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Lukas Gustafsson and Felix Rydell: Algebraic Geometry and Optimization (Lukas) + Triangulation in Algebraic Vision (Felix)

Time: Tue 2022-11-29 10.15

Location: 3721, Lindstedtsvägen 25, and Zoom

Video link: Meeting ID: 621 8808 6001

Lecturer: Lukas Gustafsson and Felix Rydell (KTH)

Abstract

10:15 Lukas: A common problem in applications is fitting data to a model. This requires an objective function that acts as a notion of 'distance' to points in and outside your model. Our main examples of non-linear objective functions are the Euclidean distance and the log-likelihood functions, which we then restrict to semi-algebraic sets. When passing over to the complex numbers, the number of critical points of these functions is pre-determined, regardless of the input data. This brings us to the topic of the first part of the talk: what are these numbers and how can we compute them? Can we classify the statistical models where there is a unique complex critical point?

10:45 Felix: Algebraic vision is the study of the algebraic geometry that arises from reconstruction problems in computer vision. Given a fixed set of cameras that have taken pictures of an object, the goal is to reconstruct a model of it in the computer. Triangulation is the act of using for instance point and line correspondences to reconstruct a point and line cloud for this model. In this talk we discuss this problem and especially the denoising of correspondences and related Euclidean distance degrees.