International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
  
shadow in 1D condition. Consider a row of the rotated DSM. It is 
a ID height field now. One point in this row, if possible, will cast 
a shadow point, called fore-end shadow, along the equivalent 
zenith angle. The points between these two points must be 
shadow points too, called same-section shadows (when no other 
models supplied besides of DSM). 
2.2 Shadow Traced In Image 
A shadow in space computed by photogrammetry is traced to 
obtain its projection in level 1 image. This procedure need 
ADS40 camera model, DSM, and shadow coordinate in LSR. 
Figure 2 shows the scheme of the procedure. 
  
Searching for 
  
  
  
  
  
  
Snow its scan line by Camera 
CORRI collinearity coordinate 
S In L. equation in LSR 
y 
  
  
Reconstructing 
the line of the 
sight scan line 
  
  
  
  
   
     
Cif CX, 
occluded by ray 
tracing? 
     
   
  
  
No shadow in 
image Level 1 
output 
  
Z, refers to the 
ground 
reference 
Let Z=Z, in 
the sight line 
  
  
  
height of level 
  
  
  
   
(X,Y) when 
Z= Zr 
Shadow 
coordinate in 
image 
  
Figure 2 Flow chart of shadow tracing 
The objective of ray tracing here is to decide if a cast shadow is 
visible by a scan line. In ray tracing, a cast shadow in space is 
first determined to be scanned by a certain scan line, supposing 
not blocked by any object, which is carried out by the camera 
model. Then it is traced to decide if it is visible or blocked. If 
  
     
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visible, its position in the project image is computed by 
colinearity function. 
Ray tracing is a computationally expensive procedure. The 
height field preprocessing is used to boost the efficiency by 
parameterizing the empty space above the height field surface, or 
DSM (Paglieroni, 1999). We improved the ray tracing algorithm 
for further boosting. Only the contours of buildings need to 
perform the parameter transform. In tracing, when the 
intersection of the ray with the cone corresponds to the current 
contour locates at a point before the current contour, the shadow 
is occluded and invisible, and the iterate procedure stops. 
Otherwise, the tracing goes on to the next contour. Figure 3 
illustrates the tracing steps as an example. Each contour 
corresponds to a cone and the associated parameter. In a 1D 
height field starting from the current camera position and 
stopping with the shadow point, tracing begins with contour cl. 
The ray intersects with the cone of c1 at point s1. Because sl is 
after cl, tracing goes on to the next contour c2. The ray 
intersects with the cone of c2 and c3 at s2 ad s3 respectively. 
Since s3 is before c3, tracing stops, and the shadow is known as 
occluded. 
If a shadow is visible its projection in the average ground height 
is then computed according to the colinearity equation( ADS40 
Information Kit). The image of level 1 is the projected image of 
the average ground height. Therefore, the projection of a 
shadow in the image can be obtained by translation, scaling, and 
rotation. 
     
| 
| 
| 
| shadow(j, z) 
  
cl ca 
Figure3 Steps of height field ray tracing 
2.3 Integrated Shadow Detection and Location 
The shadows derived from the last stage do not entirely fit with 
what we observe from the image. Because DSM itself is short of 
the details, such as the fine structure of the building, it is not