We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a
2D query shape as well as a 3D target shape and the output is a continuous matching curve
represented as a closed contour on the 3D shape. We cast the problem as finding the
shortest circular path on the product 3-manifold of the two shapes. We prove that the optimal
matching can be computed in polynomial time with a (worst-case) complexity of O (m* n^ 2*
log (n)), where m and n denote the number of vertices on the 2D and the 3D shape …