Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 196

Fig. 5.9 Dependence of the relative deviation between the estimated and the true absolute scale
on the number of processed images. Left : Bottle sequence. Right : Lava stone sequence

Fig. 5.10 Increase of the
relative scale error with
increasing average PSF radius
for the last four images of the
lava stone sequence

Wöhler et al. ( 2009 ) point out that random errors are mainly due to the grey
value noise of the CCD sensor, which affects the estimated PSF radius and also
produces random fluctuations of the positions of the extracted feature points of about
0 . 1 pixel. Further systematic effects are to be expected when the typically strongly
blurred last images of the sequences are included in the analysis. The accuracy of
the KLT tracker was found to remain stable for PSF radii of up to 5 pixels. However,
the Depth-Defocus-Function (z) according to ( 4.15 ) shows a strong gradient and

thus allows an accurate estimate of the PSF radius σ only for small and intermediate
values of σ . This effect becomes apparent from Fig. 4.11 , where the 'usable' σ range
is between 2 and 3 pixels.
The estimation of z is based on the inverse nonlinear depth-defocus func-
tion ( 4.15 ). This may result in further systematic effects, since the scatter of the
z(σ ) measurements cannot be described by a symmetric distribution of zero mean
such as a Gaussian distribution, even when the scatter of the σ(z) measurements can
be described by a Gaussian distribution. The nonlinearity of

S

(z) implies that the
average deviation between the measurements of the depth z and the values predicted
by

S

S (z) is nonzero, which becomes especially relevant for large PSF radii where the