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Fig. 5.15 Three-dimensional reconstruction of a synthetically generated surface. ( a ) Ground truth.
( b )Intensity I , polarisation angle Φ , and polarisation degree D images. The three-dimensional
reconstruction result was obtained based on photopolarimetric analysis ( c ) without and ( d ) with
depth from defocus information
images, random fluctuations of z uv of the order of 0 . 1 pixel are introduced. A per-
pendicular view on the surface along the z axis with v
( 0 , 0 , 1 ) T
=
is assumed. The
75 .Thesur-
face albedo ρ was computed from ( 5.23 ) based on the specular reflections. We set
p ( 0 )
surface is illuminated from the right-hand side at a phase angle of α
=
and q ( 0 )
p DfD
q DfD
uv in ( 5.21 ) when using depth from defocus information;
otherwise, the PSF G is set to unity and the surface gradients are initialised with
zero values due to the lack of prior information. Figures 5.15 c-d illustrate that the
main benefit of depth from defocus analysis comes from the improved initialisation,
which prevents the SfPR algorithm from converging towards a local, suboptimal
minimum of the error function. The best results are obtained by utilising a combi-
nation of polarisation angle and degree, of reflectance and polarisation angle, or a
combination of all three features (cf. Table 5.3 ).
To examine the behaviour of the local and global optimisation schemes and their
combination with sparse depth data, dependent on how many images based on cer-
tain reflectance and polarisation features are used, d'Angelo and Wöhler ( 2008 )
apply the developed algorithms to the synthetically generated surface shown in
Fig. 5.16 a. We again assume a perpendicular view on the surface along the z axis,
corresponding to v
=
=
uv
uv
uv
( 0 , 0 , 1 ) T . The scene is illuminated sequentially by L
=
=
2
light sources under an angle of 15
with respect to the horizontal plane at azimuth
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