As a result of a systematic NIR H-band (1.65 micron) imaging survey of normal galaxies in the local universe, we are able to measure in a highly homogeneous way photometric and structural properties for a sample of 1143 galaxies. We base our analysis on a quantitative structural parameter, the concentration index C_31, instead of relying on the galaxies morphological classification. The C_31 parameter provides a model independent, quantitative and continuous characterization of the light distribution within galaxies, and it is thus to be preferred to either the Hubble type or a parameter like the bulge-to-disk or bulge-to-total light ratio. We find that galaxies can be completely described by three parameters, namely: a scale parameter (the H-band luminosity), a shape parameter (the concentration index C_31) and a colour parameter (e.g. the B-H colour). At low luminosity dEs and dIs, having similar C_31, are colour-discriminated, while at very high luminosity different C_31 discriminate S0s from Scs, otherwise undistinguishable on the basis of their colour. A single, monotonic relation exists between luminosity and mu_e in the H-band, as opposed to the two separate regimes that are generally observed in the B-band. As NIR luminosity traces quite accurately the galaxy mass distribution, this relation re-enforces the indication in favour of a scale-dependent mass collapse mechanism which produces higher surface-brightness and more centrally peaked galaxies with increasing mass. However, the presence of high-luminosity low-C_31 galaxies hints at other machanisms and physical properties (such as angular momentum) playing an important role in galaxy formation. (abridged)
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