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The 3-D coordinates of the matched points are 
then computed by forward ray intersection using 
the orientation and calibration data of the cameras. 
To reduce remaining noise in the 3-D data and to 
get a more uniform density of the point cloud, a 
second filter is applied to the data. The first filter 
was based on the matching results space, the 
second filter is instead applied to the 3-D data. It 
divides the object space in voxels (whose 
dimensions can vary) and the 3-D points contained 
in each voxel are replaced by its center of gravity. 
The 3-D data resulting after this filtering process 
have a more uniform density and the noise is 
   
Figure 5. 3-D point cloud after passing filtering 
reduced. Figure 5 shows the 3-D point cloud derived from the images of Figure 4. 
Due to the poor natural texture of the shown example, the matching process produces a 3-D point cloud with relatively 
low density and high noise. In the future, it is planned to integrate in the matching process new functionalities such as 
geometric constraints and neighborhood constraints. This will improve the results in quality and density. 
2.3 Tracking Process 
23.1 Tracking single points. The basic idea of the 
tracking process is to track triplets of corresponding 
points through the sequence in the three images. 
Therefore, at the end of the process it is possible to 
compute their 3-D trajectories. 
The tracking process is based on least squares 
matching techniques. The spatial correspondences 
between the three images of the different cameras at the 
same time step (spatial L$M) and also the temporal 
correspondences between subsequent frames of each 
camera (temporal LSM) are computed using the same 
least squares matching algorithm mentioned before 
(Figure 6). 
The flowchart of Figure 7 shows the basic operations of 
the tracking process. To start the process a triplet of 
corresponding points in the three images is needed. 
This is achieved with the least squares matching 
algorithm (spatial LSM), the process can then enter the 
tracking loop. The fundamental operations of the 
tracking process are three: (/) predict the position in 
the next frame, (2) search the position with the highest 
cross correlation value and (3) establish the point in the 
next frames using least squares matching (temporal 
LSM). These three steps are computed in parallel for 
the three images. Figure 8 shows graphically the 
process. 
For the frame at time i+/, a linear prediction of the 
position of the tracked point from the two previous 
frames is determined (step 1). A search box is defined 
around this predicted position in the frame at time i+/. 
This box is scanned for searching the position which 
has the higher cross correlation between the image of 
frame at time / and the image of frame at time /+/ (step 
2). This position is considered an approximation of the 
exact position of the point to be tracked. 
  
   
    
  
  
    
right 
EM frame / 
spatial 
LSM }ompora 
LSM ; 
spatial frame +7 
centre right 
Figure 6. Temporal and spatial LSM 
ÿ IMAGE 2 IMAGE 3 
IMAGE 1 
START POINT START POINT START POINT 
Ÿ 
>( SPATIALLSM Jo 
| 
| IMAGE 1 | IMAGE 2 | IMAGE 3 
PREDICT POSITION PREDICT POSITION PREDICT POSITION 
IN NEXT TIME STEP IN NEXT TIME STEP IN NEXT TIME STEP 
V y 
FIND POSITION OF FIND POSITION OF 
BEST X-CORR IN BEST X-CORR IN 
REGION AROUND 
PREDICTION 
K 
TEMPORAL LSM: 
MATCH WITH 
PREVIOUS FRAME 
  
     
   
  
   
  
  
   
   
REGION AROUND 
PREDICTION 
   
  
    
   
  
   
V 
TEMPORAL LSM: 
MATCH WITH 
PREVIOUS FRAME 
   
    
  
   
   
CHANGE 
LSM 
CHANGE 
LSM 
PARA- 
METERS 
   
   
  
  
   
  
         
  
  
  
PARA- 
METERS 
   
  
  
   
  
CHANGE PARAMETERS 
OF BEST X-CORR SEARCH: |= 
BIGGER REGION 
  
TEMPORAL LSM 
SPATIAL LSM, 
   
  
  
Ÿ 
NEXT TIME STEP 
Figure 7. Flowchart of the LSM tracking process 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 167