Standard
Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. / Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren; Nielsen, Mads.
Computer Vision - ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI. red. / Kostas Daniilidis; Petros Maragos; Nikos Paragios. Bind Part VI Springer, 2010. s. 43-56 (Lecture notes in computer science; Nr. 6316).
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
Harvard
Sommer, SH, Lauze, FB, Hauberg, S
& Nielsen, M 2010,
Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. i K Daniilidis, P Maragos & N Paragios (red),
Computer Vision - ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI. bind Part VI, Springer, Lecture notes in computer science, nr. 6316, s. 43-56, 11th European Conference on Computer Vision, Heraklion, Grækenland,
05/09/2010.
https://doi.org/10.1007/978-3-642-15567-3_4
APA
Sommer, S. H., Lauze, F. B., Hauberg, S.
, & Nielsen, M. (2010).
Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. I K. Daniilidis, P. Maragos, & N. Paragios (red.),
Computer Vision - ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI (Bind Part VI, s. 43-56). Springer. Lecture notes in computer science Nr. 6316
https://doi.org/10.1007/978-3-642-15567-3_4
Vancouver
Sommer SH, Lauze FB, Hauberg S
, Nielsen M.
Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. I Daniilidis K, Maragos P, Paragios N, red., Computer Vision - ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI. Bind Part VI. Springer. 2010. s. 43-56. (Lecture notes in computer science; Nr. 6316).
https://doi.org/10.1007/978-3-642-15567-3_4
Author
Sommer, Stefan Horst ; Lauze, Francois Bernard ; Hauberg, Søren ; Nielsen, Mads. / Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. Computer Vision - ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI. red. / Kostas Daniilidis ; Petros Maragos ; Nikos Paragios. Bind Part VI Springer, 2010. s. 43-56 (Lecture notes in computer science; Nr. 6316).
Bibtex
@inproceedings{a427d690c7b011df825b000ea68e967b,
title = "Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations",
abstract = "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.",
author = "Sommer, {Stefan Horst} and Lauze, {Francois Bernard} and S{\o}ren Hauberg and Mads Nielsen",
year = "2010",
doi = "10.1007/978-3-642-15567-3_4",
language = "English",
isbn = "978-3-642-15566-6",
volume = "Part VI",
series = "Lecture notes in computer science",
publisher = "Springer",
number = "6316",
pages = "43--56",
editor = "Kostas Daniilidis and Petros Maragos and Nikos Paragios",
booktitle = "Computer Vision - ECCV 2010",
address = "Switzerland",
note = "11th European Conference on Computer Vision, ECCV 2010 ; Conference date: 05-09-2010 Through 11-09-2010",
}
RIS
TY - GEN
T1 - Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations
AU - Sommer, Stefan Horst
AU - Lauze, Francois Bernard
AU - Hauberg, Søren
AU - Nielsen, Mads
N1 - Conference code: 11
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-642-15567-3_4
DO - 10.1007/978-3-642-15567-3_4
M3 - Article in proceedings
SN - 978-3-642-15566-6
VL - Part VI
T3 - Lecture notes in computer science
SP - 43
EP - 56
BT - Computer Vision - ECCV 2010
A2 - Daniilidis, Kostas
A2 - Maragos, Petros
A2 - Paragios, Nikos
PB - Springer
T2 - 11th European Conference on Computer Vision
Y2 - 5 September 2010 through 11 September 2010
ER -
