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Use your hand as a 3-D mouse or relative orientation from extended sequences of sparse point and line correspondances using the affine trifocal tensor
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.ORCID iD: 0000-0002-9081-2170
1998 (English)In: Computer Vision — ECCV'98: 5th European Conference on Computer Vision Freiburg, Germany, June, 2–6, 1998 Proceedings, Volume I, Springer Berlin/Heidelberg, 1998, Vol. 1406, 141-157 p.Conference paper (Refereed)
Abstract [en]

This paper addresses the problem of computing three-dimensional structure and motion from an unknown rigid configuration of point and lines viewed by an affine projection model. An algebraic structure, analogous to the trilinear tensor for three perspective cameras, is defined for configurations of three centered affine cameras. This centered affine trifocal tensor contains 12 coefficients and involves linear relations between point correspondences and trilinear relations between line correspondences It is shown how the affine trifocal tensor relates to the perspective trilinear tensor, and how three-dimensional motion can be computed from this tensor in a straightforward manner. A factorization approach is also developed to handle point features and line features simultaneously in image sequences.

This theory is applied to a specific problem of human-computer interaction of capturing three-dimensional rotations from gestures of a human hand. A qualitative model is presented, in which three fingers are represented by their position and orientation, and it is shown how three point correspondences (blobs at the finger tips) and three line correspondences (ridge features at the fingers) allow the affine trifocal tensor to be determined, from which the rotation is computed. Besides the obvious application, this test problem illustrates the usefulness of the affine trifocal tensor in a situation where sufficient information is not available to compute the perspective trilinear tensor, while the geometry requires point correspondences as well as line correspondences over at least three views.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 1998. Vol. 1406, 141-157 p.
, Lecture Notes in Computer Science, 1406
National Category
Computer Vision and Robotics (Autonomous Systems) Computer Science Mathematics Human Computer Interaction
URN: urn:nbn:se:kth:diva-40150DOI: 10.1007/BFb0055664OAI: diva2:466218
5th European Conference on Computer Vision

QC 20111215.

Available from: 2013-04-22 Created: 2011-09-13 Last updated: 2013-04-22Bibliographically approved

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