Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains

—We propose a convex formulation for silhouette and stereo fusion in 3D reconstruction from multiple images. The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions. As a consequence, we can retain the original stereo-weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies, yet still obtain meaningful (nonempty) reconstructions which are guaranteed to be silhouette-consistent. We prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution. Compared to existing alternatives, the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets. We show that this projection c...

• Type: Journal
• Year: 2011
• Where: PAMI
• Authors: Daniel Cremers, Kalin Kolev
• Keywords: Exact Silhouette Consistency, Operations Research, PAMI 2011, Silhouette, Silhouette Consistency