  The interstellar medium seems to have an underlying fractal structure which
can be characterized through its fractal dimension. However, interstellar
clouds are observed as projected two-dimensional images, and the projection of
a tri-dimensional fractal distorts its measured properties. Here we use
simulated fractal clouds to study the relationship between the tri-dimensional
fractal dimension (D_f) of modeled clouds and the dimension resulting from
their projected images. We analyze different fractal dimension estimators: the
correlation and mass dimensions of the clouds, and the perimeter-based
dimension of their boundaries (D_per). We find the functional forms relating
D_f with the projected fractal dimensions, as well as the dependence on the
image resolution, which allow to estimatethe "real" D_f value of a cloud from
its projection. The application of these results to Orion A indicates in a
self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value
higher than the result D_per+1 = 2.3 some times assumed in literature for
interstellar clouds.
