Estimating visibility is one of the most important steps for multi-view reconstruction using volumetric scene representation. In this paper, we propose a simple approach to estimating visibility based on the current state of a scene which is implicitly represented as the zero level set of a function. Our method can determine the regions of a 3D space visible to several given viewpoints efficiently. Using this visibility method, we also present a new variational formulation for multi-view reconstruction. We cast the multi-view reconstruction problem as an op- timization of a novel energy functional amenable for minimization with an Euler-Lagrange driven evolution. The proposed algorithm has been applied to both synthetic and real datasets with promising results.