approximate height image (DTM for remote sensing). In order 
to simplify the system, we assume that the light source is 
known. This is true for most of the applications. For remote 
sensing area, we can get the illumination direction from the 
header of the image file. In close-range photogrammetry area, 
the illumination direction is also known, because the light 
source is assigned by the experimentater. If the illumination 
direction is unknown, one can calculate it by using Pentland's 
method (1982), Lee and Rosenfeld's method (1989), Zheng and 
Chellappa's method (1991) or others. 
  
    
photometric 
model 
    
    
  
  
reflectance 
properties 
  
  
  
Fig. 1 Schematic of inputs and outputs 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
              
    
   
  
    
   
  
  
  
  
  
  
  
  
  
  
     
   
    
among the three algorithms. 
candidate light source brightness fnoreTimate 
photometric Ig som image height image 
model 9t, 27) I(x, y) 2 (x, y) 
i=1,--,m 
select training select training 
regions regions 
I(x, » Z (xy) 
region gradients 
Py Y), 4, (x. y) 
| à y 
algorithm DRP algorithm DHI (SFS) 
for determining the reflectance for determining updated height 
properties regions Z'(x,y) 
and region gradients 
p(x, Y qu. y) 
end of interation ? Eh ur] 
shading algorithm to 
obtain shaded image 
01, (X.Y) 0 ; x,y) 
  
I (xy) 
m RS 
  
  
  
select the approximate 
photometric model 9 
corresponding to the 
minimum error 
and end. 
  
  
  
  
  
Fig. 3 Diagram of DPM algorithm. 
3.1 Training Frame 
The training frame contains one algorithm (DPM) for 
determining the approximate photometric model. Some small 
regions are selected as the training regions for determining the 
approximate photometric model. In our algorithm, five small 
regions are selected. One small region is located at the centre of 
the brightness image and the height image. The other four are 
located at the four centres of the upper-left, upper-right, lower- 
left and lower-right quarters of the brightness image and height 
image. Several photometric models are assigned as candidate 
models. All candidate models are tested in the training regions 
to find an approximate photometric model. For every candidate 
model, the algorithm (DRP) for determining reflectance 
properties (see the working frame) and the algorithm (DHT) for 
determining the updated improved height image (see the 
working frame) are combined to construct an iterative 
procedure to find the goodness of the approximation. A fixed 
number of iteration is used in the training frame. After the 
iterations, for every candidate photometric model, a set of 
reflectance properties (photometric parameters) with respect to 
every pixel in the training regions and the updated improved 
height data in the training regions are obtained. Using these 
reflectance properties and the improved height data, a shading 
algorithm is carried out to obtain the artificially shaded regions. 
A mean square error, corresponding to every candidate 
photometric function, between the shaded region and the 
original brightness regions are calculated. The candidate model 
corresponding to the minimum error is selected as the 
approximate photometric model. Let 3t; i=1,--,m be the i th 
model of m candidate photometric models. Let 
$1 ,(, 3) 0, (x,y) be the k photometric parameters of the 
i th candidate photometric model obtained from DRP after the 
iterations. Let p (x,y) and q/(x, y) be the updated gradients in 
the training regions obtained from DHI after the iterations. The 
shaded regions I 3x, y) is 
i (2,y) = St os». q, (x. 5), $1; 05737 $0») , 
for candidate photometric modeli. (1) 
The mean square error e, ; between the shaded training regions 
and the brightness image in the training regions is 
Ei AX [iic.» - LG.) 
for candidate photometric modeli. (2) 
The determined approximate photometric model R is thus 
given by 
R=, minfe, } 3) 
The DPM algorithm is illustrated in Fig. 3. In fact, it is similar 
to the structure of the working frame in Fig. 2. 
3.2 Working Frame 
The working frame mainly contains two algorithms. The 
algorithm DRP is for determining the reflectance properties. 
The algorithm DHI is for determining the updated improved 
height image. We developed a region growing algorithm to 
determine the surface properties within DRP. In DHI, we 
follow Zheng and Chellappa's method (1991). 
1030 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
     
   
    
      
   
  
  
  
     
   
    
  
   
   
   
    
   
     
        
   
      
   
   
    
    
   
      
    
   
  
   
     
    
    
      
By using th 
frame, the | 
the approxi 
reflectance 
reflectance 
are used in 
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image and | 
of each pp 
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DHI to img 
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iteration st 
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calculated t 
If the me 
terminates 
surface ref 
image. 
3.2.1 DRP 
Surf: 
So far, our 
properties 
brightness 
similar wi 
and the pr 
significant 
at each po 
that of Ike 
our metho 
multiple | 
sources. 
A region 
proposed t 
In the alg 
estimated 
properties 
where 2, 
LI, 1s the 
model R 
where c n 
the direct 
Torrance-