  The critical exponents for a class of one-dimensional models of interface
depinning in disordered media can be calculated through a mapping onto directed
percolation (DP). In higher dimensions these models give rise to directed
surfaces, which do not belong to the directed percolation universality class.
We formulate a scaling theory of directed surfaces, and calculate critical
exponents numerically, using a cellular automaton that locates the directed
surfaces without making reference to the dynamics of the underlying interface
growth models.
