. XXXV111. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
>d. it is necessary 
e parameter vec- 
omposed of: the 
ratio s, the data 
the quality func- 
p. Some of these 
they have an in- 
tsually set to 1 or 
ry proportion be- 
;1 parameters has 
ght parameter 7^ 
ow value of (3 is 
/ersa. Therefore. 
1 is the weight 77 
)f parameter esti- 
arameter vector 0 
the density of the 
maximize the ex- 
mration x is like- 
ods (Chatelain et 
' the Expectation- 
996) is very rele- 
te three following 
(8) 
iod: 
У) (9) 
у) (10) 
extended density 
nstant is inacces- 
) approximate the 
lesag, 1975, Bad- 
ise of incomplete 
.(du) 1 x 
(11) 
diich can be writ- 
(12) 
ring a Reversible 
>95) or a multiple 
ximization step is 
>rithm. The SEM 
ameter vector re- 
îd, we determine 
mizes the energy 
n. 
3 ELLIPSE MODEL 
3.1 From circles to ellipses 
Firstly, the estimation method was validated for a simple model of 
marked point process where the objects were circular (Chatelain 
et al., 2009b). Only one object mark corresponding to the radius 
of circles was introduced. The simulation results of the proposed 
approach on a 274 x 269 image of a flamingo colony in Camar- 
gue in France were not quite satisfactory (see figure 1). One can 
Figure 1: left: flamingo colony in Camargue. France ©Tour de 
Valat, right: flamingo extraction using a circle model: 363 circles 
©INRIA (3 = 1000. 7 d = 13.88, s = 0.3, d 0 = 1.33). 
notice misdetections on figure 1 (right). Thus, such a model does 
not deal very well with the problem of flamingo extraction. A 
model of an ellipse process may be more suitable to the flamingo 
shape. This process is defined on the following object space: 
14 = [0, A uin:r] X [0, ax ] X 7mm , ClrnaX] X [b n im • b maT ] X [0, 7r[ 
which corresponds to the parameterization space of an ellipse u 
defined by five variables u = (x, y, a, b. u). a ma x and a mi v 
are the parameters that demarcate the space of the semi-major 
axis a. and bn,ax and b n ,in are the parameters corresponding 
to the definition domain of the semi-minor axis b. The figure 
2(right) illustrates such a parameterization. This makes the esti- 
Figure 2: left: quality function, right: ellipse parameterization. 
mation algorithm time consuming since the number of parameters 
is increased using the ellipse process. 
3.2 Validation of the ellipse model 
image (see figure l(left)), 25 min for the tree image (see figure 
4(left)) and 1 h and 36 min for the boat image (see figure 5(top)). 
The set of ellipses obtained at the convergence of the SEM algo 
rithm for the flamingo image is revealed by the figure 3(right). 
After estimating the data weight, objects are extracted thanks to a 
simulated annealing algorithm. The estimates as well as the con 
figurations of ellipses corresponding to the flamingo extraction, 
tree crown extraction and ship detection are respectively depicted 
in figures 3(right). 4(right) and 5(bottom). These results show 
that the proposed approach is very relevant for flamingo and tree 
crown extraction but does not fit the problem of boat detection. 
Therefore, we suggest in the second paragraph to modify the pro 
posed model for the boat image. Moreover, to assess the accuracy 
of our solution, we have manually generated the ground truth of 
the flamingo image: the red ellipses are those that are automat 
ically generated: the black ones are those that are supposed to 
appear (7 false negatives), the crossed red ellipses correspond to 
those that are wrongly detected (4 false positives) and all the red 
ellipses which have a blue point in their midst are considered as 
correct. From these results we compute the f-measure which is 
0.98 and thus we conclude that our solution is very accurate (re 
mark that an error up to 5% is acceptable for ecologists). Be 
sides, the given results are only for one run. the table 1 gives an 
idea about the computational lime average of several runs, the 
estimate mean 7^ and the standard deviation E [7^]. 
Figure 3: left: simulation step of the SEM algorithm, right: 
flamingo extraction using an ellipse model 387 ellipses ©INRIA 
(3 = 1000, 7 d = 16.25, s = 0.3, d 0 = 1.33) 
Figure 4: left: plantation in Saone et Loire ©IFN, right: tree 
crown extraction using an ellipse model: 598 ellipses ©INRIA, 
(f3 = 1000, 7rf = 15.14, s = 0.2, d. 0 = 2). 
In order to validate the proposed estimation method associated 
with an ellipse process, we tested it on three types of images; 
the flamingo image considered in the former paragraph, an im 
age of trees in Saone-et-Loire of 229 x 196 pixels (figure 4(left)) 
and an image of boats of 385 x 275 pixels (figure 5(top)). For 
each image, we outfaced a new object structure. We manually 
initialized some parameters. The activity parameter was set as an 
over-estimation of the number of objects in the image, /3 = 1000 
for all the treated images. The maximum overlapping rate was set 
to s = 0.3. All our simulations were performed using a processor 
with 1.86 GHz frequency. The estimation algorithm appears to 
be computationally expensive. It lasted 12mm for the flamingo 
Flamingo image 
Tree image 
Boat image 
Mean time 
41 min 
24 min 
Ih and 41 min 
7d 
17.87 
14.85 
38.62 
E M 
2.5813 
0.5469 
0.5427 
Table 1 : Statistical results 
3.3 Modification of the energy model for boat detection 
As the boats of the image 5(top) are very close, the border T p (u) 
of an object u is not homogenous. That is why. we modify its def 
inition and we consider that it corresponds to the two ends of the