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.
The rank of trifocal grassmann tensors / M. Bertolini, G. Besana, G. Bini, C. Turrini. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - 41:2(2020 Apr 29), pp. 591-604.
|Titolo:||The rank of trifocal grassmann tensors|
BERTOLINI, MARINA (Primo)
TURRINI, CRISTINA (Ultimo)
|Parole Chiave:||Tensor rank, Border rank; Multiview geometry, Projective reconstruction in computer vision.|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
Settore INF/01 - Informatica
|Data di pubblicazione:||29-apr-2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1137/19M1277205|
|Appare nelle tipologie:||01 - Articolo su periodico|