论文标题
双焦格拉曼张量的品种
The Varieties of Bifocal Grassmann Tensors
论文作者
论文摘要
Grassmann张量来自计算机视觉中场景重建的经典问题。特别是，双焦点grassmann张量与从投影空间到各个维度的视图空间的一对投影有关，概括了基本矩阵的经典概念。在本文中，我们全面研究了侧重于其生育几何形状的双焦点晶型张量。为了进行此分析，从代数和几何学的角度降低了多视图几何对象，例如，通过极性明确描述了视图空间和射线空间之间的双重性。接下来，我们处理双焦格拉曼张量的模量，因此表明这种品种既适合合适的均匀空间，又是赋予格拉斯曼尼亚人的主要理性地图。
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, generalise 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 declined 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.
