Convex Solutions to SfT and NRSfM Under Algebraic Deformation Models

Summary

The authors present nonlinear formulations for Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM) that model isometric, conformal and equiareal deformations. Unlike prior methods, which rely on relaxations such as inextensibility or on optic flow around correspondences, the approach needs only point correspondences and resolves ambiguities with maximal depth and maximal isometry heuristics. Semi-Definite Programming (SDP) solves all formulations, and an adapted opposite-depth parameterisation shows a smaller relaxation gap. Experiments on real-world benchmark datasets report superior accuracy over existing methods.