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Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

11. Motion Segmentation

verfasst von : René Vidal, Yi Ma, S. Shankar Sastry

Erschienen in: Generalized Principal Component Analysis

Verlag: 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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Vorheriges Kapitel Image Segmentation
Nächstes Kapitel Hybrid System Identification
Fußnoten
1
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.
 
2
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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Metadaten
Titel
Motion Segmentation
verfasst von
René Vidal
Yi Ma
S. Shankar Sastry
Copyright-Jahr
2016
Verlag
Springer New York
Buch
Generalized Principal Component Analysis

Print ISBN: 978-0-387-87810-2

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

Copyright-Jahr: 2016

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

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