## Abstract

Matching a pair of affine invariant regions between images results in estimation of the affine transformation between the regions. However, the parameters of the affine transformations are rarely used directly for matching images, mainly due to the lack of an appropriate error metric of the distance between them. In this paper we derive a novel metric for measuring the distance between affine transformations: Given an image region, we show that minimization of this metric is equivalent to the minimization of the mean squared distance between affine transformations of a point, sampled uniformly on the image region. Moreover, the metric of the distance between affine transformations is equivalent to the l _{2} norm of a linear transformation of the difference between the six parameters of the affine transformations. We employ the metric for estimating homographies and for estimating the fundamental matrix between images. We show that both homography estimation and fundamental matrix estimation methods, based on the proposed metric, are superior to current linear estimation methods as they provide better accuracy without increasing the computational complexity.

Original language | English |
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Pages (from-to) | 481-491 |

Number of pages | 11 |

Journal | Journal of Mathematical Imaging and Vision |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 2014 |

## Keywords

- Affine invariant regions
- Epipolar geometry
- Fundamental matrix
- Homographies

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Condensed Matter Physics
- Computer Vision and Pattern Recognition
- Geometry and Topology
- Applied Mathematics