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2016 | OriginalPaper | Buchkapitel

Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons

verfasst von : Piotr Koniusz, Anoop Cherian, Fatih Porikli

Erschienen in: Computer Vision – ECCV 2016

Verlag: Springer International Publishing

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Abstract

In this paper, we explore tensor representations that can compactly capture higher-order relationships between skeleton joints for 3D action recognition. We first define RBF kernels on 3D joint sequences, which are then linearized to form kernel descriptors. The higher-order outer-products of these kernel descriptors form our tensor representations. We present two different kernels for action recognition, namely (i) a sequence compatibility kernel that captures the spatio-temporal compatibility of joints in one sequence against those in the other, and (ii) a dynamics compatibility kernel that explicitly models the action dynamics of a sequence. Tensors formed from these kernels are then used to train an SVM. We present experiments on several benchmark datasets and demonstrate state of the art results, substantiating the effectiveness of our representations.

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Vorheriges Kapitel Marker-Less 3D Human Motion Capture with Monocular Image Sequence and Height-Maps

Nächstes Kapitel Manhattan-World Urban Reconstruction from Point Clouds

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We assume that all sequences have N frames for simplification of presentation. Our formulations are equally applicable to sequences of arbitrary lengths e.g., M and N. Therefore, we apply in practice \(G_{\sigma _3}(\frac{s}{M}-\frac{t}{N})\) in Eq. (5).

In practice, we use \(G^{'}_{\sigma _2}(\mathbf {x}-\mathbf {y})=G_{\sigma _2}(x^{(x)}-y^{(x)})\!+\!G_{\sigma _2}(x^{(y)}-y^{(y)})\!+\!G_{\sigma _2}(x^{(z)}-y^{(z)})\) so the kernel \(G^{'}_{\sigma _2}(\mathbf {x}-\mathbf {y})\approx [\phi (x^{(x)}\!); \phi (x^{(y)}\!); \phi (x^{(z)}\!)]^T\![\phi (y^{(x)}\!); \phi (y^{(y)}\!); \phi (y^{(z)}\!)]\) but for simplicity we write \(G_{\sigma _2}(\mathbf {x}-\mathbf {y})\!\approx \!\phi (\mathbf {x})^T\phi (\mathbf {y})\). Note that (x), (y), (z) are the spatial xyz-components of joints.

Note that this is the length of a vector per sequence after unfolding our tensor representation and removing duplicate coefficients from the symmetries in the tensor.

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Titel: Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons
verfasst von: Piotr Koniusz
Anoop Cherian
Fatih Porikli
Verlag: Springer International Publishing
Buch: Computer Vision – ECCV 2016
Print ISBN: 978-3-319-46492-3

Electronic ISBN: 978-3-319-46493-0

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-46493-0_3

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