## Abstract

Surface reconstruction is an important problem within computer vision. This paper studies the application of the Lagrange polynomials to interpolating three-dimensional stereo data. The process consists of fitting a surface function to the given 3-D data. The value of the constructed surface at a point (X, Y) is calculated locally in finite intervals based on the data at relatively nearby points. This produces a large number of polynomials, however, it requires less computational time than a global solution. This local interpolation is of interest when considering unusual shapes where the data points are irregularly scattered throughout the 3-D space. Overlapping is used when constructing the polynomials to ensure the continuity and smoothness of the surfaces from one scene point to the next. Because the data are generally sparse, the horizontal and vertical one-dimensional operations give different results. Final approximation is based on minimizing the error based on the least square criterion. Experiments show that the method produces good results.

Original language | English (US) |
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Pages (from-to) | 27-36 |

Number of pages | 10 |

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

Volume | 1457 |

DOIs | |

State | Published - Aug 1 1991 |

Event | Stereoscopic Displays and Applications II 1991 - San Jose, United States Duration: Feb 1 1991 → Feb 7 1991 |

## All Science Journal Classification (ASJC) codes

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