  Different scaling and autocorrelation characteristics and their application
to astronomical images are discussed: the structure function, the
autocorrelation function, Fourier spectra and wavelet spectra. We recommend as
the optimal mathematical tool the wavelet spectrum with a suitable choice of
the analysing wavelet. We introduce the wavelet cross-correlation function
which enables to study the correlation between images as a function of scale.
The wavelet cross-correlation coefficient strongly depends on the scale. The
classical cross-correlation coefficient can be misleading if a bright, extended
central region or an extended disk exists in the galactic images. An analysis
of the scaling and cross-correlation characteristics of 9 optical and radio
maps of the nearby spiral galaxy NGC 6946 is presented. The wavelet spectra
allow to separate structures on different scales like spiral arms and diffuse
extended emission. Only the images of thermal radio emission and Halpha
emission give indications of 3-dimensional Kolmogorov-type turbulence on the
smallest resolved scales (160-800 pc). The cross-correlations between the
images of NGC 6946 show strong similarities between the images of total radio
emission, red light and mid-infrared dust emission on all scales. The best
correlation is found between total radio emission and dust emission. Thermal
radio continuum and Halpha emission are best correlated on a scale of about 1'
\simeq 1.6 kpc, the typical width of a spiral arm. On a similar scale, the
images of polarised radio and Halpha emission are anticorrelated, which remains
undetected with classical ross-correlation analysis.
