5.1.1. Model of area A: A stepwise multiple regression was
performed on 103 control points of known depth over the area,
for bands 1, 2, 3, 4 and 5. After sequential statistical tests and
the removal of leverages the final valid model of 89 control
points was defined (eq. 7). The statistic parameters that imply
the validation and optimization of the model (Lafazani, 2003)
are given in table 1. Band 1 and 4 do not satisfy the model.
z = 8.999 + 1.13X,— 5.241X3 + 4.491X5 (7)
where z= the estimated depth
X, X, X; - the natural logarithms of the
corresponding pixel values of bands 2, 3 and 5.
The model was tested with 230 points of known depths. The
depth estimation was considered satisfactory for the test points
that lied inside the zone of confidence interval of the estimated
individual values (fig. 2). A number of 58 points lie outside the
zone while 172, that is 75% of the total, lie inside it. The
absolute differences between known depths and estimated
depths at these points vary from 0.01 m to 1.52 m (fig. 3) with a
mean value equal to 0.6 m and a standard deviation equal to 0.4
m. The estimated zone depths vary from 6.4m to 14.0m. The
former statistical analysis indicates a very sufficient
performance of the model in this area despite the absence of
bands 1 and 4.
2350
Predicted z = 0,875°z+1, 169
80 89 10.9 12,9 14,0 16,6
Figure 2. The graphic expression of model in area A. The red
lines represent the limits of confidence interval of
estimated individual values. Blue circles depict the
control points and green circles depict the depth
estimation points. Estimated depths are on y-axis.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
X-axis:
Absolute differences
between measured
and estimated
Figure 3. The histogramme of absolute differences between
measured and estimated depths (area A). 74% of the
differences are under 1.0 m
5.1.2. Model of area B: The stepwise regression was performed
for the five bands on 67 initial control points over the area. The
final valid model of 45 points is given in equation (8) and its
statisticparameters in table 1. This model is not satisfied by
band 5 and the contribution of band 1 and 4, although
statistically significant, is small.
z=5.347 +0.302X, + 1.011X,-1.673X;-0.553X, (8)
where z-the estimated depth
Xj Xj, X, X, - the natural logarithms of the
corresponding pixel values of bands 1, 2, 3 and 4.
The model was tested with 25 points of known depths. Six
points lie out of the confidence zone while 19, that is 76% of
the total, lie inside it (fig. 4). The absolute differences between
known depths and estimated depths at these points vary from
0.02 m to 0.36 m, (fig. 5) with a mean value equal to 0.17 m
and a standard deviation equal to 0.08 m. The zone's estimated
depths vary from 2.7 m to 4.6 m. According to equation (8)
more bands satisfied the model that handled very sufficiently
the bottom reflectance variations.
Predicted z = 0,933°2+0,284
T T T T T T T
2,50 3.00 3,50 4,00 4,50 5,00 5,50
Figure 4. The graphic expression of confidence zone in area B.
The symbolisms are given in figure 2.
5.1.3. Model of area C: A strong correlation among the
independent variables X; was observed that led to a factor ana-
lysis. The statistical analysis gave one factor and therefore,
rather than the five image bands, the principal component (PC1)
Inte
was used
independ
principal
75 points
equation
Figure 5.
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