### Abstract

In this paper, we show how the translational motion of a stereo vision system relative to, and its distance from, the scene can be recovered in closed form directly from the measurements of image gradients and time derivatives. There is no need to estimate image motion or establish correspondences between features across images. The direction of translational motion is recovered using a procedure which involves minimizing the sum squared error of a linear constraint equation over the image. The solution is given in terms of the eigenvector corresponding to the smallest eigenvalue of a 3 × 3 positive semi-definite matrix. Using the average disparity, which maximizes the crosscorrelation between the left and right images, we estimate the scale-factor necessary to compute the magnitude of the translational motion, and consequently the distance to the scene.

Original language | English (US) |
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Pages (from-to) | 78-85 |

Number of pages | 8 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 1260 |

DOIs | |

State | Published - Jan 1 1990 |

Externally published | Yes |

Event | Sensing and Reconstruction of Three-Dimensional Objects and Scenes 1990 - Santa Clara, United States Duration: Feb 11 1990 → Feb 16 1990 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*1260*, 78-85. https://doi.org/10.1117/12.20006