### Abstract

The authors estimate rigid-body motion from two 3-D point sets with and without correspondences. By utilizing properties of Fourier transformation, a frequency-domain approach for determining the motion without point correspondences is obtained. In the algorithm, the problem of estimating the translation is first separated by subtracting the coordinates of the centroids from the 3-D point coordinates in the point sets. The rotation parameters are estimated by correlating the Fourier transforms of two functions defined on the two sets of the 3-D points. With the point correspondence given, an algorithm for finding the least-squares solution to the motion parameters is applied. It is proved that the least-squares solution is such that the centroids of the two point sets coincide. The determination of rotation and translation can therefore be decoupled. An iterative procedure for obtaining the rotation parameters is described.

Original language | English (US) |
---|---|

Title of host publication | Unknown Host Publication Title |

Publisher | IEEE |

Pages | 194-201 |

Number of pages | 8 |

ISBN (Print) | 0818607211 |

State | Published - Jan 1 1986 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Unknown Host Publication Title*(pp. 194-201). IEEE.

**MOTION ESTIMATION FROM 3-D POINT SETS WITH AND WITHOUT CORRESPONDENCES.** / Lin, Zse Cherng; Huang, Thomas S; Blostein, Steven D.; Lee, Hua; Margerum, E. A.

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

*Unknown Host Publication Title.*IEEE, pp. 194-201.

}

TY - GEN

T1 - MOTION ESTIMATION FROM 3-D POINT SETS WITH AND WITHOUT CORRESPONDENCES.

AU - Lin, Zse Cherng

AU - Huang, Thomas S

AU - Blostein, Steven D.

AU - Lee, Hua

AU - Margerum, E. A.

PY - 1986/1/1

Y1 - 1986/1/1

N2 - The authors estimate rigid-body motion from two 3-D point sets with and without correspondences. By utilizing properties of Fourier transformation, a frequency-domain approach for determining the motion without point correspondences is obtained. In the algorithm, the problem of estimating the translation is first separated by subtracting the coordinates of the centroids from the 3-D point coordinates in the point sets. The rotation parameters are estimated by correlating the Fourier transforms of two functions defined on the two sets of the 3-D points. With the point correspondence given, an algorithm for finding the least-squares solution to the motion parameters is applied. It is proved that the least-squares solution is such that the centroids of the two point sets coincide. The determination of rotation and translation can therefore be decoupled. An iterative procedure for obtaining the rotation parameters is described.

AB - The authors estimate rigid-body motion from two 3-D point sets with and without correspondences. By utilizing properties of Fourier transformation, a frequency-domain approach for determining the motion without point correspondences is obtained. In the algorithm, the problem of estimating the translation is first separated by subtracting the coordinates of the centroids from the 3-D point coordinates in the point sets. The rotation parameters are estimated by correlating the Fourier transforms of two functions defined on the two sets of the 3-D points. With the point correspondence given, an algorithm for finding the least-squares solution to the motion parameters is applied. It is proved that the least-squares solution is such that the centroids of the two point sets coincide. The determination of rotation and translation can therefore be decoupled. An iterative procedure for obtaining the rotation parameters is described.

UR - http://www.scopus.com/inward/record.url?scp=0022579066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022579066&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022579066

SN - 0818607211

SP - 194

EP - 201

BT - Unknown Host Publication Title

PB - IEEE

ER -