International Journal of Computer Vision
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International Journal of Computer Vision
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CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
Gaussian-like spatial priors for articulated tracking
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Statistics of shape via principal geodesic analysis on lie groups
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Shape matching by variational computation of geodesics on a manifold
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ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Gaussian-like spatial priors for articulated tracking
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Lie bodies: a manifold representation of 3D human shape
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Geodesic analysis on the gaussian RKHS hypersphere
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
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Manifolds are widely used to model non-linearity arising in a range of computer vision applications. This paper treats statistics on manifolds and the loss of accuracy occurring when linearizing the manifold prior to performing statistical operations. Using recent advances in manifold computations, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking software.