  We introduce and publicly release a new code, ADAPTSMOOTH, which serves to
smooth astronomical images in an adaptive fashion, in order to enhance the
signal-to-noise ratio (S/N). The adaptive smoothing scheme allows to take full
advantage of the spatially resolved photometric information contained in an
image in that at any location the minimal smoothing is applied to reach the
requested S/N. Support is given to match more images on the same smoothing
length, such that proper estimates of local colours can be done, with a big
potential impact on multi-wavelength studies of extended sources (galaxies,
nebulae). Different modes to estimate local S/N are provided. In addition to
classical arithmetic-mean averaging mode, the code can operate in median
averaging mode, resulting in a significant enhancement of the final image
quality and very accurate flux conservation. To this goal also other code
options are implemented and discussed in this paper. Finally, we analyze in
great detail the effect of the adaptive smoothing on galaxy photometry, in
particular in terms of surface brightness (SB) profiles and aperture
photometry: deviations in SB with respect to the original image can be limited
to <0.01 mag, with flux difference in apertures of less than 0.001 mag.
