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Fig. 3.1 ( a ) Side view of an industrial part (friction plate) displaying two ridges due to technical
failure. The ridges are perpendicular to the surface such that they do not appear in the perpendicular
( top ) view, as is the case here. Their shadows on the surface, however, can be clearly distinguished
( dashed contour lines ). ( b ) Binarised ratio images. ( c ) Analysis of the shadow contour. ( d ) Three-
dimensional reconstruction of the ridges based on their shadows
3.1.1 Extraction of Shadows from Image Pairs
This section describes a contour-based method for the extraction of shadows from
image pairs at subpixel accuracy and the subsequent reconstruction of small-scale
surface features. The presentation is adopted from Hafezi and Wöhler ( 2004 ). Two
images are required which show the same surface region illuminated from oppo-
site directions, respectively, and under oblique illumination. Pixels with identical
coordinates in these two images must correspond to the same physical points on
the surface. Possible ways to achieve this are to move neither the camera nor the
object to be reconstructed during image acquisition, or to apply image registration
techniques (Gottesfeld Brown, 1992 ). However, the same approach can be used to
extract shadow regions from single images. This section describes how shadow re-
gions can be determined from images at subpixel accuracy. Without loss of general-
ity, it will always be assumed that the scene is illuminated exactly from the left-hand
or the right-hand side.
Figure 3.1 a shows two images of the same part of the lateral surface of a friction
plate. The scene is illuminated from the left-hand side and from the right-hand side
(images I 1 and I 2 , respectively). As neither the part nor the camera is moved, no im-
age registration step is necessary. In the ratio images I 1 /I 2 and I 2 /I 1 , the shadows
cast by the respective light source appear as bright regions, as shown in Fig. 3.1 b.
This approach has the advantage of being insensitive to albedo variations of the sur-
face, because regions of low albedo that might be erroneously taken for shadows
appear dark in both images, thus producing no bright region in one of the ratio im-
ages. A disadvantage is that surface parts situated in a shadow in both images are
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