171,110 research outputs found
The rank of trifocal grassmann tensors
No full textGrassmann 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
No full textGrassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension 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
Critical configurations for 1-view in projections from P-k -> P-2
No full textIn this paper we describe, from a theoretical point of view, critical configurations for the projective reconstruction of a set of points, for a single view, i.e. for calibration of a camera, in the case of projections from P-k to P-2 for k >= 4. We give first a general result describing these critical loci in P-k, which, if irreducible, are algebraic varieties of dimension k-2 and degree 3. If k=4 they can be either a smooth ruled surface or a cone and if k = 5 they can be a smooth three dimensional variety, ruled in planes, or a cone. If k >= 6, the variety is always a cone, the vertex of which has dimension at least k - 6. The reducible cases are studied in Appendix A.
These results are then applied to determine explicitly the critical loci for the projections from P-k which arise from the dynamic scenes in P-3 considered in [13]
Sistemi di vene di estensione e scistosità in formazioni calcareo-argillose. Boll. Soc. Geol. It.
No full textSome formulas concerning nonsingular algebraic varieties embedded in some ambient variety
No full textSia V una sottovarieta` algebrica non singolare k-dimensionale di una varietà algebrica proiettiva W, non singolare, di dimensione m \leq 2k. Si determinano le relazioni che le classi di Chern di V e di W devono soddisfare nelle varie componenti graduate di codimensione \geq m-k dell'anello di Chow di V. Le formule ottenute vengono quindi applicate ai casi nei quali V e` uno spazio lineare su di una forma, una varietà` abeliana, o uno scroll in P^m
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