Shape from Planar Curves: A Linear Escape from Flatland

We revisit the problem of recovering 3D shape from the projection of planar curves on a surface. This problem is strongly motivated by perception studies. Applications include single-view modeling and fully uncalibrated structured light. When the curves intersect, the problem leads to a linear system for which a direct least-squares method is sensitive to noise. We derive a more stable solution and show examples where the same method produces plausible surfaces from the projection of parallel (non-intersecting) planar cross sections.