  A method for inverting the statistical star counts equation, including proper
motions, is presented; in order to break the degeneracy in that equation it
uses the supplementary constraints required by dynamical consistency. The
inversion gives access to both the kinematics and the luminosity function of
each population in three r\'egimes: the singular ellipsoid, the constant ratio
Schwarzschild ellipsoid plane parallel models and the epicyclic model. This
more realistic model is taylored to account for local neighbourhood density and
velocity distribution.
  The first model is fully investigated both analytically and via means of a
non-parametric inversion technique, while the second model is shown to be
formally its equivalent. The effect of noise and incompleteness in apparent
magnitude is investigated. The third model is investigated via a 5D+2D
non-parametric inversion technique where positivity of the underlying
luminosity function is explicitely accounted for.
  It is argued that its future application to data such as the Tycho catalogue
(and in the upcoming satellite GAIA) could lead -- provided the vertical
potential, and/or the asymmetric drift or w_0 are known -- to a non-parametric
determination of the local neighbourhood luminosity function without any
reference to stellar evolution tracks. It should also yield the proportion of
stars for each kinematic component and a kinematic diagnostic to split the thin
disk from the thick disk or the halo.
