Applications to Industrial Quality Inspection - 3D Computer Vision: Efficient Methods and Applications - page 259

line distance of the cameras is 320 mm, and the average distance to the object
amounts to 480 mm. The resulting field of view corresponds to 10 ◦ . The size of
the image sections used for three-dimensional reconstruction is 240

240 pixels.
The surface is illuminated by one single or subsequently by two LED point light
sources. The intensity I , polarisation angle Φ , and sparse depth Z are used for three-
dimensional reconstruction. In addition to the fact that intensity and polarisation de-
gree essentially provide redundant information, as pointed out in Sect. 5.3.4 ,forthe
regarded rough metallic surfaces the behaviour of D is strongly affected by small-
scale variations of the surface roughness. Accordingly, the value of the polarisation
degree D for specular reflection varies across the surface by up to 20 %. Hence, the
polarisation degree does not represent a useful feature for three-dimensional recon-
struction in this application context.
This unfavourable behaviour of the polarisation degree is known from previous
work in the domain of photopolarimetry and has been discussed in Sect. 3.4.2 . Based
on the experiments regarding raw forged iron materials, however, it was found that
in contrast to the polarisation degree, the polarisation angle is not perceivably in-
fluenced by slight variations of the surface roughness. As a consequence, the po-
larisation degree is a feature which may be useful for determination of the surface
orientation only for smooth dielectric surfaces, which can be accurately described
in terms of the Fresnel equations as shown by Atkinson and Hancock ( 2005b ).

×

6.3.3.1 Results Obtained with the SfPR Technique

For three-dimensional surface reconstruction of the raw forged iron surface of the
connection rod with the local SfPR approach according to d'Angelo and Wöhler
( 2005b ) described in Sect. 5.3.1.2 , two intensity images and one polarisation angle
image were employed. Figure 6.15 a shows a flawless part and a part that displays
a surface deformation. The ratio-based and thus albedo-independent intensity er-
ror term according to ( 3.48 ) was used. The deviation between the flawless and the
deformed surface becomes evident in Figs. 6.15 b-c. The comparison between the
ground truth and the corresponding cross section extracted from the reconstructed
profile yields a root-mean-square error (RMSE) of 220 m.

Two experiments concerning the application of the global SfPR approach to the
connection rod surface were performed by d'Angelo and Wöhler ( 2008 ). In the first
experiment, we initialised the surface gradients by zero values and determined the
uniform surface albedo ρ 0 according to ( 5.23 ), relying on specular reflections. The
reflectance and the polarisation angle image as well as the stereo reconstruction
result are shown in Fig. 6.16 . The dashed line indicates the cross section for which
ground truth data are available. Cross sections extracted from the corresponding
reconstructed surface profiles and their comparison to ground truth are shown in
Fig. 6.17 . The RMSE values are 56

μ

mfor
the shape from shading approach which neglects polarisation information. While
the SfPR approach yields a very accurate reconstruction of the surface, the shape
from shading approach estimates a largely uniform value of the surface gradient

μ m for the SfPR approach and 281 μ