from incomplete dataset (EM). As for the backscattered
waveform decomposition, the procedure is as follow:
a): model parameters
initiation: UN eo po E zm] ek, . Where
k denote the components number in the backscattered
waveform, and a );
waveform, u gu. a;
is the weight of components in the
(0 is specified as the parameters in
model function respectively.
Then likelihood function is computed according to the
initiated EORR by
Le = „Los ooo, Lf. qua)
i=l (2)
b): E-step:
pal gu atm
i. cab | 4
ie
Ya” 00, Lea)
1=0
nm (m) +
MA m
(4)
c): Mestep:
(m
git J jl ; k
(5)
uen (m) =].
ume dA Yo =Lk
Th (6)
gu = po) 53 4 y, — 2 Ny, -umy Vi id Te ek
(7)
d): convergence check:
Based on the estimated parameters in previous steps,
the final likelihood function is computed as the waveform
decomposition accomplishing criteria.
IU + Sloat, um m gm
(8)
The iteration. ends once meet [zu fos or the
predefined criteria.
3. SPACE TRANSFORMATION
3.1 A/W/C-S Space
In this paper, the components in backscattered waveform
were modelled as generalized Gaussian function, and we take
the curve fitting approach accomplished the decomposition
procedure. And the corresponding results are four parameters,
and here we just take amplitude, width and cross-section to
form this space. We calibrated the scanner by using standard
reflectance targets before flight and measured albedo of roads
and roofs in the experiments region. The definitions of the three
parameters are as follows respectively (Plataniotis et al;
Wolfgang et al., 2006).
Amplitude: p, . D, 5 9)
4xR} ß} Sas
Where p;is the amplitude of cluster 7 , D, is the receive
©
aperture, Ris the distance from scanner to cluster; , 5 is
the transmitter beam width, Sis emitted pulse amplitude,
S. is the emitted pulse standard deviation, § »i is the
standard deviation of the echo P component i :
Width: W =2xs, 24s 5? (0)
Where 5; denotes the standard deviation of emitted pulse.
4
Cross Section: og = CR Ps. (11)
Where © — AnB; is the calibration constant.
cal — 9
Ha Ss,
Although the A/W/C parameter space could present a
general distinguishability among different objectives and targets,
there exists high correlation between the parameters. To a
certain component, its Amplitude and Cross section are positive
correlation, and has a related coefficient of 0.4-0.6 according to
experiments, while the Width and Amplitude/Cross section
have negative correlation, has an average related coefficient of -
0.3. Thus, in order to make good use of the components
parameters for point cloud classification, the A/W/C space is
mapped to IHSL space to obtain a uniform distinguishability
among all components and class.
3.2 Mapping to IHSL .
Because of the parameters in A/W/C-S space have non-
uniform distinguishability, this highly restrains the classification
performance. In this part, the IHSL transformation is performed
to map the original space parameters to HSV space. The
relationships of the parameters are described as follows:
A- I,
(12)
H sp
90
S zc
Then, inverse transformation is applied to the space and
obtained the final space parameters for the classification.
V3 £13)
" 2sin(120" — H)
H « H,-kx60? (14)
R L,
G |- R|c, (15)
B C
where: (18 C cos H,
C,=-CsinH,
The fuzzy C-means algorithm was first brought out in
(Bezdek,1981), and received extensive attention in colour
image segmentation based on pixel(Castleman et al., 1996). The
fuzzy C-means algorithm based on the minimization of C-means
function, defined as
CN .
J,(U,V)= SIS YD (16), where 44, is the fuzzy
i=l kzl
membership value of pixel k in cluster centre? , D,isa squared
inner-product distance norm given by
Dy zx, -w (17), where X, (k 21,2,..., N) is the given
set of input data, v, (7 — 1,..., C) is the set of C cluster centres.
The minimization of (11) can be solved by using the iteration
through t
The stati
Lagrange
TO
Setting th
0, when ;
Hy =
;
Thus, we
performir
Two
classifica
classifica
41 Su
In the stu
of 1.2poi
houses, 1
training c
Fig
The cla:
Shows tl
amplitud
objects c
section
neighbor
intensity
classifica
