Applications to Industrial Quality Inspection - 3D Computer Vision: Efficient Methods and Applications - page 270

initial blockmatching stage yields a large number of three-dimensional points (cf.
centre row in Fig. 6.28 ) which appear to form a plane surface. The depth values are
fairly noisy, and some outliers are apparent which deviate from the plane by several
millimetres. This behaviour presumably results from points on the surface appearing
more or less strongly dissimilar in the stereo images. The point cloud obtained by
specular stereo (bottom row) is significantly less noisy, and the bent cross section of
the ring-shaped surface is clearly apparent. The shallow depression in the surface is
also visible (it has already been shown above that its reconstructed depth is in good
correspondence with tactile measurement).
For the connection rod and the star pattern, the initially very small fraction of
image pixels for which a stereo correspondence can be established increases by
several orders of magnitude in the course of the iteration process (cf. left row of
Fig. 6.29 , top). For the ring-shaped flange, the number of (initially very noisy)
three-dimensional points decreases by about a factor of 2, but the accuracy of the
measured depth values significantly increases. At the end of the iteration process,
the average disparity correction is smaller than 0 . 7 pixel for all three examples
(cf. Fig. 6.29 , left row, middle). A nonzero average value of d corresponds to
a uniform offset of the surface profile in the z direction. Another important self-
consistency measure is the standard deviation σ d of the disparity correction, which
directly quantifies how closely the rendered images derived from the reconstructed
surface match the observed stereo images (cf. Fig. 6.29 , left row, bottom). Initially,
σ d is larger than 8 pixels for the connection rod, while it amounts to about 3 pix-
els for the star pattern and the flange. These fairly large values indicate large-scale
discrepancies between the initial three-dimensional reconstruction and the stereo
images. The specular stereo algorithm yields values for σ d of about 1 pixel for
the connection rod and the flange and 0 . 4 pixel for the star pattern (for our stereo
configuration, a disparity difference of 1 pixel corresponds to a depth difference of
0 . 135 mm in the regarded range of depth values). If the polarisation information
is neglected, the self-consistency measures still show a similar behaviour (cf. right
column in Fig. 6.29 ).
As a whole, the average values and the standard deviations of the disparity correc-
tion inferred for the three examples provide self-consistency measures for the accu-
racy of the three-dimensional reconstruction result of the specular stereo algorithm
that indicate residual errors which are comparable to the deviations between the
three-dimensional reconstruction result and independently measured ground truth
data.

6.3.4.4 Consequences of Poorly Known Reflectance Parameters

The specular stereo algorithm of Wöhler and d'Angelo ( 2009 ) requires knowledge
about the parameters of the photometric and polarimetric reflectance functions. This
section discusses the behaviour of the specular stereo algorithm for poorly known
reflectance parameters, regarding the connection rod example. For the reflectance
function according to ( 3.14 ) we determined the parameters σ 1 =

3 . 85 and m 1 = 2 . 61