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