  We present H-band surface photometry of 57 galaxies drawn from the Local
Sphere of Influence (LSI) with distances of less than 10 Mpc from the Milky
Way. The images with a typical surface brightness limit 4 mag fainter than
2MASS (24.5 mag arcsec^-2 < sb_lim < 26 mag arcsec ^-2) have been obtained with
IRIS2 on the 3.9 m Anglo-Australian Telescope. A total of 22 galaxies that
remained previously undetected in the near-IR and potentially could have been
genuinely young galaxies were found to have an old stellar population with a
star density 1-2 magnitudes below the 2MASS detection threshold. The cleaned
near-IR images reveal the morphology and extent of many of the galaxies for the
first time. For all program galaxies, we derive radial luminosity profiles,
ellipticities, and position angles, together with global parameters such as
total magnitude, mean effective surface brightness and half-light radius. Our
results show that 2MASS underestimates the total magnitude of galaxies with
<mu_H>_eff between 18-21 mag arcsec^-2 by up to 2.5 mag. The Sersic parameters
best describing the observed surface brightness profiles are also presented.
Adopting accurate galaxy distances and a H-band mass-to-light ratio of
Upsilon_H=1.0 +/- 0.4, the LSI galaxies are found to cover a stellar mass range
of 5.6 < log_10 (M_stars) < 11.1. The results are discussed along with
previously obtained optical data. Our sample of low luminosity galaxies is
found to follow closely the optical-infrared B versus H luminosity relation
defined by brighter galaxies with a slope of 1.14 +/- 0.02 and scatter of 0.3
magnitudes. Finally we analyse the luminosity - surface brightness relation to
determine an empirical mass-to-light ratio of Upsilon_H=0.78 +/- 0.08 for
late-type galaxies in the H-band.
