Based 
  
al in the 
which is 
instruction 
nearity of 
previously 
instruction 
account a 
ng the sun, 
isors which 
es results 
estimation 
n method, 
sensor is 
ance based 
ship among 
t, sensor 
sun, and a 
del. The 
unction of 
slationship 
) DEM. Then 
mizing the 
e actual 
d radiance 
| order to 
2e, Least 
in general. 
near nature 
timation of 
ce so that 
o estimated 
onstruction 
r the case 
minimal in 
imation. 
inear least 
Levenberg 
a 1996 
Markard method would give us Aa 
solution to avoid local minimal. 
Furthermore, Simulated Annealing 
also would give us another solution. 
Two candidates of the methods are 
proposed in this paper for 
overcoming the aforementioned 
situation. 
The proposed method allows us to 
designate the region for minimizing 
the difference so that the estimated 
DEM is optimum in the sense of 
minimizing all the difference 
between actual radiance and 
estimated radiance based on the 
models for the region of interest. 
The existing surface reconstruction 
method focuses on the pixel of 
interest, not the region. When the 
pixel of interest, however, is 
suffered from occlusion, then the 
estimation accuracy of DEM get worth. 
Turns out, the proposed method takes 
into account the region, not the 
only one pixel of interest, 
minimizing the total difference in 
the region so that a good estimation 
accuracy is expected in such case. 
2. SURFACE RECONSTRUCTION WITH 
SIMULATED ANNEALING 
2.1 Surface Reconstruction Method 
for DEM Estimation 
Heinrich Enber and Christian 
Heiphe (1988) and the others proposed 
Surface Reconstruction Method for 
estimation of Digital Elevation 
Mode! (DEM) with stereo pair of 
images. In the method, a 
relationship between the surface of 
interest and the intensity of the 
pixel corresponding to the surface 
is X assumed, namely the pixel 
intensity is a function of DEM and 
the other factor. Thus the 
difference between real pixel 
intensity and the estimated pixel 
  
intensity is expressed by the 
following equation, 
^ A ^ 
d- g-g(z. p) (1) 
^ A À 
where d. g. g. z. P are the difference 
between real and estimated pixel 
intensities, real pixel intensity, 
estimated pixel intensity, estimated 
DEM and the other factor, 
respectively. |f the difference can 
be minimized, then the DEM of the 
pixel of interest can be estimated. 
This is the fundamental principle 
for Surface Reconstruction method. 
This equation is a non-linear 
equat ion SO that non-linear 
optimization methods are applicable 
to solve this equation. On the other 
hand, the equation can be linearized 
with Gauss method or Taylor 
expansion, 
^ A 
d-9g-(09/0z)A 2 
—(09/0P)A 7-22 £») (2) 
^ A 
where 2% 0 Az A0 are initial 
values and unknown variables for DEM 
and the other factors, respectively. 
If co-linear condition can be 
assumed, then the initial values are 
determined. 
2. 2 Methodology 
In this proposed method, equation 
(1) will be solved as a non-linear 
optimization problem There are 
several well known optimization 
problem solving methods. In this 
study, some of the typical methods 
are attempted. One of the methods is 
non-linear least square method like 
37 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996