Convolutional sparse coding for trajectory reconstruction

Zhu. Yingying and Lucey, Simon (2013) Convolutional sparse coding for trajectory reconstruction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 1: 1-12. doi:10.1109/TPAMI.2013.2295311

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Author Zhu. Yingying
Lucey, Simon
Title Convolutional sparse coding for trajectory reconstruction
Journal name IEEE Transactions on Pattern Analysis and Machine Intelligence   Check publisher's open access policy
ISSN 0162-8828
Publication date 2013-06-01
Year available 2013
Sub-type Article (original research)
DOI 10.1109/TPAMI.2013.2295311
Open Access Status Not yet assessed
Volume 6
Issue 1
Start page 1
End page 12
Total pages 12
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
Abstract Trajectory basis Non-Rigid Structure from Motion (NRSfM) refers to the process of reconstructing the 3D trajectory of each point of a non-rigid object from just their 2D projected trajectories. Reconstruction relies on two factors: (i) the condition of the composed camera & trajectory basis matrix, and (ii) whether the trajectory basis has enough degrees of freedom to model the 3D point trajectory. These two factors are inherently conflicting. Employing a trajectory basis with small capacity has the positive characteristic of reducing the likelihood of an ill-conditioned system (when composed with the camera) during reconstruction. However, this has the negative characteristic of increasing the likelihood that the basis will not be able to fully model the object’s “true” 3D point trajectories. In this paper we draw upon a well known result centering around the Reduced Isometry Property (RIP) condition for sparse signal reconstruction. RIP allow us to relax the requirement that the full trajectory basis composed with the camera matrix must be well conditioned. Further, we propose a strategy for learning an over-complete basis using convolutional sparse coding from naturally occurring point trajectory corpora to increase the likelihood that the RIP condition holds for a broad class of point trajectories and camera motions. Finally, we propose an `1 inspired objective for trajectory reconstruction that is able to “adaptively” select the smallest sub-matrix from an over-complete trajectory basis that balances (i) and (ii). We present more practical 3D reconstruction results compared to current state of the art in trajectory basis NRSfM.
Keyword Nonrigid structure from motion
Convolutional sparse coding
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2014 Collection
School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 16 times in Thomson Reuters Web of Science Article | Citations
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