6533b82ffe1ef96bd1295d50
RESEARCH PRODUCT
The Rank of Trifocal Grassmann Tensors
Gian Mario BesanaCristina TurriniMarina BertoliniGilberto Binisubject
Rank (linear algebra)Tensor rankAlgebraMathematics - Algebraic GeometryDimension (vector space)Computer Science::Computer Vision and Pattern Recognitiongrassmann tensors computer vision tensor rankFOS: MathematicsProjective spaceSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Analysis14N05 15A21 15A69Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-07-24 |