The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection
Lecture notes in computer sciencePublished 14 May 2007
Xiaodong Fan, Renè Vidal
Citations13
SJR quartileQ2
SJR score0.35
SNIP0.55
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TL;DR
The rank and geometry of the multibody fundamental matrix, a geometric entity characterizing the two-view geometry of dynamic scenes consisting of multiple rigid-body motions, are studied and an upper bound on the rank is derived that depends on the number of independent translations.
Abstract
We study the rank and geometry of the multibody fundamental matrix, a geometric entity characterizing the two-view geometry of dynamic scenes consisting of multiple rigid-body motions. We derive an upper bound on the rank of the multibody fundamental matrix that depends on the number of independent translations. We also derive an algebraic characterization of the SVD of a multibody fundamental matrix in the case of two or odd number of rigid-body motions with a common rotation. This characterization allows us to project an arbitrary matrix onto the space of multibody fundamental matrices using linear algebraic techniques.
Keywords
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