  The goal of this work is two-fold. In the first part of this paper we regard
classical Plebanski's action as a BF action supplemented by constraints. We
introduce a spin foam model for Riemannian general relativity by systematically
implementing these constraints as restrictions on paths in the state-sum of the
BF theory. The spin foam model obtained is precisely the Barrett-Crane model.
This provides a clear-cut connection of the model with a simplicial action.
  In the second part of the paper we study the quantization of the effective
action corresponding to the degenerate sectors of Plebanski's theory and obtain
a very simple spin foam model. This model turns out to be precisely the one
introduced by De Pietri et al. as an alternative to the one proposed by Barrett
and Crane.
