Triangulation-Based Approaches to Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 47

Based on a standard calibration of the intrinsic camera parameters (Krüger et
al., 2004 ), it was found that the lens displays only insignificant distortions. The
lens distortion was measured to be less than 0 . 2 pixel between the distorted and the
undistorted image near the image corners, leading to a maximum relative shortening
of displacements in the image corners of 0.1 %.
As the random scatter (standard deviation) of all chequerboard corner localisation
techniques examined in this study is always higher than 1 % of the displacement and
corresponds to about 10 % for the most accurate method when averaged over all
displacements, it can be safely assumed that the ground truth is sufficiently accurate
for our evaluation.
The xy -table was moved to the positions 0, 10, 20, 30, 40, 50, 60, 70, 80, 90,
100, 150, 200, 250, 300, and 400

m along the horizontal axis, translating into
horizontal displacements of 0 . 00, 0 . 09, 0 . 18, 0 . 27, 0 . 36, 0 . 45, 0 . 53, 0 . 62, 0 . 71,
0 . 80, 0 . 89, 1 . 34, 1 . 78, 2 . 23, 2 . 67, and 3 . 56 pixels.
The camera was operated in automatic exposure mode. Controlled illumina-
tion was provided by ceiling-mounted fluorescent lamps. This resulted in a fairly
uniform illumination of the targets, but on some targets local intensity gradients
occurred. We did not attempt to compensate these effects and did not use retro-
reflective targets in order to illustrate the robustness of our method with respect to
slightly uneven illumination.
The images were processed beginning with manually entered starting points. The
window size was set to 19

μ

9 pixels. For each of the nine corner
targets in each image we computed the location using the methods of Lucchese and
Mitra ( 2002 ), Krüger et al. ( 2004 ), and Sect. 1.4.8.2 . For the circular targets, the
position was computed using the weighted mean method with the square of the grey
levels as weights.
As we have no absolute positions in the ground truth—but accurate displace-
ments—the ground truth displacements were compared with the displacements es-
timated by the various operators. This was accomplished by selecting two random
images of the same target and computing the pixel distance between the estimated
absolute corner positions. Identical image pairs were selected for different opera-
tors.
The stability of the three methods with respect to the starting position was also
evaluated. The subpixel accurate corner position was computed starting from the
eight pixels around the manually selected starting position and the starting position
itself along with the resulting error due to offset from the manually selected starting
position. The Tukey box plots in Figs. 1.13 , 1.14 , 1.15 display the median, the 25 %
and 75 % quantiles, and the minimum and maximum values of the error between
ground truth and estimated displacement for all four methods. Each error bar was
computed based on 10 6 image pairs. The error depending on the target position in
the image (centre, edge, corner), on the target rotation, and on the target shear is also
displayed. All targets were acquired with two different contrasts (white on black and
light grey on dark grey). Another set shows the targets with a different PSF, which
was obtained by acquiring slightly defocused images.
Table 1.2 relates the methods to the plot labels. An intuitive measure of the local-
isation error is the difference between the 75 % and the 25 % quantiles, depicted in

× 19 pixels, i.e. r =