Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 237

where the summation is carried out over all image pixels (u, v) . The minus sign
in ( 5.45 ) arises from the fact that our optimisation scheme aims to determine the
minimum of the error function.

5.6.3 Defocus Information

We utilise the depth from defocus technique described in Sect. 4.2.3.2 to esti-
mate depth values from the amount of defocus. This approach requires two pixel-
synchronous images; one is acquired with a small aperture ( κ = 8), while the second

one is acquired with a large aperture ( κ = 2). This procedure may be automated us-

ing a lens equipped with a motorised iris. For the first image we assume that no
perceivable amount of defocus is present. The images are partitioned into windows
of size 32 32 pixels. The PSF radius Σ in frequency space is computed by fitting

a Gaussian to the ratio of the amplitude spectra of the corresponding windows of
the first and the second image, respectively. Only the range of intermediate spatial
frequencies is regarded in order to reduce the influence of noise on the resulting
value of Σ . The depth-defocus function according to ( 4.15 ) is calibrated using the
combined chequerboard and random dot pattern shown in Fig. 4.9 .

×

5.6.4 Total Error Optimisation

To start the optimisation process, an initial object pose has to be provided. With
this pose a first set of images (intensity, polarisation angle, edges, and depth map)
is rendered. Each measured cue provides an error term, denoted by e I , e Φ , e E , and
e D , respectively. We use these error terms to compute an overall error e T which is
minimised in order to obtain the object pose. As the individual error terms are of
different orders of magnitude, we introduce the weight factors β I , β Φ , β E , and β D
to appropriately take into account the individual terms in the total error e T according
to

β D e D . (5.46)
The individual error terms are not independent of each other, such that they have to
be minimised simultaneously via minimisation of the total error e T . This may be-
come a fairly intricate nonlinear optimisation problem. The value of each weight
factor is chosen inversely proportional to the typical relative measurement er-
ror, respectively. However, we found that the influence on the observed inten-
sity, polarisation, edge, and depth cues is different for small variations of each
pose parameter (cf. Table 5.5 ). For example, a slight lateral translation has a
strong influence on the edges in the image but may leave the observed intensity
and polarisation angle largely unchanged. On the other hand, under certain view-
ing conditions, rotations around small angles are hardly visible in the edge im-
age and yet have a significant effect on the observed intensity or polarisation be-
haviour.

e T = β I e I + β Φ e Φ + β E e E +