  We present a generalisation of surface photometry to the higher-order moments
of the line-of-sight velocity distribution of galaxies observed with
integral-field spectrographs. The generalisation follows the approach of
surface photometry by determining the best fitting ellipses along which the
profiles of the moments can be extracted and analysed by means of harmonic
expansion. The assumption for the odd moments (e.g. mean velocity) is that the
profile along an ellipse satisfies a simple cosine law. The assumption for the
even moments (e.g velocity dispersion) is that the profile is constant, as it
is used in surface photometry. We find that velocity profiles extracted along
ellipses of early-type galaxies are well represented by the simple cosine law
(with 2% accuracy), while possible deviations are carried in the fifth harmonic
term which is sensitive to the existence of multiple kinematic components, and
has some analogy to the shape parameter of photometry. We compare the
properties of the kinematic and photometric ellipses and find that they are
often very similar. Finally, we offer a characterisation of the main velocity
structures based only on the kinemetric parameters which can be used to
quantify the features in velocity maps (abridged).
