  A topographical study on an ensemble of height profiles obtained from atomic
force microscopy techniques on various independently grown samples of tungsten
oxide WO$_3$ is presented by using ideas from percolation theory. We find that
a continuous 'geometrical' phase transition occurs at a certain critical
level-height $\delta_c$ below which an infinite island appears. By using the
finite-size scaling analysis of three independent percolation observables i.e.,
percolation probability, percolation strength and the mean island-size, we
compute some critical exponents which characterize the transition. Our results
are compatible with those of long-range correlated percolation. This method can
be generalized to a topographical classification of rough surface models.
