### Abstract

We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure parameters are defined. These parameters can be determined uniquely from the two given image frames by solving a set of linear equations. Then, the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth-order polynomial of one variable only, and there exists a certain efficient algorithm for solving a sixth-order polynomial. Aside from a scale factor for the translation parameters, the number of real solutions never exceeds two. In the special case of three-dimensional translation, the motion parameters can be expressed directly as some simple functions of the eight pure parameters Thus, only a few arithmetic operations are needed.

Original language | English (US) |
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Pages (from-to) | 1147-1152 |

Number of pages | 6 |

Journal | IEEE Transactions on Acoustics, Speech, and Signal Processing |

Volume | 29 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1981 |

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### ASJC Scopus subject areas

- Signal Processing

### Cite this

**Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch.** / Tsai, Roger Y.; Huang, Thomas S.

Research output: Contribution to journal › Article

*IEEE Transactions on Acoustics, Speech, and Signal Processing*, vol. 29, no. 6, pp. 1147-1152. https://doi.org/10.1109/TASSP.1981.1163710

}

TY - JOUR

T1 - Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch

AU - Tsai, Roger Y.

AU - Huang, Thomas S

PY - 1981/12

Y1 - 1981/12

N2 - We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure parameters are defined. These parameters can be determined uniquely from the two given image frames by solving a set of linear equations. Then, the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth-order polynomial of one variable only, and there exists a certain efficient algorithm for solving a sixth-order polynomial. Aside from a scale factor for the translation parameters, the number of real solutions never exceeds two. In the special case of three-dimensional translation, the motion parameters can be expressed directly as some simple functions of the eight pure parameters Thus, only a few arithmetic operations are needed.

AB - We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure parameters are defined. These parameters can be determined uniquely from the two given image frames by solving a set of linear equations. Then, the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth-order polynomial of one variable only, and there exists a certain efficient algorithm for solving a sixth-order polynomial. Aside from a scale factor for the translation parameters, the number of real solutions never exceeds two. In the special case of three-dimensional translation, the motion parameters can be expressed directly as some simple functions of the eight pure parameters Thus, only a few arithmetic operations are needed.

UR - http://www.scopus.com/inward/record.url?scp=0019680384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019680384&partnerID=8YFLogxK

U2 - 10.1109/TASSP.1981.1163710

DO - 10.1109/TASSP.1981.1163710

M3 - Article

AN - SCOPUS:0019680384

VL - 29

SP - 1147

EP - 1152

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 6

ER -