# CHANGE-POINT DETECTION ON THE LIE GROUP SE(3) FOR SEGMENTING GESTURE-DEFINED SPATIAL RIGID MOTION

### Loic Merckel, Toyoaki Nishida

#### Abstract

Common CAD interfaces for editing spatial motion of virtual objects, which includes both position and orientation information, are often hampered by complexity and lack of intuitiveness. As the demand for motion data is increasing, e.g., in computer graphics or mixed reality, the development of new interfaces that offer a natural means of specifying arbitrary motion becomes essential. A solution consists in relying on live motion capture systems to record user’s gestures through space. In this context, we present a novel method for discovering change-points in a time series of elements in the set of rigid-body motion in space SE(3). The goal is to segment gesture-defined motion with in mind the development of a method for enhancing the user’s intent. Although numerous change-points detection techniques are available for dealing with scalar, or vector, time series, the generalization of these techniques to more complex structures may require overcoming difficult challenges. The group SE(3) does not satisfy closure under linear combination. Consequently, most of the statistical properties, such as the mean, cannot be properly estimated in a straightforward manner. We present a method that takes advantage of the Lie group structure of SE(3) to adapt a difference of means method. Especially, we show that the change-points in SE(3) can be discovered in its Lie algebra se(3) that forms a vector space. The performance of our method is evaluated through both synthetic and real data.

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#### Paper Citation

#### in Harvard Style

Merckel L. and Nishida T. (2010). **CHANGE-POINT DETECTION ON THE LIE GROUP SE(3) FOR SEGMENTING GESTURE-DEFINED SPATIAL RIGID MOTION** . In *Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)* ISBN 978-989-674-026-9, pages 284-295. DOI: 10.5220/0002839702840295

#### in Bibtex Style

@conference{grapp10,

author={Loic Merckel and Toyoaki Nishida},

title={CHANGE-POINT DETECTION ON THE LIE GROUP SE(3) FOR SEGMENTING GESTURE-DEFINED SPATIAL RIGID MOTION},

booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)},

year={2010},

pages={284-295},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002839702840295},

isbn={978-989-674-026-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)

TI - CHANGE-POINT DETECTION ON THE LIE GROUP SE(3) FOR SEGMENTING GESTURE-DEFINED SPATIAL RIGID MOTION

SN - 978-989-674-026-9

AU - Merckel L.

AU - Nishida T.

PY - 2010

SP - 284

EP - 295

DO - 10.5220/0002839702840295