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Perspective Nonrigid Shape and Motion Recovery

Hartley, Richard; Vidal, Rene

Description

We present a closed form solution to the nonrigid shape and motion (NRSM) problem from point correspondences in multiple perspective uncalibrated views. Under the assumption that the nonrigid object deforms as a linear combination of K rigid shapes, we show that the NRSM problem can be viewed as a reconstruction problem from multiple projections from ℙ3K to ℙ2. Therefore, one can linearly solve for the projection matrices by factorizing a multifocal tensor. However, this projective...[Show more]

dc.contributor.authorHartley, Richard
dc.contributor.authorVidal, Rene
dc.coverage.spatialMarseille France
dc.date.accessioned2015-12-08T22:43:19Z
dc.date.createdOctober 12-18 2008
dc.identifier.isbn9783540886921
dc.identifier.urihttp://hdl.handle.net/1885/37226
dc.description.abstractWe present a closed form solution to the nonrigid shape and motion (NRSM) problem from point correspondences in multiple perspective uncalibrated views. Under the assumption that the nonrigid object deforms as a linear combination of K rigid shapes, we show that the NRSM problem can be viewed as a reconstruction problem from multiple projections from ℙ3K to ℙ2. Therefore, one can linearly solve for the projection matrices by factorizing a multifocal tensor. However, this projective reconstruction in ℙ3K does not satisfy the constraints of the NRSM problem, because it is computed only up to a projective transformation in ℙ3K . Our key contribution is to show that, by exploiting algebraic dependencies among the entries of the projection matrices, one can upgrade the projective reconstruction to determine the affine configuration of the points in ℙ3, and the motion of the camera relative to their centroid. Moreover, if K ≥ 2, then either by using calibrated cameras, or by assuming a camera with fixed internal parameters, it is possible to compute the Euclidean structure by a closed form method.
dc.publisherSpringer
dc.relation.ispartofseriesEuropean Conference on Computer Vision (ECCV 2008)
dc.sourceProceedings of European Conference on Computer Vision (ECCV 2008)
dc.source.urihttp://www.springer.com/computer/image+processing/book/978-3-540-88692-1
dc.subjectKeywords: Computer vision; Holograms; Image processing; Modernization; Repair; Restoration; Calibrated cameras; Closed form methods; Closed-form solutions; Euclidean structures; Internal parameters; Linear combinations; Multifocal; Multiple perspectives; Multiple p
dc.titlePerspective Nonrigid Shape and Motion Recovery
dc.typeConference paper
local.description.notesImported from ARIES
local.description.refereedYes
dc.date.issued2008
local.identifier.absfor080104 - Computer Vision
local.identifier.ariespublicationu4334215xPUB146
local.type.statusPublished Version
local.contributor.affiliationHartley, Richard, College of Engineering and Computer Science, ANU
local.contributor.affiliationVidal, Rene, Johns Hopkins University
local.description.embargo2037-12-31
local.bibliographicCitation.startpage276
local.bibliographicCitation.lastpage289
local.identifier.doi10.1007/978-3-540-88682-2-22
dc.date.updated2016-02-24T10:58:29Z
local.identifier.scopusID2-s2.0-56749176976
CollectionsANU Research Publications

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