# Algebraic vision

May 2 to May 6, 2016

at the

American Institute of Mathematics, San Jose, California

organized by

Sameer Agarwal, Max Lieblich, and Rekha Thomas

## Original Announcement

This workshop will focus on multi-view geometry, the sub-discipline of computer vision that studies 3D scene reconstructions from images, and has deep foundations in projective geometry and linear algebra. The field has recently made successful use of computational algebraic methods such as Groebner bases.

Multi-view geometry offers a rich collection of unexplored problems in a range of aspects of algebraic geometry. On the other hand, algebro-geometric tools have the potential to make fundamental advances in the understanding and practice of 3D computer vision.

The time is ripe to build a broader bridge between the two areas, driving new ideas from moduli theory, representation theory, and numerical, real, and combinatorial algebraic geometry into computer vision, and carrying a host of new motivating problems and ideas back into the pure algebro-geometric fold.

We call this bridge ''Algebraic Vision'', and this AIM workshop will be a crucial step in constructing it.

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Factoring a homography to analyze projective distortion
by  Annalisa Crannell, Marc Frantz, and Fumiko Futamura
Looking through the glass
by  Annalisa Crannell,  Handbook of the Mathematics of the Arts and Sciences pp 1-25, Springer, Cham, Online ISBN 978-3-319-70658-0
A $C_2$-equivariant analog of Mahowald's Thom spectrum theorem
by  Mark Behrens and Dylan Wilson
The euclidean distance degree of orthogonally invariant matrix varieties
by  Dmitriy Drusvyatskiy, Hon-Leung Lee, Giorgio Ottaviani and Rekha R. Thomas,  Israel J. Math. 221 (2017), no. 1, 291–316 MR3705855  MR3705855
A clever elimination strategy for efficient minimal solvers
by  Zuzana Kukelova, Joe Kileel, Bernd Sturmfels and Tomas Pajala
Distortion varieties
by  Joe Kileel, Zuzana Kukelova, Tomas Pajdla, and Bernd Sturmfels
General models for rational cameras and the case of two-slit projections
by  Matthew Trager, Bernd Sturmfels, John Canny, Martial Hebert, and Jean Ponce
Congruences and Concurrent Lines in Multi-View Geometry
by  Jean Ponce, Bernd Sturmfels, and Matthew Trager,  Adv. in Appl. Math. 88 (2017), 62–91  MR3641809