  In this paper we describe an adaptive and multi-scale algorithm for the
parsimonious fit of the corneal surface data that allows to adapt the number of
functions used in the reconstruction to the conditions of each cornea. The
method implements also a dynamical selection of the parameters and the
management of noise. It can be used for the real-time reconstruction of both
altimetric data and corneal power maps from the data collected by keratoscopes,
such as the Placido rings based topographers, decisive for an early detection
of corneal diseases such as keratoconus.
  Numerical experiments show that the algorithm exhibits a steady exponential
error decay, independently of the level of aberration of the cornea. The
complexity of each anisotropic gaussian basis functions in the functional
representation is the same, but their parameters vary to fit the current scale.
This scale is determined only by the residual errors and not by the number of
the iteration. Finally, the position and clustering of their centers, as well
as the size of the shape parameters, provides an additional spatial information
about the regions of higher irregularity. These results are compared with the
standard approximation procedures based on the Zernike polynomials expansions.
