Ansatte – Københavns Universitet

Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

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 dierences 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-eectors acquired using a stereo camera and tracking software.
OriginalsprogEngelsk
TitelComputer Vision - ECCV 2010 : 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI
RedaktørerKostas Daniilidis, Petros Maragos, Nikos Paragios
Antal sider14
Vol/bindPart VI
ForlagSpringer
Publikationsdato2010
Sider43-56
ISBN (Trykt)978-3-642-15566-6
ISBN (Elektronisk)978-3-642-15567-3
DOI
StatusUdgivet - 2010
Begivenhed11th European Conference on Computer Vision - Heraklion, Grækenland
Varighed: 5 sep. 201011 sep. 2010
Konferencens nummer: 11

Konference

Konference11th European Conference on Computer Vision
Nummer11
LandGrækenland
ByHeraklion
Periode05/09/201011/09/2010
NavnLecture notes in computer science
Nummer6316
ISSN0302-9743

ID: 22194856