Felix Rydell

I am a PhD in Mathematics and AI. I am currently an AI researcher at FOI - Swedish Defence Research Agency. 

I did my PhD at KTH Royal Institute of Technology as part of WASP - Wallenberg AI, Autonomous Systems and Software Program. My thesis studies Computer Vision using Algebraic Geometry. 

Research Interests

Hobbies

Current Position

AI researcher at FOI - Swedish Defence Research Agency

Applied Algebra

Number Theory of Quadratic Forms

PhD

PhD in mathematics at KTH Royal Institute of Technology

Popular Science Research Overview - Coming Soon

AI


Applied Algebra


Number Theory of Quadratic Forms

AGAVE Reading Group - Active from May 2022 to June 2024

Myself, Elima Shehu and Angélica Torres organized this reading group in algebraic vision. Website: https://sites.google.com/view/agave-mission/hem.

THESIS

Algerbraic Advances in Multiview Geometry

Preprints

Number Theory

with Gustav Mårdby and Julie Rowlett.

Preprint: https://arxiv.org/abs/2412.16709

Algebraic Vision

with co-authors.

Preprint: Coming Soon.

with Isak Sundelius.

Preprint: http://arxiv.org/abs/2404.03063

with Timothy Duff.

Preprint: https://arxiv.org/abs/2402.00648

with Erin Connelly.

Preprint: https://arxiv.org/abs/2402.00495 

single-authored.

Preprint: https://arxiv.org/abs/2309.10262                                         

Metric Algebraic Geometry

single-authored.

Preprint: https://arxiv.org/abs/2402.00475                                                                         

Accepted and Published Articles

Algebraic Vision

with Viktor Larsson and Angélica Torres. Accepted for publication in CVPR 2024.

Preprint: https://arxiv.org/abs/2401.07114  

with Paul Breiding, Timothy Duff, Lukas Gustafsson and Elima Shehu. Accepted for publication in Communications in Algebra.

Preprint: http://arxiv.org/abs/2303.02066    

with Martin Bråtelund. Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3328-3336. 

Preprint: https://arxiv.org/abs/2303.10658

with Elima Shehu and Angélica Torres.  Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3748-3757.

Preprint: https://arxiv.org/abs/2303.13593     

with Paul Breiding, Elima Shehu and Angélica Torres. SIAM Journal on Applied Algebra and Geometry, 2023, 7.2: 470-504. 

Preprint: https://arxiv.org/abs/2203.01694

Number Theory

with Erik Nilsson and Julie Rowlett.  Bulletin of the American Mathematical Society, 2023, 60.1: 39-83.

Preprint: https://arxiv.org/abs/2110.09457              

Algebraic Geometry 

with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Boris Shapiro, Rainer Sinn,  Miruna-Stefana Sorea and Simon Telen. Accepted for publication in Documenta Mathematica.

Preprint: http://arxiv.org/abs/2108.11747       

Algebraic Statistics

with Stefan Dye,  Kathlén Kohn and Rainer Sinn.  Part of the LSSM Collaborative Project. Le Mathematiche, Special Issue on Linear Spaces of Symmetric Matrices, pages 399-414.

Preprint: https://arxiv.org/abs/2011.08989                                                

A Selection of Illustrations

For surfaces in 3-space, skew-tubes are unions of circles such that the normal lines along these circles intersect in a point. The union of all intersection points forms a curve. Each point of this curve has infinitely many ED-critical points on the surface. To the left is a skew-tube around a twisted cubic. This surface is given by a degree-10 polynomial of 123 terms.

Two back-projected cubic cones are shown, through the two green centers. The twisted cubic defining the cones is illustrated in thick orange. The surfaces also intersect in a degree-6 curve drawn in thin orange. Indeed, since the surfaces are degree-3, the expected total degree of the intersection is 9.

Refracted rays (in blue and orange) given a black radiant point and a black ellipse. As Bruce and Giblin (1992) write, "These [lines] appear to cluster along another curve, which the eye immediately picks out ... The  new curve is called the envelope." 

This figure illustrates the Sampson approximation scheme for the purpose of fitting data to an algebraic variety. Here, our mathematical model is the ellipse C(x, y) = x^2+2y^2−4 = 0. 

We studied how to best reconstruct point and line such that incidence relations are preserved.  The left picture illustrates individual triangulation of the points and line, and the right picture illustrates a reconstruction algorithm which ensures that the reconstructed points lie on the reconstructed line. 

The main theorem of line multiview varieties is says that a line multiview variety is cut out by the condition that the back-projected planes meet in a line if and only if the centers are pairwise disjoint and no four centers are collinear.  The foundational idea for its proof uses basic theory of smooth quadrics and is illustrated in the image to the right. 

Graduate Student Meeting on Applied Algebra and Combinatorics, KTH April 2023

Myself, Xiangying Chen, Danai Deligeorgaki, Oskar Henriksson, Filip Jonsson Kling and Mariel Supina organized a conference for young researches on applied algebra and combinatorics, with plenary speakers Carlos Améndola and Kris Shaw.  

Website: https://sites.google.com/view/applied-alg-comb-2023/graduate-student-meeting-on-applied-algebra-and-combinatorics

WASP AI Courses


WASP Activities

Talks and Posters

2024

2023

2022

2021

Research Activities

Attended Conferences

Visits

Workshops

Teaching 

Teaching Experience

Teaching Assistance at KTH

Supervision

Education

Contact Information

felixry@kth.se