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Graph Embedding for Pattern Analysis pp 157–175Cite as

Graph-Embedding Discriminant Analysis on Riemannian Manifolds for Visual Recognition

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Abstract

Recently, several studies have utilised non-Euclidean geometry to address several computer vision problems including object tracking [17], characterising the diffusion of water molecules as in diffusion tensor imaging [24], face recognition [23, 31], human re-identification [4], texture classification [16], pedestrian detection [39] and action recognition [22, 43].

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Notes

  1. 1.

    In a Hausdorff space, distinct points have disjoint neighbourhoods. This property is important to establish the notion of a differential manifold, as it guarantees that convergent sequences have a single limit point.

  2. 2.

    Special orthogonal group SO(n) is the space of all n ×n orthogonal matrices with the determinant + 1. It is not a vector space but a differentiable manifold, i.e. it can be locally approximated by subsets of a Euclidean space.

  3. 3.

    A pseudo kernel is a function where the positive definiteness is not guaranteed to be satisfied for whole range of the function’s parameters. Nevertheless, it is possible to convert a pseudo kernel into sa true kernel, as discussed, for example, in [9].

  4. 4.

    The study in [40] addresses the problem of recognising actions in still images, which is different from the work presented here.

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Acknowledgements

This project is supported by a grant from the Australian Government Department of the Prime Minister and Cabinet. NICTA is funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council. The first and second authors contributed equally.

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Authors and Affiliations

  1. NICTA, 6020, St Lucia, QLD, 4067, Australia

    Sareh Shirazi, Azadeh Alavi, Mehrtash T. Harandi & Brian C. Lovell

  2. The University of Queensland, School of ITEE, St Lucia, QLD, 4072, Australia

    Sareh Shirazi, Azadeh Alavi, Mehrtash T. Harandi & Brian C. Lovell

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  1. Sareh Shirazi
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  2. Azadeh Alavi
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  3. Mehrtash T. Harandi
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  4. Brian C. Lovell
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Correspondence to Mehrtash T. Harandi .

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  1. , Dept. of ECE, College of Engineering, Northeastern University, 403 Dana Research Center, 360 Huntington Ave, Boston, 02115, Massachusetts, USA

    Yun Fu

  2. Honeywell, Douglas Drive North 1985, Golden Valley, 55422, USA

    Yunqian Ma

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Shirazi, S., Alavi, A., Harandi, M.T., Lovell, B.C. (2013). Graph-Embedding Discriminant Analysis on Riemannian Manifolds for Visual Recognition. In: Fu, Y., Ma, Y. (eds) Graph Embedding for Pattern Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4457-2_7

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  • DOI: https://doi.org/10.1007/978-1-4614-4457-2_7

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