The multiview variety

Point correspondences of pinhole cameras is a fundamental study of algebraic vision, which is the study of algebraic geometry for reconstruction problems in computer vision. These correspondences are well-understood by now. More recently, line correspondences were characterized mathematically. In this talk, we generalize this study to correspondences of arbitrary k-planes in P^n. The geometry of this problem is interesting by itself, but also sees potential applications in modeling more difficult reconstruction problems, and for understanding certain determinantal varieties.