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.
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Fan, X., Vidal, R. (2007). The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection. In: Vidal, R., Heyden, A., Ma, Y. (eds) Dynamical Vision. WDV WDV 2006 2005. Lecture Notes in Computer Science, vol 4358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70932-9_1
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DOI: https://doi.org/10.1007/978-3-540-70932-9_1
Publisher Name: Springer, Berlin, Heidelberg
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