We investigate the statistics of isoheight lines of some rough surfaces  (simulated and grown) at different level sets around the mean height in the saturation regime.  We find that these contour lines are closely related to Schramm-Leowner evolutions, therefore suggesting that conformal invariance is present.
We show that the isoheight lines on the WO3 surface are conformally invariant with the same statistics of domain walls in the critical Ising model.  They belong to the family of Schramm-Loewner evolutions with diffusivity coefficient of 3 (or SLE3).  This can be regarded as the firstexperimental observation of SLE curves.
We also investigate the statistics of isoheight lines of 2+1 dimensional Kardar-Parisi-Zhang (KPZ) model. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged.  The statistics of the winding angle also confirms this observation in particular that the contour lines of the KPZ model lie in the same universality class as self-avoiding random walks, or SLE8/3.