### Abstract

In this paper, we propose a novel approach to solving the vertex/edge correspondence problem for stereo images. Assume an object is placed on a calibration plate (C-plate) and two perspective views of them are given. The C-plate vertex correspondence, determined by cross-ratios, is used to reduce the search space for determining object vertex/edge correspondence. First, the correspondence of object edges lying on the C-plate (called the object base edges) is considered. This is because the subpolygons obtained from the division of the C-plate by the extended line of each of these base edges are viewpoint invariant, i.e. the cross-ratio of each of their vertices in different images will have equal value. Assume that at least one of the base edges is visible in each image. Since a visible object base edge has to be an object boundary edge in an image, only object boundary edges will be considered for the cross-ratios check for the associated subpolygons as well as other geometric constraint checks in determining the object base vertex/edge correspondence. These geometric constraints include (i) the position of the edges along the boundary of object faces, and (ii) the division of the C-plate vertices by the extended lines of these edges. Based on one of the determined corresponding base edge pairs, the correspondence of all other edges can be determined by constraints similar to (i). Finally, some additional viewpoint invariant measures about the object faces and the C-plates are introduced to resolve the ambiguity problem which may arise for specific viewpoints and some special object shapes. The proposed approach only needs 2-D image data and has no constraint on the number of vertices of an object face. Experimental results are presented for some polyhedral as well as curved objects.

Original language | English |
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Pages (from-to) | 1387-1400 |

Number of pages | 14 |

Journal | Pattern Recognition |

Volume | 30 |

Issue number | 9 |

DOIs | |

State | Published - 1 Jan 1997 |

### Keywords

- Calibration plate
- Cross-ratio
- Feature correspondence
- Stereo vision
- Viewpoint invariant

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## Cite this

*Pattern Recognition*,

*30*(9), 1387-1400. https://doi.org/10.1016/S0031-3203(96)00180-X