Convex Solutions to SfT and NRSfM Under Algebraic Deformation Models

This paper presents mathematical approaches to solve Shape-from-Template (SfT, reconstructing a 3D object's shape from a single image using a known template) and Non-Rigid Structure-from-Motion (NRSfM, figuring out how a flexible object moves and its 3D structure from video). The researchers use Semi-Definite Programming (SDP, a mathematical optimization technique for solving certain types of problems) to find solutions that work with different types of object deformation models, requiring only point correspondences (matching points between images) rather than additional impractical assumptions.