Applications to Industrial Quality Inspection - 3D Computer Vision: Efficient Methods and Applications - page 257

Fig. 6.13 Three-dimensional reconstruction of a metallic surface of non-uniform albedo ( dark line
traversing the left half of the image from top to bottom ). A constriction is visible at the right image
border. The input images ( left ) are acquired at illumination angles of 12 . 1 ◦ and 30 . 3 ◦ , respec-
tively. The surface reconstruction ( right ) is obtained by applying the ratio-based iterative update
rule ( 3.51 )
This scenario is addressed by Wöhler and Hafezi ( 2005 ), and the presentation in this
section is adopted from that work. The surface shown in Fig. 6.13 displays a dark
line in the left half of the image, which is an acceptable surface property that may be
due to small particles deposited on the surface during the production process, and a
constriction in the right half of the image, which is a defective thinning of the sheet
metal that may lead to mechanical instabilities.
The three-dimensional reconstruction of the surface is performed relying on the
ratio-based intensity error term ( 3.50 ) and the ratio-based iterative update rule ac-
cording to ( 3.51 ). The specular component of the surface reflectance was found to
be weak, such that it could be neglected for the viewing and illumination geometry
applied to acquire the images shown in Fig. 6.13 . Under a perpendicular view on the
surface, two images were acquired at phase angles of 77 . 9 ◦ and 59 . 7 ◦ . This config-
uration corresponds to elevation angles of the light source of 12 . 1 ◦ and 30 . 3 ◦ above
the average surface plane, respectively. In the ratio image, the dark line disappears
while the constriction stands out clearly. The reconstructed surface profile shows
that the constriction with a depth of less than 0 . 1 mm is recovered, while no arte-
facts occur at the location of the dark line. Hence, the ratio-based approach achieves
successful separation of pixel brightness variations due to non-uniform albedo from
those caused by changing surface gradients.
As another example, Fig. 6.14 shows the reconstructed surface of a steel sheet
with a shallow deformation along with the corresponding albedo map ρ uv .Thesur-
face profile was obtained by extending the fusion scheme for shading and shadow
features outlined in Sect. 5.2 to several light sources as pointed out in Sect. 3.3 .The
reconstruction procedure consisted of applying the ratio-based iterative update rule
equation ( 3.51 ) including the shadow-related error term ( 5.10 ), and subsequently