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Published in:
2011 | OriginalPaper | Chapter
Change-Point Detection on the Lie Group SE(3)
Authors : Loic Merckel, Toyoaki Nishida
Published in: Computer Vision, Imaging and Computer Graphics. Theory and Applications
Publisher: Springer Berlin Heidelberg
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This paper presents a novel method for discovering change-points in a time series of elements in the set of rigid-body motion in space
SE
(3). 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-point 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.