  Consider an affine Gaussian field X : R 2 $\rightarrow$ R, that is a process
equal in law to Z(At), where Z is isotropic and A : R2 $\rightarrow$ R2 is a
self-adjoint definite positive matrix. Denote 0 < $\lambda$ = $\lambda$\_2 /
$\lambda$\_1 \le 1 the ratio of the eigenvalues of A. This paper is aimed at
testing the null hypothesis '' X is isotropic'' versus the alternative '' X is
affine''. Roughly speaking, this amounts to testing '' $\lambda$ = 1 '' versus
'' $\lambda$ < 1 ''. By setting level u in R, this is implemented by the
partial observations of process X through some particular level functionals
viewed over a square T, which grows to R2. This leads us to provide estimators
for the affinity parameters that are shown to be almost surely consistent.
Their asymptotic normality provide confidence intervals for parameters. This
paper offered an important opportunity to study general level functionals near
the level u, part of the difficulties arises from the fact that the topology of
level set CT,X (u) = {t $\in$ T : X(t) = u} can be irregular, even if the
trajectories of X are regular. A significant part of the paper is dedicated to
show the L2-continuity in the level u of these general functionals.
