The space of multibody fundamental matrices: rank, geometry and projection

Authors:
Xiaodong Fan;René Vidal
Affiliations:
Microsoft Corporate, Redmond, WA;Center for Imaging Science, Department of BME, Johns Hopkins University, Baltimore, MD
Venue:
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Year:
2006

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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.