Triangulation-Based Approaches to Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 45

are initialised based on the polynomial coefficients obtained with the approach by
Lucchese and Mitra ( 2002 ), but can also be set to fixed values. The parameter

σ is

initialised by 1, and u 0 and v 0 by zero values.

1.4.8.3 Experimental Evaluation

The performance of the nonlinear fit described in Sect. 1.4.8.2 is evaluated using real
images. Traditionally, this is done either using synthetic data (Lucchese and Mitra,
2002 ) or by performing a bundle adjustment-based scene reconstruction or camera
calibration (Luhmann, 2006 ; Olague and Hernández, 2005 ). We do not compare our
algorithm and the reference methods on synthetic data for two major reasons.
1. Synthetic data only show how well the synthesis and the analysis algorithms
match and may—to a limited extent—provide quantitative information about the
noise sensitivity.
2. The number of influencing parameters that have to be modelled is quite large.
Apart from general and statistical influences (e.g. brightness, contrast, digital-
isation noise) there are a lot of local influences with even more parameters
(e.g. brightness gradient, inhomogeneity of illumination and pattern). Modelling
all these influences realistically in a way that does not accidentally favour one
method over another is difficult, if not unfeasible.
In a bundle adjustment-based calibration (Olague and Hernández, 2005 ), the vari-
ous sources of error (e.g. camera model, calibration rig error) are mixed; thus clear
distinctions between them are hard or even impossible to obtain when it is desired
to determine the accuracy of the employed technique for chequerboard corner local-
isation.
For these reasons images of real planar patterns were recorded. The patterns were
photoset on non-glossy paper from 8-bit greyscale images. The prints were attached
to the planar surface of a high-precision xy -table. The xy -table allows a motion in
either direction with a gauge stepping of 10 μ m. In order to obtain accurate dis-

placements we only used full 10 m steps in the x (horizontal) direction.

A batch of 100 images was recorded depicting the pattern (cf. Fig. 1.12 for some
examples), then we moved the pattern in front of the camera with the high-precision
xy -table, and recorded the next set of images. In order to attribute the images with
the relative motion in pixels we obtained the overall scaling factor by measuring the
subpixel accurate width of the box of size 64

μ

48 mm 2 around the targets. The grey
levels of the box borders along a row were each approximated by a parabola, and
the positions of the local extrema were used to compute the width d p of the box in
pixels at an accuracy of about 0 . 2 pixel. The resulting horizontal pixel scale amounts
to s x =

×

0 . 003 pixels/mm on the surface of the xy -table, implying a maxi-
mum systematic error of the chequerboard corner displacements due to inaccurate
knowledge of the pixel scale s x of about 0.03 %.
The images were acquired with a Sony DFW-V500 VGA 8-bit grey level cam-
era using a 12 . 5 mm lens, giving a horizontal field of view of 21 . 7 ◦ . The cam-
era was mounted at a distance of 190 mm from the xy -table with the optical axis

8 . 910 ±