  The assumption of Gaussianity of the primordial perturbations plays an
important role in modern cosmology. The most direct test of this hypothesis
consists in testing Gaussianity of the CMB maps. Counting the pixels with the
temperatures in given ranges and thus estimating the one point probability
function of the field is the simplest of all the tests. Other usually more
complex tests of Gaussianity generally use a great deal of the information
already contained in the probability function. However, the most interesting
outcome of such a test would be the signal of non-Gaussianity independent of
the probability function. It is shown that the independent information has
purely morphological character i.e. it depends on the geometry and topology of
the level contours only. As an example we discuss in detail the quadratic model
$v=u+\alpha (u^2-1)$ ($u$ is a Gaussian field with $\bar{u}=0$ and $<u^2>=1$,
$\alpha$ is a parameter) which may arise in slow-roll or two-field inflation
models. We show that in the limit of small amplitude $\alpha$ the full
information about the non-Gaussianity is contained in the probability function.
If other tests are performed on this model they simply recycle the same
information. A simple procedure allowing to assess the sensitivity of any
statistics to the morphological information is suggested. We provide an
analytic estimate of the statistical limit for detecting the quadratic
non-Gaussianity $\a_c$ as a function of the map size in the ideal situation
when the scale of the field is resolved. This estimate is in a good agreement
with the results of the Monte Carlo simulations of $256^2$ and $1024^2$ maps.
The effect of resolution on the detection quadratic non-Gaussianity is also
briefly discussed.
