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2016 | OriginalPaper | Chapter

11. Motion Segmentation

Authors : René Vidal, Yi Ma, S. Shankar Sastry

Published in: Generalized Principal Component Analysis

Publisher: Springer New York

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Abstract

The previous two chapters have shown how to use a mixture of subspaces to represent and segment static images. In those cases, different subspaces were used to account for multiple characteristics of natural images, e.g., different textures. In this chapter, we will show how to use a mixture of subspaces to represent and segment time series, e.g., video and motion capture data. In particular, we will use different subspaces to account for multiple characteristics of the dynamics of a time series, such as multiple moving objects or multiple temporal events.

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previous chapter Image Segmentation

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The special Euclidean group is defined as \(SE(3) =\{ (R,\boldsymbol{T}): R \in SO(3),\boldsymbol{T} \in \mathbb{R}^{3}\}\), where \(SO(3) =\{ R \in \mathbb{R}^{3\times 3}: R^{\top }R = I\ \text{and}\ \det (R) = 1\}\) is the special orthogonal group.

The inverse of \(g \in SE(3)\) is \(g^{-1} = (R^{\top },-R^{\top }\boldsymbol{T}) \in SE(3)\), and the product of two transformations \(g_{1} = (R_{1},\boldsymbol{T}_{1})\) and \(g_{2} = (R_{2},\boldsymbol{T}_{2})\) is defined as \(g_{1}g_{2} = (R_{1}R_{2},R_{1}\boldsymbol{T}_{1} +\boldsymbol{ T}_{2})\).

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Title: Motion Segmentation
Authors: René Vidal
Yi Ma
S. Shankar Sastry
Publisher: Springer New York
Book: Generalized Principal Component Analysis
Print ISBN: 978-0-387-87810-2

Electronic ISBN: 978-0-387-87811-9

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-0-387-87811-9_11

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