Factorization for non-rigid and articulated structure using metric projections

By Marco Paladini, Alessio Del Bue, Marko Stosic, Marija Dodig, Joao Xavier, Lourdes de Agapito. 2009

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Lifting Object Detection Datasets into 3D (2015, background): “A third option would be to build large datasets with objects in videos and use structure-from-motion techniques [3], [4], [5] to recover their shape.”
Visual SLAM and Structure from Motion in Dynamic Environments (2018, methodology): “[123] project the motion matrix onto the manifold of matrix constraints and thus the factorization can be done iteratively through least squares.”
Video Pop-up: Monocular 3D Reconstruction of Dynamic Scenes (2014, background): “Non-rigid structure from motion (nrsfm) approaches reconstruct 3D models of non-rigid objects from monocular video, typically by fitting a global lowrank shape model [31,22] to 2D tracks.”
Lifting AutoEncoders: Unsupervised Learning of a Fully-Disentangled 3D Morphable Model Using Deep Non-Rigid Structure From Motion (2019, methodology): “NRSfM, developed originally to establish a 3D model of a deformable object by observing its motion [4], was developed to solve increasingly accurately the underlying mathematical optimization problems [43, 30, 1, 9], extending to dense reconstruction [11], lifting object cat-”
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization (2012, methodology): “’s EM-PPCA [25]; (3) Metric projection [21]; (4) Trajectory basis method [3]; and (5) Column space fitting (CSF) [14].”