May 2 to May 6, 2016
American Institute of Mathematics,
San Jose, California
and Rekha Thomas
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
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
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