Robust Recovery of Shapes with Unknown Topology from the Dual Space

In this paper, we address the problem of reconstructing an object surface from silhouettes. Previous works by other authors have shown that, based on the principle of duality, surface points can be recovered, theoretically, as the dual to the tangent plane space of the object. In practice, however, the identification of tangent basis in the tangent plane space is not trivial given a set of discretely sampled data. This problem is further complicated by the existence of bitangents to the object surface. The key contribution of this paper is the introduction of epipolar parameterization in identifying a well-defined local tangent basis. This extends the applicability of existing dual space reconstruction methods to fairly complicated shapes without making any explicit assumption on the object topology. We verify our approach with both synthetic and real-world data and compare it both qualitatively and quantitatively with other popular reconstruction algorithms. Experimental results demonstrate that our proposed approach produces more accurate estimation while maintaining reasonable robustness toward shapes with complex topologies.