Emily Berghofer: Multiview Varieties of Rolling Shutter Cameras

Abstract.

This study looks at the rolling shutter camera model and how pictures taken by moving cameras of this model can be used in 3D reconstruction. Unlike how the widely used pinhole camera model takes the entire picture in one go, a rolling shutter camera takes a picture by scanning each pixel line individually. This poses an issue when the cameras are moving as they photograph since the pictures will become skewed. These skewed images in turn pose a problem in the 3D reconstruction process as it complicates the process of finding points in the different pictures that depict the same 3D point.

In this thesis, we study two rolling shutter cameras moving with constant speed along independent direction vectors as they photograph a subject in between them. We compute the function that maps points in the projective 3 space to their projective 2 space counterparts in each of the two pictures. The Zariski closure of this function is the multiview variety of the two cameras. The multiview variety is defined by a polynomial whose zero-locus contains all pairs of points in the two pictures that depict the same 3D point.

Finally, we further study the multiview variety by looking at the Newton polytope.