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In this paper, we investigate the problem of determining the visible regions of multiple cameras in a 3D scene without a priori knowledge of the scene geometry. Our approach is based on a variational energy functional where both the unresolved visibility information of multiple cameras and the unknown scene geometry are included. We cast visibility estimation and scene geometry reconstruction as an optimization of the variational energy functional amenable for minimization with the Euler-Lagrange driven evolution. Starting from any initial value, the accurate visibility of multiple cameras as well as the true scene geometry can be obtained at the end of the evolution. Experimental results show the validity of our approach.