Dense Non-rigid Structure-from-Motion and Shading with Unknown Albedos

Significant progress has been recently made in Non-Rigid Structure-from-Motion (NRSfM). However, existing methods do not handle poorly-textured surfaces that deform non-smoothly. These are nonetheless common occurrence in real-world applications. An important unanswered question is whether shading can be used to robustly handle these cases. Shading is complementary to motion because it constrains reconstruction densely at textureless regions, and has been used in several other reconstruction problems. The challenge we face is to simultaneously and densely estimate non-smooth, non-rigid shape from each image together with non-smooth, spatially-varying surface albedo (which is required to use shading). We tackle this using an energy-based formulation that combines a physical, discontinuity-preserving deformation prior with motion, shading and contour information. This is a large-scale, highly non-convex optimization problem, and we propose a cascaded optimization that converges well without an initial estimate. Our approach works on both unorganized and organized small-sized image sets, and has been empirically validated on four real-world datasets for which all state-of-the-art approaches fail.