Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann tensors, thus showing that this variety is both birational to a suitable homogeneous space and endowed with a dominant rational map to a Grassmannian.

Bertolini Marina, Bini Gilberto, Turrini Cristina (2023). The varieties of bifocal Grassmann tensors. ANNALI DI MATEMATICA PURA ED APPLICATA, 202, 2195-2217 [10.1007/s10231-023-01317-y].

The varieties of bifocal Grassmann tensors

Bini Gilberto
;
2023-10-01

Abstract

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann tensors, thus showing that this variety is both birational to a suitable homogeneous space and endowed with a dominant rational map to a Grassmannian.
ott-2023
Settore MAT/03 - Geometria
Bertolini Marina, Bini Gilberto, Turrini Cristina (2023). The varieties of bifocal Grassmann tensors. ANNALI DI MATEMATICA PURA ED APPLICATA, 202, 2195-2217 [10.1007/s10231-023-01317-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/588112
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