Joe Kileel presents Using Computational Algebra for Computer Vision
On 2017-06-07 15:00:00 at CIIRC Seminar Room B-670, the 6th floor of B building, Jugoslavskych partyzanu 3
(CIIRC Seminar Room B-670, the 6th floor of B building, Jugoslavskych partyzanu
3)
Scene reconstruction is a fundamental task in computer vision: given multiple
images from different angles, create a 3D model of a world scene. Nowadays
self-driving cars need to do 3D reconstruction in real-time, to navigate their
surroundings. Large-scale photo-tourism is also a popular application. In
this talk, we will explain how key subroutines in reconstruction algorithms
amount
to solving polynomial systems, with special geometric structure. We will
answer
a
question of Sameer Agarwal (Google Research) about recovering the motion of two
calibrated cameras. Next, we will quantify the "algebraic complexity" of
polynomial systems arising from three calibrated cameras. In terms of
multi-view geometry, we deal with essential matrices and trifocal tensors. The
first part applies tools like resultants from algebra, while the second part
will offer an introduction to numerical homotopy continuation methods. Those
wondering "if algebraic geometry is good for anything practical" are especially
encouraged to attend.
References:
[1] G. Floystad, J. Kileel, G. Ottaviani: “The Chow form of the essential
variety in computer vision,” J. Symbolic Comput., to appear.
[https://arxiv.org/pdf/1604.04372]
[2] J. Kileel: “Minimal problems for the calibrated trifocal variety,” SIAM
Appl. Alg. Geom., to appear. [https://arxiv.org/pdf/1611.05947]
3)
Scene reconstruction is a fundamental task in computer vision: given multiple
images from different angles, create a 3D model of a world scene. Nowadays
self-driving cars need to do 3D reconstruction in real-time, to navigate their
surroundings. Large-scale photo-tourism is also a popular application. In
this talk, we will explain how key subroutines in reconstruction algorithms
amount
to solving polynomial systems, with special geometric structure. We will
answer
a
question of Sameer Agarwal (Google Research) about recovering the motion of two
calibrated cameras. Next, we will quantify the "algebraic complexity" of
polynomial systems arising from three calibrated cameras. In terms of
multi-view geometry, we deal with essential matrices and trifocal tensors. The
first part applies tools like resultants from algebra, while the second part
will offer an introduction to numerical homotopy continuation methods. Those
wondering "if algebraic geometry is good for anything practical" are especially
encouraged to attend.
References:
[1] G. Floystad, J. Kileel, G. Ottaviani: “The Chow form of the essential
variety in computer vision,” J. Symbolic Comput., to appear.
[https://arxiv.org/pdf/1604.04372]
[2] J. Kileel: “Minimal problems for the calibrated trifocal variety,” SIAM
Appl. Alg. Geom., to appear. [https://arxiv.org/pdf/1611.05947]