### 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 |
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Title of host publication | BMVC 2014 - Proceedings of the British Machine Vision Conference 2014 |

Publisher | British Machine Vision Association, BMVA |

Publication status | Published - 2014 |

Externally published | Yes |

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 |
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Country | United Kingdom |

City | Nottingham |

Period | 14/9/1 → 14/9/5 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition

### Cite this

*BMVC 2014 - Proceedings of the British Machine Vision Conference 2014*British Machine Vision Association, BMVA.

**Geodesic finite mixture models.** / Simo Serra, Edgar; Torras, Carme; Moreno-Noguer, Francesc.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*BMVC 2014 - Proceedings of the British Machine Vision Conference 2014.*British Machine Vision Association, BMVA, 25th British Machine Vision Conference, BMVC 2014, Nottingham, United Kingdom, 14/9/1.

}

TY - GEN

T1 - Geodesic finite mixture models

AU - Simo Serra, Edgar

AU - Torras, Carme

AU - Moreno-Noguer, Francesc

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

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M3 - Conference contribution

BT - BMVC 2014 - Proceedings of the British Machine Vision Conference 2014

PB - British Machine Vision Association, BMVA

ER -