2019/07/24 by Marina Bertolini, Bertolini, Marina, Gian Mario Besana +5
Mathematics · #14N05 #15A21 #15A69 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N05 #msc:15A21 #msc:15A69
paper · pdf · doi:10.48550/arxiv.1907.10415
18 pages
arxiv created 2019/07/24 · arxiv updated 2019/07/25
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 the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. 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.