In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). 1APRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
Symmetrie Scoring Function 
Area Constrain (U d ) 
So far data energy can be calculated as equation (14): 
u d = Ud" J] = w s U d + uyU r d + w d Uj (14) 
where w s + uy + w d = 1. 
However, to more heavily penalize the trees which were appar 
ently not “true’' from empirical knowledge and accelerate the 
convergence rate of optimization process, an area constrain is 
added given by equation (15). 
if R < 3 
otherwise 
(15) 
-1.5- 
0 
1.5 
aR(s) 
where s is treetop s and R is the average radius of s. 
Finally, the data energy is computed as equation (16). 
Figure 2: Symmetric scoring function. 
U d =ma^ r ' rf} ^) 
(16) 
Boundary Point Depth (U d ) 
The valley depth of the most possible boundary point in the pro 
file between two local maxima indicates the possibility of the 
local maxima to be “true" treetops or not. So boundary point 
depth scoring function (see Figure 3) is given by equation (12). 
U d i(s) = 
I Sin y—(d(s) + £ d ) 
if 0 < d(s) < 2e d 
if d(s) > 2e d 
(12) 
Where s is a treetop, d(s) is the boundary point depth ratio giv 
en by equation (13). 
d(s) = (h s - h Hs) )/(h s - h 0 ) (13) 
Where h s is the height of treetop s, is the height of the 
most possible boundary point and h 0 is the threshold set for to 
stretch the value of high difference ratio, which is set as 5m. 
Boundary Point Depth Scoring Function 
i 
4.2.2 Contextual Energy: The contextual energy introduces 
a priori knowledge concerning the objects layout. It is natural 
for us to incorporate a constraint that penalizes severe 
overlapping of tree crowns. However, the design of constrain to 
penalize over-pruning situations might result in too much gaps 
on the tree crowns. To address this problem, the two scoring 
functions are proposed in detail below. 
Profile Connectivity (U c c ) 
As it is mentioned, this scoring function is used to penalize the 
over-pruning situation during the optimization process which 
leads to gaps between tree crowns. The disconnected ratio of i- 
th profile of treetop s is defined by equation (17). 
dpi) = Kr r - R rf \ßi (U) 
where p l s is the i-th profile of treetop s, R s is the average radius 
of s, and R°f ter R m f are the radius of the outermost and most 
Ps Ps 
possible boundary points of s on the i-th profile. 
The disconnect ratio of treetop 5 is then calculated as equation 
(18). 
c(s) = max (c(ps)) (z = 1 ~N) (18) 
where N is the number profiles of treetop s. 
Then the disconnected ratio c(s) is used as input to calculate 
the profile connectivity score given by equation (19). 
U c c (s) = 
1 if c(s) > c 2 
sin ( c (s) - j if q < c(s) < c 2 (19) 
if c(s) < c x 
-1 
Profile Overlap (t/°) 
Figure 3: Boundary point depth scoring function