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Keywords
(6)
3d reconstruction
Dynamic Scenes
Euclidean Space
Image Sequence
Moving Object
Line of Sight
Related Publications
(28)
Reconstruction of a Scene with Multiple Linearly Moving Objects
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Interpolating View and Scene Motion by Dynamic View Morphing
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Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence
Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence,10.1109/34.845377,IEEE Transactions on Pattern Analysis a
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Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence
(
Citations: 76
)
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Shai Avidan
,
Amnon Shashua
We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from lineofsight measurements only. The task is feasible only when some constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as "trajectory triangulation." We investigate the solutions for points moving along a straightline and along conicsection trajectories. We show that if the point is moving along a straight line, then the parameters of the line (and, hence, the 3D position of the point at each time instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conicshaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D
Euclidean space
for which seven views are sufficient). The paradigm of trajectory triangulation, in general, pushes the envelope of processing
dynamic scenes
forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point).
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, vol. 22, no. 4, pp. 348357, 2000
DOI:
10.1109/34.845377
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Citation Context
(54)
...This technique has been reprised by
Avidan and Shashua (2000)
for the so called “Trajectory triangulation”, i.e...
Simone Gasparini
,
et al.
Line Localization from Single Catadioptric Images
...Avidan and Shashua proposed the idea of trajectory triangulation [
1
]...
Mingyu Chen
,
et al.
Trajectory triangulation: 3D motion reconstruction with ℓ1 optimizatio...
...The principal work in ‘triangulating’ moving points from a series of images is by Avidan and Shashua [
7
], who coined the term trajectorytriangulation .T hey demonstrated two cases where a moving point can be reconstructed: (1) if the point moves along a line, or (2) if the point moves along a conic section...
Hyun Soo Park
,
et al.
3D Reconstruction of a Moving Point from a Series of 2D Projections
...From stationary configurations [3], [2], [4], [5] to dynamic configurations [6], [
7
], [8], [9], the multiple view geometry has been extensively developed...
...However, previous multiple view geometry involving dynamic scenes are constrained from the translational motions of the cameras [9] or a configuration of points in which each point can move independently along some restricted trajectory, i.e., straight line path and in some cases secondorder [6], [
7
], [8]...
Cheng Wan
,
et al.
Multiple View Geometry for Nonrigid Motions Viewed from Curvilinear M...
...Since SfM techniques rely on triangulation, they cannot be used to recover the structure and motion of moving objects [
16
]...
...The pioneering work in [
16
] referred to the SaMfM problem as "trajectory triangulation" and provided a solution where at least five views are required if the motion of the object is constrained to a straight line and at least nine views are required if the object is moving with conic trajectories...
Ashwin P. Dani
,
et al.
Structure and motion estimation of a moving object using a moving came...
References
(12)
3D Reconstruction from TangentofSight Measurements of a Moving Object Seen from a Moving Camera
(
Citations: 10
)
Dana Segal
,
Amnon Shashua
Conference:
European Conference on Computer Vision  ECCV
, pp. 621631, 2000
Trajectory Triangulation of Lines: Reconstruction of a 3D point Moving along a Line from a Monocular Image Sequence
(
Citations: 15
)
Shai Avidan
,
Amnon Shashua
Conference:
Computer Vision and Pattern Recognition  CVPR
, vol. 2, pp. 20622066, 1999
Trajectory Triangulation over Conic Sections
(
Citations: 12
)
Amnon Shashua
,
Shai Avidan
,
Michael Werman
Conference:
International Conference on Computer Vision  ICCV
, pp. 330336, 1999
Motion Clustering using the Trilinear Constraint over Three Views
(
Citations: 31
)
P. H. S. Torr
,
A. Zisserman
,
D. W. Murray Robotics
Published in 1995.
Statistical Bias of Conic Fitting and Renormalization
(
Citations: 89
)
Kenichi Kanatani
Journal:
IEEE Transactions on Pattern Analysis and Machine Intelligence  PAMI
, vol. 16, no. 3, pp. 320326, 1994
Sort by:
Citations
(76)
Line Localization from Single Catadioptric Images
Simone Gasparini
,
Vincenzo Caglioti
Journal:
International Journal of Computer Vision  IJCV
, vol. 94, no. 3, pp. 361374, 2011
Trajectory triangulation: 3D motion reconstruction with ℓ1 optimization
Mingyu Chen
,
Ghassan AlRegib
,
BiingHwang Juang
Conference:
International Conference on Acoustics, Speech, and Signal Processing  ICASSP
, pp. 40204023, 2011
Videoobject segmentation and 3Dtrajectory estimation for monocular video sequences
Feng Xu
,
KinMan Lam
,
Qionghai Dai
Journal:
Image and Vision Computing  IVC
, vol. 29, no. 23, pp. 190205, 2011
3D Reconstruction of a Moving Point from a Series of 2D Projections
(
Citations: 2
)
Hyun Soo Park
,
Takaaki Shiratori
,
Iain Matthews
,
Yaser Sheikh
Conference:
European Conference on Computer Vision  ECCV
, pp. 158171, 2010
Multiple View Geometry for Nonrigid Motions Viewed from Curvilinear Motion Projective Cameras
Cheng Wan
,
Jun Sato
Conference:
International Conference on Pattern Recognition  ICPR
, pp. 181184, 2010