Postdoctoral position in Algebraic Vision
KTH Royal Institute of Technology, Stockholm
Contact • Kathlén Kohn kathlen@kth.se
The research group on Applied Algebraic Geometry in Data Science and AI led by Kathlén Kohn at the Department of Mathematics at KTH Stockholm has an open postdoctoral position:
- Starting date: upon agreement, in 2025
- Duration: employment for 2 years, with the possibility of extension by 1 more year
- Requirements: a doctoral degree or an equivalent foreign degree, obtained within the last three years prior to the application deadline (with exceptions for special reasons, e.g., sick or parental leave)
- How to apply: TBA
- Application deadline: January 7, 2025
The position is financed by Kathlén Kohn's Swedish Foundations' Starting Grant Algebraic Vision.
The successful candidate will be part of the vibrant and diverse research groups in algebraic geometry and data science in Stockholm.
Required profile
Besides a doctoral degree as specified above, the successful candidate is expected to have:
- a strong background in algebraic, complex, differential, or discrete geometry, or mathematics of computer vision,
- written and spoken English proficiency, very good communication and teamwork skills, in particular a willingness to collaborate with both engineers and mathematicians, and
- strong motivation and ability to work independently.
Project proposal:
Algebraic vision is the two-way street between algebraic geometry and computer vision. The primary goal of this project is to develop the theoretical foundations for 3D scene reconstruction from images taken by unknown rolling-shutter cameras, which is the overwhelming camera technology of today. Implementing fast reconstruction algorithms for rolling-shutter cameras - without restricting assumptions - is a major open challenge in computer vision. Algebraic geometry provides the natural tools for rigorous theoretical foundations for that challenge. Images of rolling-shutter cameras have peculiar features: A 3D point can appear more than once on the same image, and 3D lines become higher-degree image curves. Thus, the existing theory for traditional global-shutter cameras does not apply. The project will start from scratch and describe rolling-shutter cameras algebraically. From the algebro-geometric perspective, such cameras parametrize algebraic surfaces in the Grassmannian of 3D lines, and 3D reconstruction amounts to computing fibers under rational maps. The project will exploit this inherent geometry to 1) find complete catalogs of efficiently solvable algebraic reconstruction problems (so-called minimal problems), 2) develop new intersection-theoretic tools to measure their intrinsic complexity, and 3) describe the critical loci of 3D reconstruction where problem instances are ill-conditioned and prone to numerical instability. If successful, the algebro-geometric foundations developed in this project will lead to the implementation of fast 3D reconstruction algorithms with rolling-shutter cameras.
