THE RANK OF TRIFOCAL GRASSMANN TENSORS

被引：3
|
作者：
Bertolini, Marina [1 ]
Besana, Gianmario [2 ]
Bini, Gilberto [3 ]
Turrini, Cristina [1 ]
机构：
[1] Univ Milan, Dipartimento Matemat F Enriques, Via Saldini 50, I-20133 Milan, Italy
[2] DePaul Univ, Coll Comp & Digital Media, 243 South Wabash, Chicago, IL 60604 USA
[3] Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo, Italy
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2020年 / 41卷 / 02期
关键词：
tensor rank; border rank; multiview geometry; projective reconstruction in computer vision; RECONSTRUCTION;
D O I：
10.1137/19M1277205
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：591 / 604
页数：14
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