Given two linear projections of maximal rank from (Formula presented.) to (Formula presented.) and (Formula presented.) with (Formula presented.) and (Formula presented.) the Grassmann tensor introduced by Hartley and Schaffalitzky (Int J Comput Vis 83(3):274–293, 2009. doi:10.1007/s11263-009-0225-1), turns out to be a generalized fundamental matrix. Such matrices are studied in detail and, in particular, their rank is computed. The dimension of the variety that parameterizes such matrices is also determined. An algorithmic application of the generalized fundamental matrix to projective reconstruction is described.
Generalized fundamental matrices as Grassmann tensors / M. Bertolini, G. Besana, C. Turrini. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2017 Apr). [10.1007/s10231-016-0585-4]
Generalized fundamental matrices as Grassmann tensors
M. Bertolini;C. Turrini
2017
Abstract
Given two linear projections of maximal rank from (Formula presented.) to (Formula presented.) and (Formula presented.) with (Formula presented.) and (Formula presented.) the Grassmann tensor introduced by Hartley and Schaffalitzky (Int J Comput Vis 83(3):274–293, 2009. doi:10.1007/s11263-009-0225-1), turns out to be a generalized fundamental matrix. Such matrices are studied in detail and, in particular, their rank is computed. The dimension of the variety that parameterizes such matrices is also determined. An algorithmic application of the generalized fundamental matrix to projective reconstruction is described.File | Dimensione | Formato | |
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