Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension $k$ onto view spaces of varying dimensions, are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [M. Bertolini, G. Besana, and C. Turrini, Ann. Mat. Pura Appl. (4), 196 (2016), pp. 539--553]. The rank of sequences of tensors converging to tensors associated with degenerate configurations of projection centers is also considered, giving concrete examples of a wide spectrum of phenomena that can happen.

Marina Bertolini, G.M.B. (2020). The rank of trifocal grassmann tensors. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 41(2), 591-604 [10.1137/19M1277205].

The rank of trifocal grassmann tensors

Gilberto Bini;
2020-04-29

Abstract

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension $k$ onto view spaces of varying dimensions, are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [M. Bertolini, G. Besana, and C. Turrini, Ann. Mat. Pura Appl. (4), 196 (2016), pp. 539--553]. The rank of sequences of tensors converging to tensors associated with degenerate configurations of projection centers is also considered, giving concrete examples of a wide spectrum of phenomena that can happen.
Settore MAT/03 - Geometria
https://epubs.siam.org/doi/abs/10.1137/19M1277205?mobileUi=0#secKeywords
Marina Bertolini, G.M.B. (2020). The rank of trifocal grassmann tensors. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 41(2), 591-604 [10.1137/19M1277205].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/566662
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