Algebra and Geometry Seminar

USC, Kapraelian Hall rm 414

Algebraic vision, 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:

• Triangulation: Given multiple images as well as (relative) camera locations, can we reconstruct the scene or object being photographed?
• Resectioning: Given a 3-D object or scene and multiple images of it, can we determine the (relative) positions of the cameras in the world?

We will discuss and characterize certain algebraic varieties associated with the camera resectioning problem. As an application, we will derive and re-interpret celebrated results in computer vision due to Carlsson, Weinshall, and others related to camera-point duality.