The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
scale and 9 fragments of images in small scale. Prior to the
analysis of noise content, coloured images were replaced with a
resultant luminance image, using equation:
/ = 0,299R + 0,587G + 0,1142? (8)
where / = luminance image
R,G,B = channels of colour image
Matrix algorithm with the third order Coiflet filters was used
for the wavelet transform. The transform was carried out with
the aid of procedures written in the R environment. Selected
fragments were sized 1024 * 1024 pixels. Additionally, frames
in individual pairs were so masked to have the same contents.
That was indispensable due to various scales of the analogue
and digital photographs.
The wavelet decomposition was continued until the third
resolution level, in which the components had the size of 256 *
256 pixels. Kurtosis and variance for individual components
was established. Afterwards, the equation of preservation of
image relative variance was formulated.
4.3 The research results
It was found that the kurtosis for analogue photographs is
always lower than that of the digital photographs. The kurtosis
for analogue photographs varies between 3 and 3.5, irrespective
of the method of use and scale of the photos. The variability of
the kurtosis between detailed components is not visible. For the
analogue photographs examined, the distribution of detailed
components may be modelled with the aid of a normal
distribution, the kurtosis of which equals 3.
According to the studies, the kurtosis for digital photographs is
generally larger and, at the same time, exhibits greater diversity.
Both for the medium and small-scale photographs, the detail
kurtosis is above 10, with one exception however. The
exception refers to forested areas and parks of dense forest
stand. The kurtosis in such areas is smaller: for the medium
scale, the kurtosis is around 6, and 4 for the small scale
accordingly. Such phenomenon may be explained by the fact
that the distribution of the wavelet components is sensitive to
the natural image structure. The image of trees in the
photographs is of grainy structure, the finer the lower the scale
of the photos is.
As the results prove, noise conclusions based on the kurtosis are
not always objective. There are cases observed in which a flat
distribution, resembling the Gaussian one, does not result from
the random noise, but is the effect of natural fine structure of
the image.
Based on the analysis of the equation of preservation of image
relative variance, the following rules were established:
- the relative variance of details in images from digital
camera increases along with the decomposition - as
indicated by the grey zone in figures 5 and 6, which
encompass the results for all examined fragments of
photographs,
- the relative variance in images from analogue camera
decreases between 1 and 2 decomposition level and,
then increases slowly or is stable - as shown by the
zone with signature marks in figures 5 and 6, which
encompass the results for all examined fragments of
photographs
In order to better mark the changes of variance for further levels
of decomposition, in figures 5 and 6, the average changing
tendency was marked with an open polygon. From the
theoretical point of view, figure 2 is more appropriate, which
shows the values of relative variance of discrete, not continuous,
character. Moreover, figures 5 and 6 do not include the variance
of the coarse component. The value of that variance can be
easily established based on the formula (5).
Figure 5. The changes of relative variance for images in
medium scale
scale
5. CONCLUSIONS
It has been confirmed in the paper that, based on the
distribution of wavelet components, the share of random noises
in an image can be established. It has been shown that the
flattening of the histogram of wavelet coefficients is also