3:00pm - 5:00pmAlgebraic vision
Chair(s): Max David Lieblich (University of Washington, United States of America), Tomas Pajdla (Czech Technical University in Prague), Matthew Trager (Courant Institute of Mathematical Sciences at NYU)
There has been a burst of recent activity focused on the applications of modern abstract and numerical algebraic geometry to problems in computer vision, ranging from highly-optimized Gröbner-basis techniques, to homotopy continuation methods, to Ulrich sheaves and Chow forms, to functorial moduli theory. We will discuss this recent progress, with a focus on multiview geometry, both in theory and in practice.
(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)
"Real" Algebraic Vision
Sameer Agarwal
Google
Computer Vision is rarely done over the complex numbers. On the other hand, it does often involve semi-algebraic sets, non-genericity and finite precision arithmetic. Dealing with these complications leads to a variety of interesting and hard mathematical questions. I will talk about a few of my favorite ones.
A geometric construction of the essential variety
Lucas Van Meter
University of Washington
We give a new construction of the essential variety using a geometric definition of calibration. This construction recovers classical results about the essential variety while also yielding a new 2-1 cover that is strongly related to previous work of Kileel-Fløystad-Ottaviani.
Classification of Point-Line Minimal Problems in Complete Multi-View Visibility
Timothy Duff1, Kathlén Kohn2, Anton Leykin1, Tomas Pajdla3
1Georgia Tech, 2University of Oslo, 3CIIRC, CTU Prague
We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there are only 30 minimal problems in total, no problems exist for more than 6 cameras, for more than 5 points, and for more than 6 lines. For all minimal problems discovered, we present their algebraic degrees, i.e. the number of solutions, which measure their intrinsic difficulty. Our classification shows that there are many interesting new minimal problems. Our results also show how exactly the difficulty of problems grows with the number of views. Importantly, we discovered several new minimal problems with small degrees that might be practical in image matching and 3D reconstruction.