arXiv subjects

Andrew Pryhuber

Publications and source records attributed to Andrew Pryhuber.

3 recordsLinked to original sources

arXiv2022

The Chiral Domain of a Camera Arrangement

We introduce the chiral domain of an arrangement of cameras $\mathcal{A} = \{A_1,\dots, A_m\}$ which is the subset of $\mathbb{P}^3$ visible in $\mathcal{A}$. It generalizes the classical definition of chirality to include all of $\mathbb{P}^3$ and offers a unifying framework for studying multiview chirality. We give an algebraic description of the chiral domain which allows us to define and describe a chiral version of Triggs' joint image. We then use the chiral domain to re-derive and extend prior results on chirality due to Hartley.

math.AG↗

arXiv2021

Existence of Two View Chiral Reconstructions

A fundamental question in computer vision is whether a set of point pairs is the image of a scene that lies in front of two cameras. Such a scene and the cameras together are known as a chiral reconstruction of the point pairs. In this paper we provide a complete classification of k point pairs for which a chiral reconstruction exists. The existence of chiral reconstructions is equivalent to the non-emptiness of certain semialgebraic sets. For up to three point pairs, we prove that a chiral reconstruction always exists while the set of five or more point pairs that do not have a chiral reconstruction is Zariski-dense. We show that for five generic point pairs, the chiral region is bounded by line segments in a Schläfli double six on a cubic surface with 27 real lines. Four point pairs have a chiral reconstruction unless they belong to two non-generic combinatorial types, in which case they may or may not.

cs.CV↗

arXiv2019

Ideals of the Multiview Variety

The multiview variety of an arrangement of cameras is the Zariski closure of the images of world points in the cameras. The prime vanishing ideal of this complex projective variety is called the multiview ideal. We show that the bifocal and trifocal polynomials from the cameras generate the multiview ideal when the foci are distinct. In the computer vision literature, many sets of (determinantal) polynomials have been proposed to describe the multiview variety. We establish precise algebraic relationships between the multiview ideal and these various ideals. When the camera foci are noncoplanar, we prove that the ideal of bifocal polynomials saturate to give the multiview ideal. Finally, we prove that all the ideals we consider coincide when dehomogenized, to cut out the space of finite images.

math.AC↗