### Abstract

We present a novel approach for learning a finite mixture model on a Riemannian manifold in which Euclidean metrics are not applicable and one needs to resort to geodesic distances consistent with the manifold geometry. For this purpose, we draw inspiration on a variant of the expectation-maximization algorithm, that uses a minimum message length criterion to automatically estimate the optimal number of components from multivariate data lying on an Euclidean space. In order to use this approach on Riemannian manifolds, we propose a formulation in which each component is defined on a different tangent space, thus avoiding the problems associated with the loss of accuracy produced when linearizing the manifold with a single tangent space. Our approach can be applied to any type of manifold for which it is possible to estimate its tangent space. In particular, we show results on synthetic examples of a sphere and a quadric surface, and on a large and complex dataset of human poses, where the proposed model is used as a regression tool for hypothesizing the geometry of occluded parts of the body.

Original language | English |
---|---|

Publication status | Published - 2014 Jan 1 |

Event | 25th British Machine Vision Conference, BMVC 2014 - Nottingham, United Kingdom Duration: 2014 Sep 1 → 2014 Sep 5 |

### Other

Other | 25th British Machine Vision Conference, BMVC 2014 |
---|---|

Country | United Kingdom |

City | Nottingham |

Period | 14/9/1 → 14/9/5 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition

### Cite this

*Geodesic finite mixture models*. Paper presented at 25th British Machine Vision Conference, BMVC 2014, Nottingham, United Kingdom.