D'Apuzzo, Nicola 
  
2.2 Surface Measurement 
Our approach is based on multi-image photogrammetry. Three images are 
acquired simultaneously by three synchronized cameras. A multi-image matching 
process (D'Apuzzo 1998) establishes correspondences in the three images 
starting from a few seed points. It is based on the adaptive least squares method 
(Gruen 1985) which considers an image patch around a selected point. One image 
is used as template and the others as search images. The patches in the search 
images are modified by an affine transformation (translation, rotation, shearing 
and scaling). The algorithm finds the corresponding point in the neighbourhood of 
the selected point in the search images by minimizing the sum of the squares of the differences between the grey levels in 
these patches. Figure 2 shows the result of the least squares matching with an image patch of 13x13 pixels. The black box 
represents the patches selected (initial location in the search image) and the white box represents the affinely transformed 
patch in the search image. 
An automated process based on least squares matching 
determines a dense set of corresponding points. The 
process starts from a few seed points, which have to be 
manually selected in the three images. The template image 
is divided into polygonal regions according to which of the 
seed points is closest (Voronoi tessellation). Starting from 
the seed points, the stereo matcher automatically 
determines a dense set of correspondences in the three 
images. The central image is used as a template image and 
the other two (left and right) are used as search images. Figure 3: Search strategy for the establishment of 
The matcher searches the corresponding points in the two correspondences between images 
search images independently. At the end of the process, the 
data sets are merged to become triplets of matched points. The matcher uses the following strategy: the process starts 
from one seed point, shifts horizontally in the template and in the search images and applies the least squares matching 
algorithm in the shifted location. If the quality of the match is good, the shift process continues horizontally until it 
reaches the region boundaries. The covering of the entire polygonal region of a seed point is achieved by sequential 
horizontal and vertical shifts (Figure 3). 
To evaluate the quality of the result, 
different indicators are used (resulted a 
posteriori standard deviation of the least 
squares adjustment, resulted standard 
deviation of the shift in x and y directions, 
displacement from the start position in x and 
y direction). Thresholds for these values can 
be defined for different cases (level of 
texture in image, type of template). If the 
quality of the match is not satisfactory 
(quality indicators are bigger than the 
thresholds), the algorithm computes again y "T E ini 
the matching process changing some : C qr Deae "n 
parameters (e.g. smaller shift from the s 
neighbour, bigger size of the patch). The 
search process is repeated for each 
polygonal region until the whole image is 
covered. At the end of the process, holes of areas not analyzed can appear in the set of matched points. The algorithm 
tries to close these holes by searching from all directions around. In case of poor natural texture, local contrast 
enhancement of the images is required for the least squares matching. Figure 4 shows the original images taken by the 
three cameras, the results after contrast enhancement and the matched points which result from the matching process. 
Before computing the 3-D coordinates of the matched points, the data pass through a neighborhood filter. It checks the 
data for neighbor similarity of the matched points comparing each point with the local mean values of the affine 
transformation parameters of the matching results. A matching process is repeated after filtering to measure the removed 
points. 
  
Figure 2. Least squares matching 
algorithm (LSM). Left: template 
image, right: search image 
  
  
    
    
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O seed points 
  
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e matched points 
  
  
  
Figure 4. Original triplet (first row), enhanced images (second row) and 
matched points (third row); the first image on the left is the template 
  
166 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
  
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