### Abstract

This paper presents an approach to understanding general 3-D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Specifically, the model constrains the motion, over a local frame subsequence, to be a superposition of precession and translation. Thus, the instantaneous rotation axis of the object is allowed to change through the subsequence. The trajectory of the rotation center is approximated by a vector polynomial. The parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics. The nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence. The estimation algorithm presented in this paper is linear, i.e., the algorithm consists of solving simultaneous linear equations. Based on the assumption that the motion is smooth, object positions and motion in the near future can be predicted, and short missing subsequences can be recovered. Noise smoothing is achieved by overdetermination and a leastsquares criterion. The framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames. The number of frames from which the model is derived can be varied according to the complexity of motion and the noise level so as to obtain stable and good estimates of parameters over the entire image sequence. Simulation results are given for noisy synthetic data and images taken of a model airplane.

Original language | English (US) |
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Pages (from-to) | 370-389 |

Number of pages | 20 |

Journal | IEEE transactions on pattern analysis and machine intelligence |

Volume | PAMI-9 |

Issue number | 3 |

DOIs | |

State | Published - May 1987 |

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### Keywords

- Computer vision
- analysis
- dynamic model
- image sequence
- motion
- motion estimation
- motion prediction
- motion under-
- standing

### ASJC Scopus subject areas

- Software
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics

### Cite this

*IEEE transactions on pattern analysis and machine intelligence*,

*PAMI-9*(3), 370-389. https://doi.org/10.1109/TPAMI.1987.4767920