International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Loading of raw
LIDAR data of sub-
y
1. Selection of initial
(outlier-free) no-size subset
2. Selection of trend
surface type
F-Fisher Test
3. Estimation of meaningful trend
surface parameters
4. Enlarging of subset with
*best possible point"
5. Estimation of SAR unknowns
and outliers
F-Fisher & Chi-
Square Tests
Classification of points:
“ground” and “non-ground”
Figure 1: Work-flow ofthe SFS filtering algorithm.
1. Selection of the initial subset of (ng «« n)- size: this is
meant to be outlier free, containing then terrain (ground)
points only. Many automatic criteria could be implemented
for this purpose, mostly evaluating data variations statistics
(e.g. least median), but as a general statement, a user
defined graphic selection has to be preferred.
2. Selection of trend surface type: for modelling the subset
ground surface by (3), the user chooses a redundant k-
degree polynomial (e.g. cubic k = 3) (see Figure 2).
fe Ey pe ESTE perp ee er ro me
Select Trend Surface” a
; Surface Degree - YR Sc d
t7 Preview ——
(*. Plane i |
(^ 2nd Order
C 3rd Order
C 4th Order
+ Trend Surface Type
(v Othogonal Polynomial
^
-1000 QU $200
(” Polynomial all Cross Terms. |
"Polynomial Cubic Spline
(C^ Natural Cubic Spline
Help |
Figure 2: Selection of trend surface type in SFS: 3D-view of
(simulated and noisy) LIDAR points and initial subset.
3. Estimation of meaningful subset trend surface parameters:
Once estimated 6 by (8), the assessment of a reduced s « k
degree, describing with plenty sensitivity the trend, is
performed by an inferential F-Fisher Test, so skipping not
meaningful (k-s) parameters in 6. In such a way, r = 2s+1
is the size of the engaged polynomial coefficient vector.
Once steps 1.-3. are accomplished, the program goes on
iteratively enlarging the initial no -size subset up to the n-size
dataset. For each m-th iteration, p,0, 6 datasets O subset » € Are re-
estimated by (7), (8) and (9). Furthermore, also other statistical
quantities are computed, allowing to diagnostically monitor
either the trend surface modelling (see Figures 3. & 4.) or the
outlier searching (see Figure 5).
4. Enlarging of subset: its size grows from m to (m+1) adding
the point with smallest absolute standardised residual e,
given by (9). This point is called “best possible point”, since
it best fits the trend surface although it does not (yet) belong
to the subset; anyway, it can be classified as "ground" point.
5. Estimation of SAR unknowns and the best point detection is
iteratively computed by (7), (8) and (9), on the (m+1)-th
subset of (m+1)-size composed with ground points only.
Steps 4. & 5. are then iteratively repeated until Chi-square Test
on 6? variation and F-Fisher Test on Ô variation (with respect
to the initial ones) do not reveal that best possible point is really
an outlier. In fact, as known, the presence of outliers among
observations damages the estimation of 6? and 9, as can be
easily view in the right sides of Figures 3. & 4. Moreover, any
new point included from now on up to the whole dataset, can be
classified as outlier or “non-ground”.
As last consideration, it has to stress how the same classification
of points as ground/non-ground would be impossible
considering instead the whole dataset for masking effect on
components of e (see Figure 6 for last iteration/abscissa).
Figure 3: Values of Sgataset (green), Ssupser (blue), p (red).
3 "
zl :
25 s EN
* rae pom Ut 4
2}
z^
1.5 | i
4 |-- rene qe ra pren a ce 2 J
0.5 | :
o rrr a
0.5 ‘ A .
400 800 1200 1600 2000
Figure 4: Values of 0 (red), 0, (blue), 0, (green).
= 7 C =
4.5 F as a reams i
1 tit
: / v
o {
o T" ne ERR isse tieu erai ES er 1 ;
400 800 1200 1600 2000
400 800 1 200 1600 2000
Figure 5: Values of n components of e along the iterations.
Once the SFS program has been carried out, the trend
parameters of the ground are those relating to the maximum
subset outlier-free and every point is binary classified as
“ground” (0, green in Figure 11) or “non-ground” (1, red in
same Figure 11). Starting now from this classification, could be
possible to repeat whole SFS processing on outlier points only,
to find other small surfaces, e.g. building roofs; the developing
and implementation of this idea is currently in progress.
International A.
5. APPLICA]
The SFS progra
LIDAR dataset:
Optech® ALTM
5.1 Testing on :
As far as simul:
has been carrie
type (plane and
for mean noise
points, the pres
surface) has be
ground points |
the algorithm c«
General charac
survey conditio
Surfac
Polynomial
Uncorrelate
over 5
Spatial int
Raw data
Points s
Datast
A
Table
Processing suc
has given very
building/outlie
Coeffic
Statistical err
1* kinc
2" kin
D AR
Table 7: SFS
The performe
significantly ^
program Terr:
software for L
Ltd. A binary
by suitably exi
1. “Classify
building a
2. "Low poit
points in t
error point
