Full text: XVIIth ISPRS Congress (Part B5)

    
    
   
   
    
   
      
   
   
    
    
   
  
  
  
  
  
  
  
  
  
   
    
    
   
    
    
    
    
    
    
    
    
    
  
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Digital Images 
| Image Preprocessing | 
i 
Generation of the Approximate 
Surface model 
5 
- 
i ES 
Area Based Matching Edge Based Matching 
aestu ina (Dynamic Programming) 
Combination of Matching 
Results 
| 
Elimination of Matching Errors 
and Interpolation 
Criteria Fulfilled ? 
Yes 
Digital Surface Model 
Figure 3. A schema of the algorithm for reconstruction of 
a surface with discontinuities by digital image matching 
technique. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
      
  
An approximate surface is built hierarchically with a pyramid 
structure by digital image matching. This process begins with 
an image pair of reduced resolution and a sparse grid on the 
XY plane in the object space. At every grid point in the object 
space, Z values are determined by Vertical Line Locus (VVL) 
Matching (Cogan and Hunter, 1984, Li, 1990). The image pair 
with a larger format size is used and the grid is densified after 
Z values for all grid points are calculated. Z values of grid 
points calculated during the previous iteration, are used to 
estimate approximate values in the current iteration. This 
procedure continues until the image pair reaches its original 
resolution. This insures a reliable approximate surface and 
reduces computing time. 
With the approximated surface model, an area based image 
matching module, namely a least squares matching in object 
space (Li, 1990), is used to calculate grid points in the object 
space point after point. This refines the Z values at all grid 
points in relative flat regions. At the same time edges are 
extracted and matched by a dynamic programming procedure 
to determine discontinuities of the surface. In this procedure, 
there are three similarity criteria for recognizing identical 
edges in the objective function: a) similarity of gray value 
distributions near edges, b) differences between edge 
directions, and c) image texture characteristics. This edge 
matching procedure (using dynamic programming) is 
constrained by edge continuity and geometric consistence with 
the obtained object surface. The first condition requires that a 
pair of correctly matched edges should be matched at all 
intersection points between these edges and epipolar lines. The 
second constraint implies that correctly matched edges in the 
object space should be within a proper tolerance to the 
calculated surface model. Thus, elimination of a part of 
mismatched edges is included in the matching procedure itself. 
À detailed description of this edge based image matching can 
be found in Li (1990). 
In order to acquire a complete surface model in continuous 
and discontinuous regions, results achieved by the area based 
and edge based image matching methods have to be combined. 
One of most important considerations is the preservation of 
local surface discontinuities during the integration of the 
results. It is realized in such a way that a) unmatched points 
along an edge are linearly interpolated; b) points with 
matching failures, which often appear near surface 
discontinuities are interpolated separately on both sides of 
edges. This local interpolation method makes it possible, to 
prevent depression of surface discontinuities due to global 
interpolation. 
Because of lack of image texture, effects of 
object-camera-geometry, and surface discontinuities, 
mismatches are unavoidable. False matches are detected by 
checking points in their neighborhood. They are then replaced 
by values calculated according to their neighborhood. Until 
here, a complex surface model is generated. 
In the image matching procedures, area and edge based image 
matching modules run separately (Figure 3). That is, the result 
from one image matching module does not benefit the other 
directly. In fact, area based matching improves the digital 
surface model and could provide better geometric constrains 
for the edge based matching. Conversely, the reconstructed 
discontinuities may improve the estimation of surface points 
near edges (potential surface discontinuities) by area based 
matching. In that sense, it is necessary to restart the image 
matching procedure with the improved digital surface model 
as an approximate surface, and to refine the digital surface 
model iteratively. This iterative procedure continues until 
some criteria such as the number of iterations and/or the 
percentage of total mismatched points are satisfied. The final 
result is a digital surface model, which approximates the real 
object surface as closely as possible. 
The presented algorithm for the reconstruction of digital 
surface models is applied successfully to different image 
types, e.g. aerial photography, close-range photography and 
electron-microscopic images (Li, 1990). 
3.3 Conversion from a Digital Surface Model to 
an Octree Representation 
3.3.1 Octree Representation 
Octree representations describe objects by a spatial numerical 
structure. Octree micro cells approach geometric details of 
objects hierarchically. An original octant is defined as a cube 
which contains the object to be described by an octree 
representation (Spur et al, 1989, 1990, Samet, 1990, Li, 
1991). The original octant is then divided into suboctants 
which fit the object shape by their hierarchical spatial 
structure. As shown in Figure 4(a), at first level, the original 
octant is divided into eight suboctants by halving it in three 
directions. Each suboctant is then checked whether it is 
occupied by the object. The suboctants are classified into three 
categories: a) F=Full (occupied by the object); b) E=Empty 
(no object element in the suboctant); and c) P=Partial (the 
suboctant is partially occupied by the object). On the other 
hand, these eight suboctants correspond to eight digits from 0 
to 7, which enable the suboctants to be related to the 3D 
  
  
  
  
   
	        
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