## Abstract

Model-based invariants are relations between model parameters and image measurements, which are independent of the imaging parameters. Such relations are true for all images of the model. Here we describe an algorithm which, given L independent model-based polynomial invariants describing some shape, will provide a linear re-parameterization of the invariants. This re-parameterization has the properties that: (i) it includes the minimal number of terms, and (ii) the shape terms are the same in all the model-based invariants. This final representation has 2 main applications: (1) it gives new representations of shape in terms of hyperplanes, which are convenient for object recognition; (2) it allows the design of new linear shape from motion algorithms. In addition, we use this representation to identify object classes that have universal invariants.

Original language | American English |
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Pages (from-to) | 75-85 |

Number of pages | 11 |

Journal | Journal of Mathematical Imaging and Vision |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - 1999 |

### Bibliographical note

Funding Information:This research was supported by the Israeli Ministry of Science under Grant 032.7568. Vision research at the

Funding Information:

We described an automatic process to simplify model-based invariants by re-parameterizing them in a linear way, and with a minimal number of terms. We demonstrated this process on two examples, using model-based invariants of six and seven points under Hebrew University is supported by the U.S. Office of Naval Research under Grant N00014-93-1-1202, R&T Project Code 4424341-01.