  Most of the known methods for estimating the fractal dimension of fractal
sets are based on the evaluation of a single geometric characteristic, e.g. the
volume of its parallel sets. We propose a method involving the evaluation of
several geometric characteristics, namely all the intrinsic volumes (i.e.\
volume, surface area, Euler characteristic etc.) of the parallel sets of a
fractal. Motivated by recent results on their limiting behaviour, we use these
functionals to estimate the fractal dimension of sets from digital images.
Simultaneously, we also obtain estimates of the fractal curvatures of these
sets, some fractal counterpart of intrinsic volumes, allowing a finer
classification of fractal sets than by means of fractal dimension only. We show
the consistency of our estimators and test them on some digital images of
self-similar sets.
