This paper presents a novel method for reconstructing complex 3D objects with unknown topology using silhouettes extracted from image sequences. This method exploits the duality principle governing surface points and their corresponding tangent planes, and enables a direct estimation of points on the contour generators. A major problem in other related works concerns with the search for a tangent basis at singularities in the dual tangent space. This problem is addressed here by utilizing the epipolar parameterization for identifying a well-defined basis at each point, and thus avoids any form of search. For the degenerate cases where epipolar parameterization breaks up, a fast on-the-fly validation is performed for each computed surface point, which consequently leads to a significant improvement in robustness. As the resulting contour generator points are not suitable for direct triangulation, a topologically correct surface extracting method based on slicing plane is presented. Both experiments on synthetic and real world data show that the proposed method has comparable robustness as those existing volumetric methods regarding surface of complex topology, whilst producing more accurate estimation of surface points.