Multiview geometry, lying in the intersection of computer vision and projective geometry, is the study of three-dimensional objects being photographed by multiple pinhole cameras. Two natural questions arise: (1) Given a 3-D object or scene and multiple images of it, can we determine the (relative) positions of the cameras in the world? And, (2) given multiple images as well as (relative) camera locations, can we reconstruct the scene or object being photographed? We focus on this second question, called the camera resectioning problem. We will introduce algebraic varieties related to the resectioning problem and as an application derive and reinterpret celebrated results in computer vision due to Carlsson, Weinshall, and others related to camera-point duality. Time-permitting, we will also introduce and discuss the Euclidean distance degree of a resectioning variety, which allows us to relate formal reconstruction algorithms to real-life “noisy” data.
Algebra and Geometry of Camera Reseactioning
Jessie Loucks-Tavitas, University of WashingtonAuthors: Erin Connelly, Timothy Duff, Jessie Loucks-Tavitas
2023 AWM Research Symposium
Pure and Applied Talks by Mathematicians Enhancing Diversity in Graduate Education (EDGE) [Organized by Quiyana M. Murphy and Sofía Martínez Alberga]