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Fig. 5.19 Transformation of image 2 into the image coordinate system of camera 1 after the av-
erage and the standard deviation of the disparity correction d j have decreased to less than about
one pixel
measured between the observed rectified images with coordinate systems S 1 and
S 2 , while the disparity corrections d (m j are measured between the rendered and
the observed image in the rectified coordinate system S 2 .
Once this degree of self-consistency is reached, it is favourable to additionally take
into account the photopolarimetric information of camera 2. In our experiments (cf.
Sect. 6.3.4 ), we do not acquire a second polarisation image—it would be necessary
to perform the difficult task of absolutely calibrating the rotation angles of two po-
larising filters with respect to each other—but merely use the intensity information
of camera 2. In ( 5.20 ), the intensity error e I then consists of two parts according to
e I = e ( 1 )
I + e ( 2 I . For this purpose, the image of camera 2 is transformed during step 1
of the iteration scheme from coordinate system C 2 to C 1 (cf. Fig. 5.19 ). In iteration
cycle m , the appropriate transformation is obtained based on the three-dimensional
surface profile defined by the points C 2 x (m 1 i obtained during the previous iteration
cycle. The resulting transformed image of camera 2 and the image of camera 1 are
pixel-synchronous at reasonable accuracy due to the already achieved smallness of
the disparity corrections.
Including the accordingly transformed intensity information of camera 2 into
the optimisation scheme corresponds to a photometric stereo approach which ex-
ploits the effect of different viewpoints on the measured brightness of the surface,
while the direction of illumination remains constant. This technique does not pro-
vide additional photometric constraints for Lambertian surfaces, as their brightness
is independent of the viewing direction, which is the main reason why traditional
photometric stereo (Horn, 1986 ) relies on multiple illumination directions rather
than multiple viewpoints.
The described iterative scheme for specular stereo analysis is visualised in
Fig. 5.18 for the connection rod example regarded in detail in Sect. 6.3.4 . The initial
SfPRD step according to the left part of Fig. 5.18 (marked as step 1) yields a dense
three-dimensional surface profile which results in a rendered image in the rectified
camera coordinate system S 2 (step 2) that does not correspond very well with the
rectified image observed by camera 2. Determining correspondences between the
rendered and the observed image (step 3) and generating an accordingly corrected
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