In this survey article, we present interactions between algebraic geometry and computer
vision, which have recently come under the header of algebraic vision. The subject has …

We present an algebraic study of line correspondences for pinhole cameras, in contrast to
the thoroughly studied point correspondences. We define the line multiview variety as the …

We describe the twisted $ K $-polynomial of multiplicity-free varieties in a multiprojective
setting. More precisely, for multiplicity-free varieties, we show that the support of the twisted …

We present a new framework for multi-view geometry in computer vision. A camera is a
mapping between P 3 and a line congruence. This model, which ignores image planes and …

This article discusses the design of the Apprenticeship Program at the Fields Institute, held
21 August–3 September 2016. Six themes from combinatorial algebraic geometry were …

A congruence is a surface in the Grassmannian Gr (1, ℙ 3) Gr\nolimits (1, P^ 3) of lines in
projective 3-space. To a space curve C, we associate the Chow hypersurface in Gr (1, ℙ 3) …

What is the image of a cube in a two-slit camera? That is the question this paper explores. In
a traditional pinhole camera, as in traditional perspective drawings, the image of a cube can …

We generalize the notion of coisotropic hypersurfaces to subvarieties of Grassmannians
having arbitrary codimension. To every projective variety X, Gel'fand, Kapranov and …

We describe convex hulls of the simplest compact space curves, reducible quartics
consisting of two circles. When the circles do not meet in complex projective space, their …

We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of
products of projective spaces. Two new phenomena arise: first, the construction turns out to …