### Abstract

We consider a problem of recovering motion of object moving in space under perspective observation. It is assumed that the motion equation is described by a linear system with unknown constant motion parameters and that a single feature point on the object is perspectively observed by two cameras. Then we analyze the identifiability of motion parameters from the stereo image data observed over an interval of time. The identifiability problem is solved by employing theories on linear dynamical systems. It is shown that the parameters are identifiable genetically. Moreover, the only cases where the parameters can not be determined uniquely imply very much restrictive motions, confined either in certain planes or lines, in which case any identification algorithms will fail. Moreover whenever the parameters can be determined uniquely, the parameters can be recovered from stereo image data over any time interval of arbitrary length. The problem is also analyzed in discrete-time settings, which can be used for the case of continuous-time motion with discrete-time observations.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 3605-3610 |

Number of pages | 6 |

Volume | 4 |

Publication status | Published - 2004 |

Event | 2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: 2004 Dec 14 → 2004 Dec 17 |

### Other

Other | 2004 43rd IEEE Conference on Decision and Control (CDC) |
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Country | Bahamas |

City | Nassau |

Period | 04/12/14 → 04/12/17 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 4, pp. 3605-3610)

**Identifiability of motion parameters under perspective stereo vision.** / Kano, Hiroyuki; Fujioka, Hiroyuki; Chen, Xinkai.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*vol. 4, pp. 3605-3610, 2004 43rd IEEE Conference on Decision and Control (CDC), Nassau, Bahamas, 04/12/14.

}

TY - GEN

T1 - Identifiability of motion parameters under perspective stereo vision

AU - Kano, Hiroyuki

AU - Fujioka, Hiroyuki

AU - Chen, Xinkai

PY - 2004

Y1 - 2004

N2 - We consider a problem of recovering motion of object moving in space under perspective observation. It is assumed that the motion equation is described by a linear system with unknown constant motion parameters and that a single feature point on the object is perspectively observed by two cameras. Then we analyze the identifiability of motion parameters from the stereo image data observed over an interval of time. The identifiability problem is solved by employing theories on linear dynamical systems. It is shown that the parameters are identifiable genetically. Moreover, the only cases where the parameters can not be determined uniquely imply very much restrictive motions, confined either in certain planes or lines, in which case any identification algorithms will fail. Moreover whenever the parameters can be determined uniquely, the parameters can be recovered from stereo image data over any time interval of arbitrary length. The problem is also analyzed in discrete-time settings, which can be used for the case of continuous-time motion with discrete-time observations.

AB - We consider a problem of recovering motion of object moving in space under perspective observation. It is assumed that the motion equation is described by a linear system with unknown constant motion parameters and that a single feature point on the object is perspectively observed by two cameras. Then we analyze the identifiability of motion parameters from the stereo image data observed over an interval of time. The identifiability problem is solved by employing theories on linear dynamical systems. It is shown that the parameters are identifiable genetically. Moreover, the only cases where the parameters can not be determined uniquely imply very much restrictive motions, confined either in certain planes or lines, in which case any identification algorithms will fail. Moreover whenever the parameters can be determined uniquely, the parameters can be recovered from stereo image data over any time interval of arbitrary length. The problem is also analyzed in discrete-time settings, which can be used for the case of continuous-time motion with discrete-time observations.

UR - http://www.scopus.com/inward/record.url?scp=14244260557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14244260557&partnerID=8YFLogxK

M3 - Conference contribution

VL - 4

SP - 3605

EP - 3610

BT - Proceedings of the IEEE Conference on Decision and Control

ER -