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) 
    
  
  
   
   
   
   
    
   
    
    
     
    
    
    
   
   
  
    
     
    
     
  
    
  
   
  
  
  
  
  
  
  
  
   
  
   
  
   
    
   
   
  
    
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