A Linear Least-Squares Solution to Elastic Shape-From-Template

We cast SfT (Shape-from-Template) as the search of a vector field (X,dX), composed of the pose X and the displacement dX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints SBC to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints RBC of the deformed shape X+dX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computational cost.