Division of Informatics

Forrest Hill & 80 South Bridge

## Research Paper #737 | |
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Title: | A Comparison of Four Algorithms for Estimating 3-D Rigid Transformations |

Authors: | Lorusso,A; Eggert,D; Fisher,RB |

Date: | Mar 1995 |

Presented: | Submitted to the International Conference on Computer Vision |

Keywords: | |

Abstract: | A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points in a coordinate system for which corresponding pairs have been determined. Several solutions to this problem have been devised. in this paper a comparative analysis of four popular algorithms is given. Each of them computes the translation and rotation of the transform in closed-form, as the solution to a least squares formulation of the problem. They differ in terms of the representation of the transform and the method of solution, using respectively: singular value decomposition of a matrix, orthonormal matrices, unit quaternions and dual quaternions. This comparison presents results of several experiments designed to determine (1) the accuracy of each algorithm in the presence of different levels of noise, (2) the stability of each technique with respect to degenerate data sets, and (3) the relative computation time of each approach for different sizes and forms of data. |

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