Being able to recover the shape of 3D deformable surfaces from a single video stream would make it possible to field reconstruction systems that run on widely available hardware without requiring specialized devices. However, because many different 3D shapes can have virtually the same projection, such monocular shape recovery is inherently ambiguous. In this survey, we will review the two main classes of techniques that have proved most effective so far: The template-based methods that rely on establishing correspondences with a reference image in which the shape is already known, and non-rigid structure-from-motion techniques that exploit points tracked across the sequences to reconstruct a completely unknown shape. In both cases, we will formalize the approach, discuss its inherent ambiguities, and present the practical solutions that have been proposed to resolve them. To conclude, we will suggest directions for future research. Table of Contents: Introduction / Early Approaches to Non-Rigid Reconstruction / Formalizing Template-Based Reconstruction / Performing Template-Based Reconstruction / Formalizing Non-Rigid Structure from Motion / Performing Non-Rigid Structure from Motion / Future Directions
Author(s): Matthieu Salzmann, Pascal Fua
Edition: 1
Publisher: Morgan & Claypool Publishers
Year: 2010
Language: English
Pages: 114
Acknowledgments......Page 9
Figure Credits......Page 11
Introduction......Page 15
Physics-Based Models......Page 19
The Finite Element Method......Page 20
Physics-Based Methods for Computer Graphics......Page 21
Physics-Based Methods for Computer Vision......Page 22
Learned Deformation Models......Page 23
Statistical Learning Methods......Page 24
Learned Models for Non-Rigid Modeling......Page 25
Regularization via Shape Parameterization......Page 27
Legacy of the Previous Approaches......Page 28
Motivation......Page 31
Camera Models......Page 32
3D-to-2D Correspondences......Page 33
Ambiguities under Weak Perspective Projection......Page 34
Ambiguities under Full Perspective Projection......Page 37
Performing Template-Based Reconstruction......Page 43
Imposing Temporal Consistency......Page 44
Developable Surfaces......Page 47
Smooth Surfaces......Page 48
Distance Constraints......Page 57
Problem Definition......Page 65
NRSFM under Weak Perspective Projection......Page 67
NRSFM under Full Perspective Projection......Page 68
Ambiguities of NRSFM......Page 70
The Missing Data Problem......Page 71
Performing Non-Rigid Structure from Motion......Page 73
Orthonormality Constraints......Page 74
Imposing Temporal Consistency......Page 75
From Basis Shapes to Basis Trajectories......Page 79
Global Constraints......Page 81
Local Constraints......Page 88
Splitting a Global Surface into Local Ones......Page 90
Future Directions......Page 95
Bibliography......Page 97
Authors' Biographies......Page 113
