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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zoom
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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