Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
An Invitation to 3-D Vision: From Images to Geometric Models
An Invitation to 3-D Vision: From Images to Geometric Models
A General Framework for Trajectory Triangulation
Journal of Mathematical Imaging and Vision
Photo tourism: exploring photo collections in 3D
ACM SIGGRAPH 2006 Papers
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Perspective Nonrigid Shape and Motion Recovery
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Nonrigid shape and motion from multiple perspective views
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Efficient articulated trajectory reconstruction using dynamic programming and filters
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
A unified view on deformable shape factorizations
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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This paper presents a linear solution for reconstructing the 3D trajectory of a moving point from its correspondence in a collection of 2D perspective images, given the 3D spatial pose and time of capture of the cameras that produced each image. Triangulation-based solutions do not apply, as multiple views of the point may not exist at each instant in time. A geometric analysis of the problem is presented and a criterion, called reconstructibility, is defined to precisely characterize the cases when reconstruction is possible, and how accurate it can be. We apply the linear reconstruction algorithm to reconstruct the time evolving 3D structure of several real-world scenes, given a collection of non-coincidental 2D images.