A new method for binary reconstruction of the left ventricle from two orthogonal projections is presented. A priori knowledge has to be incorporated to reduce the ambiguity of the problem. A minimum cost capacitated network flow algorithm is discussed, which yields the optimal solution with respect to the priori information. It is shown that this method can also be used in the presence of observation noise. The method is demonstrated by reconstructing several cross sections of a dog's left ventricle.