In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3, 2010
Similarly, a profile overlap scoring function is designed to pe
nalize severely overlapped tree crowns. The overlapping ratio
of i-th profile of treetop s is defined by equation (20).
o(pi) = (R s + R S ' ~lp)/lp
(20)
where p l s is the i-th profile of treetop s, R s is average radius of s,
R s > is the average radius of s' which is connected with s by pro
file Ps, and Ip is the length of p l s .
The profile overlap ratio of treetop s is then calculated as equa
tion (21).
o(s) = max (o(pj)) (t = 1 —/V)
where N is the number profiles of treetop s.
(21)
Then the profile overlap score of treetop s is given bv equation
(22).
U?(s) =
Sin (¿7 (°( S ) ” “?)) [ f °1 - °( S ) - °2 ( 22 )
-1
At last, the contextual energy is computed as equation (23).
U c = w c U£ + w 0 U? (23)
where w c + w 0 = 1.
4.2.3 Parameters Settings: There are three categorizes of
parameter setting in the model: physical parameters, and
weights and thresholds.
The physical parameters have a physical meaning in the appli
cation and are fixed according to the scene. There are two phys
ical parameters in the model. h 0 set as the height of low vegeta
tion and the threshold used to penalize local maxima which
locate near the edge of tree crowns, both in the scoring func
tions of data energy.
Weights are assigned to data energy and contextual energy in
the calculation of global energy, respectively cr and (1 — a).
And more are used in the computation of data energy and con
textual energy respectively, as more than one constrains are in
corporated in the model. The settings of weights are basically
intuitive and tuned through dial and errors.
Thresholds are also necessary in the design of the scoring func
tions, as we want to set tolerances to different constraints. For
example, we can set a smaller tolerance of e s in the symmetric
scoring function, if we want to penalize more effectively about
treetops with asymmetric crown. It is the same case with s d , c 1
and c 2 . Oi and o 2 . In our application, we set a = 0.6, £ s =
1, = 0.25, Cj = 0.5, c 2 = 1.5, Oi = 0.4 and o 2 = 0.8.
4.3 Model Optimization
In the preliminary tests of our method, we used relatively sim
ple model evolving scheme to find the configuration of objects
with “minimum” global energy. This scheme simulates a dis
crete Markov Chain (2f f ) teM on the configuration space in
which only death process is considered. For each iteration, the
■ШШ
.
site with the highest global energy in the configuration is re
garded as the weakest site and removed from the configuration.
The iteration continues until there are only 3 sites left, which is
the minimum number of points required to construct a TIN.
As the initial site number is finite and relatively small, the itera
tions can be completed in a short period of time and the confi
guration with the minimum global energy during the Markov
Chain evolving process can be recovered quickly.
5. EXPERIMENTAL RESULTS
The ALS data used for this study was acquired by Riegl LMS-
Q560 in a coniferous forest area about 60km east to Sault Ste.
Marie, Canada. The point density is about 30 pt/m 2 . The ALS
data was first processed into CHM image with a resolution of
0.5m. We just used the highest point in each cell to reconstruct
the CHM and no smoothing operation was done to it.
After CHM was prepared, the a priori information was ex
tracted from the data and trees are then modeled as object in the
data using local maxima and crown radius as shown in figure 4.
As can be seen from the figure, trees are over-populated with a
total number of 169. Crown radiuses are reasonably extracted
' from the data.
20
40
60
80
100
120
140
160
20 40 60 80 100 120 140 160 180
20-
40-
100-
120-
140-
160-
20 40 60 80 100 120 140 160 180
Figure 4: Result of tree detection: (Up) initial configuration
with 169 tree objects shown in red circle; (Below) optimal con
figuration when minima global energy reached, with 127 trees
labeled as true.
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