PhD position in Mathematics, specialization in Algebraic Geometry & Computer Vision

KTH Royal Institute of Technology, Stockholm

Application deadline • January 7, 2025 11:59 PM CET

How to apply• TBA

Contact • Kathlén Kohn kathlen@kth.se

The successful candidate will pursue a PhD project at the intersection of algebraic geometry and computer vision under the supervision of Kathlén Kohn. The position is a time-limited, full-time, five year position starting August 2025 or at an agreed upon date. The position is fully funded for four years and will be extended to five years by assigning teaching duties. The student will be enrolled in the Doctoral program in Mathematics. 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. Students interested in fields related to the following are encouraged to apply: algebra, geometry, computer vision, artificial intelligence, data science.

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.