Performance analysis of opto-mechatronic image stabilization for a ...

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There is a clearly observable monotone dependency
between the width of the spectral density of the random
image model and the parameters of the image shift
measurement error. Matching of more smoothed images
produces larger error. It is important, that similar spectra
represent similar error parameters. For close spectral
densities 1 and 2 the difference of the standard deviation
is rather small (14–18%), whereas for wide apart spectral
densities 5 and 6 the difference is 80%, which is about 4
times larger.
The range of image shifts for which a linear error model
can be approximated is larger for more smoothed images.
In the experiment carried out, an interval of [71...710]
pixels has been estimated.
It can be assumed, that the comparison of the power
spectrum of a given real image with spectral densities of
reference image models can allow the estimation of
parameters of the image shift measurement error.
Decreasing the size of the image blocks can reduce the
calculation time but results in reduced accuracy. The
measurement error is increased due to larger non-symmetric
distortions of the correlation peak. Fig. 13 shows
estimated results for different image size. Image texture
model was of type 4 (according to spectral density in
Fig. 12). The range of image shift is 74 pixels.
It can be concluded, that for different image size the
residual error g changes approximately inverse to the
image area, whereas the time for calculation of the
correlation function is proportionally to the image area.
5.3. Tracking robustness to image content
The robustness of the shift vector determination with
respect to different image texture has been analyzed by a
variety of different images. Fig. 14 shows such a test image
with a ground resolution of 0.25 m per pixel from an aerial
test campaign of High Resolution Stereo Camera HRSC-
AX and processed at DLR, Institut fu¨r Planetenforschung.
The image contains areas with different texture, what
makes it possible to test the system operation with different
image content. For the 2D correlation all fragments of the
base image were re-sampled to a resolution of 0.75 m per
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K. Janschek et al. / Control Engineering Practice 15 (2007) 333–347
pixel. Subpixel image motion has been simulated by
shifting (also subpixel) of the base image fragments before
re-sampling. The motion blur has been simulated in
Fourier domain, by multiplication with Fourier transform
of the motion vector.
The image block size for image motion tracking was
chosen 128 128 pixel with grey scale 0y255 and random
additive image noise 20 grey scale bit (1s).
Fig. 15 shows the 2D-distribution of the image shift
estimation error (sum of bias and random errors 1s). In
Fig. 16 the error distribution pattern is superimposed onto
the test image. The error varies from 0.013 pixels for areas
with strong texture up to 0.104 pixels for low texture areas.
The average error value for the whole test image was 0.027
pixels.
Fig. 14. Test image.
Fig. 13. Parameters of image shift measurement error versus image size: (a) estimated parameters of error linear regression k11 and k22; (b) estimated
standard deviations of error components.