Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 189

Fig. 5.1 True ( dots ) and reconstructed ( crosses ) three-dimensional pose of the chequerboard, ob-
tained with a weight factor of α = 0 . 42

m 2 . In order to
validate our approach, we first reconstructed a planar object with reference points
of precisely known mutual distance. A chequerboard, as shown in Fig. 5.1 , with
10

length, was used. The pixels are skewless and of size 4 . 65 × 4 . 65 μ

15 mm 2 , was used. The 99 corners serve as features and
were extracted in every image using the method described by Krüger et al. ( 2004 )to
ensure subpixel accuracy. The reference pose of the chequerboard was obtained ac-
cording to Bouguet ( 2007 ) based on the given size of the squares (cf. Sect. 2.1 ). Note
that Bouguet ( 2007 ) determines the reference pose of the chequerboard by applying
a least-mean-squares fit on a single image, whereas the proposed algorithm esti-
mates the three-dimensional structure of a scene by using a least-mean-squares fit
applied to the whole image sequence. Comparing the obtained results with the deter-
mined reference pose of the object is therefore a comparison between two methods
conducting different least-mean-squares fits.
Experiments involving real-world objects were conducted based on image se-
quences that display a cuboid with markings at known positions, a bottle of known
diameter, and a lava stone with a pronounced surface texture. Images from the be-
ginning, the middle, and the end of each sequence are shown in Fig. 5.2 (Wöhler et
al., 2009 ).

× 8 squares of size 15 ×

5.1.3.1 Evaluation of the Offline Algorithm

To analyse the three-dimensional reconstruction results of the combined structure
from motion and depth from defocus approach, we define several error measures.
The deviation E reconstr of the reconstructed three-dimensional scene point coordi-
nates W x k from the ground truth values W x ref is given by

k

K

W x re k

1
K

W x k − 2 ,

E reconstr = (5.2)

k = 1

where K denotes the number of scene points. To determine an appropriate weight
parameter α in ( 5.1 ) we computed E reconstr for different α values in the range be-
tween 0 and 1. For α

= 0 the global minimisation is equivalent to structure from