Simplifications of Multilinear forms for Sequences of Images

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Abstract

This paper contains a simplified framework for the analysis of sequences of images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. Corresponding points in a sequence of n images are related to each other by a fixed n-linear form. This form is an object invariant property, closely linked to the motion of the camera relative to the fixed world. We first describe a reduced setting in which these multilinear forms are easier to understand and analyse. This new formulation of the multilinear forms is then extended to the calibrated case and the traditional uncalibrated case, thus highlighting the similarities between the different settings. The framework is of importance as a theoretical tool for understanding the algebra of multiple view geometry, but it is also a basis for constructing linear algorithms for the recovery of structure and motion from image sequences. This is illustrated in experiments. (C) 1997 Elsevier Science B.V.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • computer vision, visual reconstruction, projective geometry, multiple-view, invarian
Original languageEnglish
Pages (from-to)749-757
JournalImage and Vision Computing
Volume15
Issue number10
Publication statusPublished - 1997
Publication categoryResearch
Peer-reviewedYes